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Construction of a genetic toggle switch in Escherichia coli

2015-02-05T10:02:57Z

UrbanB:

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

(Urban Bezeljak)

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

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<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

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To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the small difference in maximal particle numbers per cell between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to less efective TetR repression compared to CI (pTAK constructs). As accurately predicted form the model, less efficient synthesis of LacI repressor (lower ''α2'') due to modified RBS sequence, and thus more comparable production rates for the two repressors, successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-05T22:03:56Z

UrbanB: /* Demonstration of bistability */

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the small difference in maximal particle numbers per cell between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to less efective TetR repression compared to CI (pTAK constructs). As accurately predicted form the model, less efficient synthesis of LacI repressor (lower ''α2'') due to modified RBS sequence, and thus more comparable production rates for the two repressors, successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-05T21:58:44Z

UrbanB: /* Mathematical model */

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the small difference in maximal particle numbers per cell between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations. As accurately predicted form the model, less efficient synthesis of LacI repressor (lower ''α2'') due to modified RBS sequence, and thus more comparable production rates for the two repressors, successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-05T21:30:32Z

UrbanB: /* Demonstration of bistability */

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the small difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations. As accurately predicted form the model, less efficient synthesis of LacI repressor (lower ''α2'') due to modified RBS sequence, and thus more comparable production rates for the two repressors, successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-05T21:21:40Z

UrbanB: /* Demonstration of bistability */

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the small difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations. As accurately predicted form the model, less efficient synthesis of LacI repressor (lower ''α1'') due to modified RBS sequence, and thus more comparable production rates for the two repressors, successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-05T20:41:04Z

UrbanB: /* Mathematical model */

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the small difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-03T23:41:25Z

UrbanB:

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

[[SB students resources]]

Construction of a genetic toggle switch in Escherichia coli

2015-01-03T17:44:38Z

UrbanB:

Gardner, T., Cantor, C. & Collins, J. [http://web.mit.edu/biophysics/sbio/PDFs/Gardner.pdf Construction of a genetic toggle switch in Escherichia coli]. Nature 403, 339–342 (2000).

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T19:51:56Z

UrbanB: /* Switch design */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. [http://commons.wikimedia.org/wiki/File:R-S.gif In schematic representation of the SR latch], input 1 (S) is analogous to Inducer 1 and Input 2 (R) is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 (Q') corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 (Q) to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T16:20:05Z

UrbanB: /* Switching time */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

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<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

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To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F6.html FIG. 6]). The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T16:15:10Z

UrbanB: /* Toggle switch induction threshold */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there should exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5]). The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F5.html FIG. 5c]) as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T16:07:56Z

UrbanB: /* Stability of the switch */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time ([http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4c]), the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T16:02:32Z

UrbanB: /* Demonstration of bistability */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4a]) and one pIKE plasmid (pIKE107; [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F4.html FIG. 4b]) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T15:56:13Z

UrbanB: /* Efficacy of repression */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

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<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

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To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. In this experiment, the ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. Additionally, the λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T15:41:28Z

UrbanB: /* Results */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA constructs are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-02T15:40:33Z

UrbanB: /* Results */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

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To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The DNA construct are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information] The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-01T17:26:23Z

UrbanB: /* DNA constructs and implementation */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network (FIG. 3)] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-01T17:25:23Z

UrbanB: /* Mathematical model */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). It is favorable for a switch to have the bistable region as large as possible to facilitate the switching process. If the monostable regions are very large, the difference in numbers between Repressor 1 and 2 (corresponding to ''α1'' and ''α2'') required to begin switching (i.e. transition from monostable to bistable region on the plots in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]), is significantly harder to reach. These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-01T11:53:54Z

UrbanB: /* Mathematical model */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations (FIG. 2a)]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see in FIG. 2a], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can observe in FIG. 2b] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch, see the bistable area in [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html FIG. 2c and 2d]). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2015-01-01T11:42:42Z

UrbanB: /* Switch design */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch (FIG. 1)]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

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<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

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To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can see] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html Other valuable information] that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-31T17:06:45Z

UrbanB: /* DNA constructs and implementation */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can see] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html Other valuable information] that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F3.html The toggle switch network] was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-31T17:05:12Z

UrbanB: /* Mathematical model */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html plot these two equations]. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html As we can see], the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html we can see] that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F2.html Other valuable information] that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-31T16:58:31Z

UrbanB: /* Comment */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner ''et al.'' presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-31T16:58:11Z

UrbanB: /* Promoter strengths determination */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner ''et al.'' determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-31T16:57:11Z

UrbanB: /* Switch design */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their [http://www.nature.com/nature/journal/v403/n6767/fig_tab/403339a0_F1.html synthetic genetic toggle switch]. The genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />. An animated explanation on how the RS latch works can be found [http://commons.wikimedia.org/wiki/File:R-S.gif here] and [http://commons.wikimedia.org/wiki/File:R-S_mk2.gif here].

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-31T16:31:34Z

UrbanB: /* Toggle switches in nature */

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. To further elucidate, a schematic representation of discussed portion of λ genome can be accessed [http://commons.wikimedia.org/wiki/File:Viral_DNA_setup.svg here]. Additionally, the λ switch architecture can be compared with genetic toggle switch designed by Gardner ''et al.'' [http://www.nature.com/nature/journal/v420/n6912/fig_tab/nature01257_F2.html here]. The blunted lines represent transcription downregulation by repressor proteins. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T19:33:13Z

UrbanB:

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into ''E. coli'' cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (''E. coli'' doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold of induction that is characteristic for each switch. At this tipping point, the cell population should suddenly switch (or bifurcate) to one of the stable states. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level<ref name="ref1" /><ref name="ref6" />.

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing<ref name="ref1" />. An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004<ref name="ref13">Kramer, B. P. et al. An engineered epigenetic transgene switch in mammalian cells. Nat. Biotechnol. 22, 867–70 (2004).</ref>.

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T19:22:34Z

UrbanB:

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as CI inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive CI repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CI and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning ''GFPmut3'' or ''GFPuv'' reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The ''lac'' repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-''rbs E'' promoter-RBS pair and prevented ''GFPmut3'' transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in ''E. coli''. The only difference among vectors of the same group was the RBS sequence upstream of ''lacI'' repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they encode for only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].

The experiment lasted for 23.5 hours from plasmid transformation into ''E. coli'' JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure the high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of ''lac'' repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of CI-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (''α'' in the mathematical model) from Ptrc-2 – ''rbs B'' and PLtetO-1 – ''rbs A'' promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower ''α1'') due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T19:09:57Z

UrbanB:

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [[#Mathematical model]]).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T19:08:44Z

UrbanB:

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (''α2'' in the [#Mathematical model]).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T19:02:10Z

UrbanB:

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid <ref name="ref7">Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857. at [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4]</ref> conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene ''GFPmut3'' with its own RBS was cloned as the second cistron adjacently to the Repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with Repressor 1 concentration (State 1: high Repressor 1 & GFP concentration, State 2: low Repressor 1 concentration).

Two different genetic networks classes were designed. Both used the ''lac'' repressor (''lacI''), whose expression controlled Promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (''cIts'') was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled ''lacI'' expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (''tetR'') as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements.

[plazmidna karta]

===Plasmid features===
* '''ColE1 ori:''' origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell<ref name="ref7" />.
* '''''bla'':''' β-lactamase ampicillin resistance gene.
* '''RBS:''' ribosomal binding site. Protein production rates (''α'' in the mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was ''rbs E'', while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the [http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf Supplementary Information].
* '''PLs1con:''' shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter<ref name="ref8">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli Supplementary Information. Nature SI (2000).</ref>.
* '''PLtetO-1:''' constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter<ref name="ref8" />.
* '''Ptrc-2:''' constitutive promoter, generated by fusing Ptrp and Plac promoter<ref name="ref8" />.
* '''''cIts'':''' gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter<ref name="ref9">Part:BBa K200016 - parts.igem.org. at [http://parts.igem.org/Part:BBa_K200016]</ref>. CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C<ref name="ref1" />.
* '''''lacI'':''' ''lac'' repressor (LacI) gene of the ''E. coli lac'' operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG)<ref name="ref5" />.
* '''''tetR'':''' tetracycline repressor (TetR) gene of the ''E. coli'' Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites<ref name="ref10">Welman, A. & Barraclough, J. Tetracycline Regulated Systems in Functional Oncogenomics. Oncogenomics 17–33 (2007).</ref>.
* '''''GFPmut3'':''' gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type<ref name="ref11">Andersen, J. B. et al. New unstable variants of green fluorescent protein for studies of transient gene expression in bacteria. Appl. Environ. Microbiol. 64, 2240–6 (1998).</ref>.
* '''T1T2:''' transcription terminator of '''E. coli''' ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1)<ref name="ref12">E. coli genotypes - OpenWetWare. at [http://openwetware.org/wiki/E._coli_genotypes#JM2.300]</ref>. Importantly, this strain doesn’t have the ''cI'' λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components<ref name="ref1" />.

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T17:37:59Z

UrbanB:

In year 2000, a seminal paper<ref name="ref1">Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref name="ref2">Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref name="ref3">Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref name="ref4">Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref name="ref5">Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref name="ref1" />

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref name="ref3" />.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref name="ref1" /><ref name="ref3" /><ref name="ref6">Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low Repressor 1 concentration and high Repressor 2 concentration, high Repressor 1 concentration and low Repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (''β'', ''γ'' > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in ''Escherichia coli'' <ref name="ref1" />.

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T17:22:49Z

UrbanB:

In year 2000, a seminal paper<ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA<ref>Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high)<ref>Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref>Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref>Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1<ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref>.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high<ref>Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref>.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

----

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of Repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where ''α1'' is the maximal production rate of Repressor 1 form Promoter 2, which includes the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. ''Kdv'' is the dissociation constant of Repressor 2 from Promoter 2, ''v'' is the concentration of Repressor 2 and ''β'' is exponent representing the degree of cooperativity of Repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied Promoters 2.

By representing the concentration of Repressor 2 ''v'' in units of ''Kdv'', we can eliminate ''Kdv'' and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of Repressor 1 and Repressor 2 over time, the equation must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where ''u'' is the concentration of Repressor 1, ''v'' is the concentration of Repressor 2, ''α1'' and ''α2'' are the relative maximal production rates of Repressor 1 and Repressor 2, respectively, and the coefficients ''β'' and ''γ'' represent the cooperativity of binding of Repressor 2 and Repressor 1 to response elements on Promoter 2 and Promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution<ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref><ref>Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref>Kaern, M., Blake, W. J. & Collins, J. J. The engineering of gene regulatory networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003).</ref>.</blockquote>

----

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of Repressor 1 ''u'' and y axis corresponds to Repressor 2 concentration ''v''.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T17:02:10Z

UrbanB:

In year 2000, a seminal paper <ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA <ref>Hasty, J., McMillen, D., Isaacs, F. & Collins, J. Computational studies of gene regulatory networks: in numero molecular biology. Nat. Rev. Genet. 2, (2001).</ref>. The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene ''cro''. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of ''cI'' gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) <ref>Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref><ref>Hasty, J., McMillen, D. & Collins, J. Engineered gene circuits. Nature 420, (2002).</ref><ref>Berg, J. M., Tymoczko, J. L., Stryer, L. & Gatto, G. J. Biochemistry. (W. H. Freeman and Company, 2012).</ref>.

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of ''cro'' gene and Cro protein inhibits transcription of ''cI'' gene. The switching is carried out by addition of an inducer (Inducer 1) that forces the system into one of the possible steady states. The added Inducer 1 prevents binding of Repressor 1 to the opposing Promoter 1 and thus induces the synthesis of Repressor 2, which in turn inhibits production of the Repressor 1. Even upon removal of Inducer 1, production of Repressor 2 remains high and the concentration of Repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with Inducer 1 <ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref>.

The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high <ref>Cherry, J. L. & Adler, F. R. How to make a biological switch. J. Theor. Biol. 203, 117–33 (2000).</ref>.

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).</blockquote>

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T15:50:39Z

UrbanB:

In year 2000, a seminal paper <ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium ''Escherichia coli'' that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes of experiments. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as ''Escherichia coli'', it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).</blockquote>

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T15:48:16Z

UrbanB:

In year 2000, a seminal paper <ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).</blockquote>

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
<references />

Construction of a genetic toggle switch in Escherichia coli

2014-12-30T15:42:01Z

UrbanB:

In year 2000, a seminal paper <ref>Gardner, T., Cantor, C. & Collins, J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).</ref> by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).</blockquote>

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
{{reflist}}

Construction of a genetic toggle switch in Escherichia coli

2014-12-29T16:33:59Z

UrbanB:

In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

<blockquote>In the simplest model, the production rate of a repressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).</blockquote>

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
1. T. Gardner, C. Cantor, J. Collins, Nature , 339–342 (2000).
2. J. Hasty, D. McMillen, F. Isaacs, J. Collins, Nat. Rev. Genet. 2 (2001).
3. J. L. Cherry, F. R. Adler, J. Theor. Biol. 203, 117–33 (2000).
4. J. Hasty, D. McMillen, J. Collins, Nature 420 (2002).
5. J. M. Berg, J. L. Tymoczko, L. Stryer, G. J. Gatto, Biochemistry (W. H. Freeman and Company, 7th ed., 2012).
6. M. Kaern, W. J. Blake, J. J. Collins, Annu. Rev. Biomed. Eng. 5, 179–206 (2003).
7. Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857 (available at http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4).
8. T. Gardner, C. Cantor, J. Collins, Nature , SI (2000).
9. Part:BBa K200016 - parts.igem.org (available at http://parts.igem.org/Part:BBa_K200016).
10. A. Welman, J. Barraclough, Oncogenomics , 17–33 (2007).
11. J. B. Andersen et al., Appl. Environ. Microbiol. 64, 2240–6 (1998).
12. E. coli genotypes - OpenWetWare (available at http://openwetware.org/wiki/E._coli_genotypes#JM2.300).
13. B. P. Kramer et al., Nat. Biotechnol. 22, 867–70 (2004).

Construction of a genetic toggle switch in Escherichia coli

2014-12-29T16:15:42Z

UrbanB:

In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

In the simplest model, the production rate of a reppressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math></div>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math></div>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math></div>

and

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math></div>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
1. T. Gardner, C. Cantor, J. Collins, Nature , 339–342 (2000).
2. J. Hasty, D. McMillen, F. Isaacs, J. Collins, Nat. Rev. Genet. 2 (2001).
3. J. L. Cherry, F. R. Adler, J. Theor. Biol. 203, 117–33 (2000).
4. J. Hasty, D. McMillen, J. Collins, Nature 420 (2002).
5. J. M. Berg, J. L. Tymoczko, L. Stryer, G. J. Gatto, Biochemistry (W. H. Freeman and Company, 7th ed., 2012).
6. M. Kaern, W. J. Blake, J. J. Collins, Annu. Rev. Biomed. Eng. 5, 179–206 (2003).
7. Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857 (available at http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4).
8. T. Gardner, C. Cantor, J. Collins, Nature , SI (2000).
9. Part:BBa K200016 - parts.igem.org (available at http://parts.igem.org/Part:BBa_K200016).
10. A. Welman, J. Barraclough, Oncogenomics , 17–33 (2007).
11. J. B. Andersen et al., Appl. Environ. Microbiol. 64, 2240–6 (1998).
12. E. coli genotypes - OpenWetWare (available at http://openwetware.org/wiki/E._coli_genotypes#JM2.300).
13. B. P. Kramer et al., Nat. Biotechnol. 22, 867–70 (2004).

Construction of a genetic toggle switch in Escherichia coli

2014-12-29T16:10:02Z

UrbanB:

In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

In the simplest model, the production rate of a reppressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.

By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:

<math>f(v) = \frac{\alpha _{1}}{1 + v^{\beta }}</math>

To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:

<math>\frac{\mathrm{d} u}{\mathrm{d} t} = \frac{\alpha _{1}}{1 + v^{\beta }} - u</math>

and

<math>\frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\alpha _{2}}{1 + u^{\gamma }} - v</math>

Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where <math>\frac{\mathrm{d} u}{\mathrm{d} t} = 0</math> and <math>\frac{\mathrm{d} v}{\mathrm{d} t} = 0</math> (concentrations of repressors don’t vary over time), we plot two curves: <math>u = \frac{\alpha _{1}}{1 + v^{\beta }}</math> and <math>v = \frac{\alpha _{2}}{1 + u^{\gamma }}</math> on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
1. T. Gardner, C. Cantor, J. Collins, Nature , 339–342 (2000).
2. J. Hasty, D. McMillen, F. Isaacs, J. Collins, Nat. Rev. Genet. 2 (2001).
3. J. L. Cherry, F. R. Adler, J. Theor. Biol. 203, 117–33 (2000).
4. J. Hasty, D. McMillen, J. Collins, Nature 420 (2002).
5. J. M. Berg, J. L. Tymoczko, L. Stryer, G. J. Gatto, Biochemistry (W. H. Freeman and Company, 7th ed., 2012).
6. M. Kaern, W. J. Blake, J. J. Collins, Annu. Rev. Biomed. Eng. 5, 179–206 (2003).
7. Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857 (available at http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4).
8. T. Gardner, C. Cantor, J. Collins, Nature , SI (2000).
9. Part:BBa K200016 - parts.igem.org (available at http://parts.igem.org/Part:BBa_K200016).
10. A. Welman, J. Barraclough, Oncogenomics , 17–33 (2007).
11. J. B. Andersen et al., Appl. Environ. Microbiol. 64, 2240–6 (1998).
12. E. coli genotypes - OpenWetWare (available at http://openwetware.org/wiki/E._coli_genotypes#JM2.300).
13. B. P. Kramer et al., Nat. Biotechnol. 22, 867–70 (2004).

Construction of a genetic toggle switch in Escherichia coli

2014-12-29T15:54:53Z

UrbanB:

In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

In the simplest model, the production rate of a reppressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. <math>\frac{K_{d}}{K_{d}v + v^{\beta }}</math> is thus the fraction of unoccupied promoters 2.
By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:
f(v)= α_1/(1+v^β )
To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:
du/dt= α_1/(1+v^β )-u
and
dv/dt= α_2/(1+u^γ )-v
Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where du/dt=0 and dv/dt=0 (concentrations of repressors don’t vary over time), we plot two curves: u= α_1/(1+v^β ) and v= α_2/(1+u^γ ) on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
1. T. Gardner, C. Cantor, J. Collins, Nature , 339–342 (2000).
2. J. Hasty, D. McMillen, F. Isaacs, J. Collins, Nat. Rev. Genet. 2 (2001).
3. J. L. Cherry, F. R. Adler, J. Theor. Biol. 203, 117–33 (2000).
4. J. Hasty, D. McMillen, J. Collins, Nature 420 (2002).
5. J. M. Berg, J. L. Tymoczko, L. Stryer, G. J. Gatto, Biochemistry (W. H. Freeman and Company, 7th ed., 2012).
6. M. Kaern, W. J. Blake, J. J. Collins, Annu. Rev. Biomed. Eng. 5, 179–206 (2003).
7. Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857 (available at http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4).
8. T. Gardner, C. Cantor, J. Collins, Nature , SI (2000).
9. Part:BBa K200016 - parts.igem.org (available at http://parts.igem.org/Part:BBa_K200016).
10. A. Welman, J. Barraclough, Oncogenomics , 17–33 (2007).
11. J. B. Andersen et al., Appl. Environ. Microbiol. 64, 2240–6 (1998).
12. E. coli genotypes - OpenWetWare (available at http://openwetware.org/wiki/E._coli_genotypes#JM2.300).
13. B. P. Kramer et al., Nat. Biotechnol. 22, 867–70 (2004).

Construction of a genetic toggle switch in Escherichia coli

2014-12-29T15:53:06Z

UrbanB:

In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

In the simplest model, the production rate of a reppressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:

<math>f(v) = \frac{\alpha _{1}\cdot K_{d}}{K_{d}v + v^{\beta }}</math>

Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. K_d/(K_d+v^β ) is thus the fraction of unoccupied promoters 2.
By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:
f(v)= α_1/(1+v^β )
To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:
du/dt= α_1/(1+v^β )-u
and
dv/dt= α_2/(1+u^γ )-v
Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where du/dt=0 and dv/dt=0 (concentrations of repressors don’t vary over time), we plot two curves: u= α_1/(1+v^β ) and v= α_2/(1+u^γ ) on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
1. T. Gardner, C. Cantor, J. Collins, Nature , 339–342 (2000).
2. J. Hasty, D. McMillen, F. Isaacs, J. Collins, Nat. Rev. Genet. 2 (2001).
3. J. L. Cherry, F. R. Adler, J. Theor. Biol. 203, 117–33 (2000).
4. J. Hasty, D. McMillen, J. Collins, Nature 420 (2002).
5. J. M. Berg, J. L. Tymoczko, L. Stryer, G. J. Gatto, Biochemistry (W. H. Freeman and Company, 7th ed., 2012).
6. M. Kaern, W. J. Blake, J. J. Collins, Annu. Rev. Biomed. Eng. 5, 179–206 (2003).
7. Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857 (available at http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4).
8. T. Gardner, C. Cantor, J. Collins, Nature , SI (2000).
9. Part:BBa K200016 - parts.igem.org (available at http://parts.igem.org/Part:BBa_K200016).
10. A. Welman, J. Barraclough, Oncogenomics , 17–33 (2007).
11. J. B. Andersen et al., Appl. Environ. Microbiol. 64, 2240–6 (1998).
12. E. coli genotypes - OpenWetWare (available at http://openwetware.org/wiki/E._coli_genotypes#JM2.300).
13. B. P. Kramer et al., Nat. Biotechnol. 22, 867–70 (2004).

Construction of a genetic toggle switch in Escherichia coli

2014-12-29T15:43:00Z

UrbanB: New page: In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gen...

In year 2000, a seminal paper (1) by Timothy Gardner and colleagues at Boston University, was published in scientific journal Nature. The paper described the construction of engineered gene-regulatory network in bacterium Escherichia coli that preformed as a toggle switch – analogous to the one we use to turn lights on or off. This work was one of the first examples in then-nascent field of synthetic biology that combined computer simulations based on mathematical models with experiments in the lab to design the complex gene circuit and predict the outcomes. This seminar will discuss both mathematical and molecular biology methods used to engineer and implement a genetic toggle switch in bacteria.

==Toggle switches in nature==
A classic example of a toggle switch in nature is the regulation of bacteriophage λ. When the phage infects its host such as Escherichia coli, it can follow lytic or lysogenic life cycle. In the lytic pathway, the phage replicates its DNA and new virus particles are produced. This leads to cell lysis and release of newly assembled virions into the environment. On the other hand, in the lysogenic life cycle, the viral DNA integrates itself into the host’s chromosome and replicates with the host DNA (2). The switching is made possible by two proteins that repress each other’s expression – λ repressor, also known as CI, and repressor Cro (controller of repressor and others). In lysogenic cycle, the only bacteriophage protein produced is CI, which represses the expression of all other phage proteins. Importantly, CI dimer binds response elements in the PR promoter (R stands for repressor) and prevents expression of viral gene cro. Bacteriophage λ switches to lytic pathway if the host DNA is damaged. During bacteria’s response to DNA damage, CI is cleaved by bacterial RecA protein and thus cannot bind its response elements. This allows production of Cro repressor, which in turn binds to PRM promoter (RM stands for repressor maintenance), which controls expression of cI gene. Cro represses synthesis of CI, which leads to production of other phage proteins, assembly of virus particles and finally host cell lysis. Presented bacteriophage λ genes act as a genetic toggle switch with two states – it achieves bistability. One stable state represents lysogenic life cycle (CI repressor concentration is high, Cro concentration is low) and the other represents lytic cycle (CI repressor concentration is low, Cro concentration is high) (3–5).

[slika fag lambda]

== Switch design ==
Gardner and colleagues used the above-described nature’s blueprint to design their synthetic genetic toggle switch. Their genetic circuit is composed of two operons that in turn both contain a constitutive promoter and a gene that encodes for a repressor. Each repressor negatively controls the production of the other, just as Cl inhibits transcription of cro gene and Cro protein inhibits transcription of cI gene. The switching is carried out by addition of an inducer (inducer 1) that forces the system into one of the possible steady states. The added inducer 1 prevents binding of the repressor 1 to the opposing promoter 1 and thus induces the synthesis of the repressor 2, which in turn inhibits production of the repressor 1. Even upon removal of the inducer 1, production of the repressor 2 remains high and the concentration of the repressor 1 remains low. This means that the engineered genetic network can store information about its past, in this case the stimulation with the inducer 1 (1).
The presented mutual repressor switch resembles the Reset-Set flip-flop or latch (RS flip-flop) in electronics. A RS flip-flop can be constructed with two coupled NOR gates. Only when a NOR gate receives two low inputs (0), the resulting output is high (1). The two inputs a NOR gate receives can be thoughts as the level of transcription (high/low) for the corresponding repressor and presence or absence of an inducer that inhibits the same repressor’s function. In schematic representation of the SR latch, input 1 is analogous to Inducer 1 and Input 2 is analogous to Inducer 2 in designed genetic toggle switch. Similarly, Output 1 corresponds to high Repressor 1 concentration (and low Repressor 2 concentration) and Output 2 to high Repressor 2 concentration (and low Repressor 1 concentration). High Input 1 forces the Output 1 to be low and Output 2 to be high (3).

[slika RS latch z logično tabelo in splošna shema stikala *step-by-step]

==Mathematical model==
The outcomes of even simplest genetic networks such as toggle switches are difficult to predict (as demonstrated above) solely with human intuition. The behavior of the switch can be captured in deterministic ordinary differential equations (ODEs) to guide the construction of genetic circuit and the rational selection of its parts. The mathematical model describes changes in the concentrations of two repressor proteins over time:

In the simplest model, the production rate of a reppressor is proportional to the fraction of unbound response elements on corresponding promoter. We can use Hill function to describe the rate of production of repressor 1:
f(v)= (α_1∙K_d)/(K_d v+v^β )
Where α1 is the maximal production rate of repressor 1 form promoter 2, which include the net effect of RNA polymerase binding, open-complex formation on DNA, transcript elongation, transcript termination, repressor binding, ribosome binding and polypeptide synthesis. Kdv is the dissociation constant of repressor 2 from promoter 2, v is the concentration of repressor 2 and β is exponent representing the degree of cooperativity of repressor 2 binding. K_d/(K_d+v^β ) is thus the fraction of unoccupied promoters 2.
By representing the concentration of repressor 2 v in units of Kdv, we can eliminate Kdv and write dimensionless equation:
f(v)= α_1/(1+v^β )
To observe the concentrations of repressor 1 and repressor 2 over time, we must include the protein decay due to constant dilution because of cell growth:
du/dt= α_1/(1+v^β )-u
and
dv/dt= α_2/(1+u^γ )-v
Where u is the concentration of repressor 1, v is the concentration of repressor 2, α1 and α2 are the relative maximal production rates of repressor 1 and repressor 2, respectively, and the coefficients β and γ represent the cooperativity of binding of repressor 2 and repressor 1 to response elements on promoter 2 and promoter 1, respectively. The first term in equations above describes the cooperative repression of constitutive promoters and the second term represents the decay of repressors due to cell growh. The decay rate is the same for both proteins. To maintain the model dimensionless, the time was rescaled to units of protein half-life on account of dilution (1, 3, 6).

To observe the gene circuit behavior using computer simulation, we must plot these two equations. Because we are interested in steady states of the switch, where du/dt=0 and dv/dt=0 (concentrations of repressors don’t vary over time), we plot two curves: u= α_1/(1+v^β ) and v= α_2/(1+u^γ ) on a graph where x axis represents the concentration of repressor 1 u and y axis corresponds to repressor 2 concentration v.

[graf steady state]

As we can see, the two curves, also called nullclines, intersect at three points. These three points represent three steady states of the toggle switch: low repressor 1 concentration and high repressor 2 concentration, high repressor 1 concentration and low repressor 2 concentration, and one unstable steady state where both repressor concentrations are equal. At this point, even the slightest difference in repressor concentrations will move the system into one of the two stable steady states. It is apparent that we get these three intersections owing to sigmoidal shape of the two curves, which occurs because of cooperative repression of the promoters (β, γ > 1). Binding cooperativity of at least one repressor protein is so the first criteria for bistability of genetic toggle switch we can deduce form derived mathematical model. If we change the values for protein production parameter, we can see that production rates for both repressors must be comparable or else the nullclines cross only once, producing a broken toggle switch with only one state. Thus, the second criteria for a mutual repressor switch to work is balanced maximal expression rate from the two constitutive promoters.

[graf a1 >> a2]

Other valuable information that were extracted from parameter observation are: increasing protein production rates and higher order of cooperativity correlate with increasing robustness of the switch (the collection of parameters that support functioning toggle switch). These findings guided the implementation of engineered mutual repressor switch in Escherichia coli (1).

[graf log(a) in coop.]

==DNA constructs and implementation==
The toggle switch network was constructed on a low copy number plasmid (7) conferring resistance to ampicillin and containing the ColE1 origin of replication. The two operons both contained constitutive promoter, ribosomal binding site (RBS), repressor genes and a double terminator of transcription. To monitor the state of the switch, green fluorescent protein (GFP) gene GFPmut3 with its own RBS was cloned as the second cistron adjacently to the repressor 1 gene. Consequently, the authors could determine the state of the switch by observing expression of the GFP, which correlated with repressor 1 concentration (State 1: high repressor 1 & GFP concentration, State 2: low repressor 1 concentration).

Two different genetic networks classes were designed. Both used the lac repressor (lacI), whose expression controlled promoter 1, and constitutive Ptrc-2 promoter as Promoter 2. Depending on the second promoter-repressor combination, the plasmids were named pTAK or pIKE class. In the pTAK plasmid class, the temperature-sensitive Cl repressor (cIts) was cloned downstream of the Ptrc-2 promoter and constitutive PLs1con promoter controlled lacI expression, whereas the pIKE family of plasmids contained PLtetO-1 promoter and Tet repressor (tetR) as Promoter 1 and Repressor 1 elements, respectively. When researchers introduced the pTAK plasmids into bacteria, they could therefore switch between stable states using isopropyl β-D-1-thiogalactopyranoside (IPTG) as Inducer 2, lifting repression off the Ptrc-2 promoter, or high-temperature pulse that destabilizes the CI repressor. Conversely, pIKE gene constructs switch from one state to the other with addition of IPTG or anhydrotetracycline (aTc), which causes TetR dissociation from its response elements, to culture medium.

[plazmidna karta]

===Plasmid features===
* ColE1 ori: origin of replication from ColE1 plasmid. It confers 50-70 plasmid copies per cell (7).
* bla: β-lactamase ampicillin resistance gene.
* RBS: ribosomal binding site. Protein production rates (α in mathematical model) were controlled by using different RBS sequences. The RBS used downstream of Ptrc-2 promoter (Promoter 2) was rbs E, while different RBS sequences were used to modify the synthesis rates of LacI (Repressor 2). The exact RBS sequences are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf ) (1).
* PLs1con: shortened version of the wild-type bacteriophage λ PL constitutive promoter with point mutations in -10 sequence region to weaken the otherwise very strong wild-type promoter (8).
* PLtetO-1: constitutive promoter containing two copies of O2 operator from Tn10 tetracycline resistance operon and -35 and -10 sequences from PL promoter (8).
* Ptrc-2: constitutive promoter, generated by fusing Ptrp and Plac promoter (8).
* cIts: gene encoding temperature-sensitive mutant of the λ repressor CI. At 42 °C, the CI repressor denatures and cannot bind to PLs1con promoter (9). CI binds to its operator as a dimer moiety. All plasmids containing CL and its responsive elements were grown at 32 °C instead of 37 °C. Thermal induction was performed at 42 °C (1).
* lacI: lac repressor (LacI) gene of the E. coli lac operon binds the operator as a tetramer. The binding is prevented with inducer molecule e.g. isopropyl β-D-1-thiogalactopyranoside (IPTG) (5).
* tetR: tetracycline repressor (TetR) gene of the E. coli Tn10 transposon that confers tetracycline resistance to the host bacteria. TetR binds its response elements as a dimer. Anhydrotetracycline (aTc) causes dissociation of the TetR homodimer from its corresponding operator sites (10).
* GFPmut3: gene encoding mutant green fluorescent protein which is 20 times more fluorescent than wild type (11).
* T1T2: transcription terminator of E. coli ribosomal RNA operon.

The E. coli strain used was JM2.300 (lacI22, λ-, e14-, rpsL135(strR), malT1(LamR), xyl-7, mtl-1, thi-1) (12). Importantly, this strain doesn’t have the cI λ gene incorporated in its genome and has a mutated non-functional LacI repressor, so it didn’t interfere with any of the switch components (1).

==Results==
All in all, six different toggle switches were constructed, where four had CI – LacI repressor combination (pTAK plasmids) and two had TetR – LacI repressor pair (pIKE plasmids). The only difference among the genetic switches of the same type was the ribosomal binding site (RBS) downstream of Promoter 1 that defined the LacI synthesis rate (α2 in the mathematical model).

===Promoter strengths determination===
Gardner et al. determined the strengths of different promoter-RBS combinations used by cloning GFPmut3 or GFPuv reporter gene downstream of the studied promoter-RBS pair (Type I plasmid type in Supplementary Information) and GFP expression was assayed by flow cytometry. The determined promoter efficiency series was: PLs1con > Ptrc-2 > PLtetO-1. The Type I plasmid map and GFP expression measurements can be found listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Efficacy of repression===
The efficacy of repression was determined in similar experiment as the relative promoter strengths. The DNA constructs used to assay repression were modified pTAK and pIKE plasmids described above. The Type II plasmids were used to measure LacI repression. The lac repressor prevented the expression of GFPmut3 from Ptrc-2 promoter. The λ and Tet repressor were expressed from Ptrc-2-rbs E promoter-RBS pair and prevented GFPmut3 transcription downstream of PLs1con or PLtetO-1 promoter on Type III plasmids. Again, the leaky GFP expression (i.e. expression from repressed promoters) data were collected using flow cytometer. The fold repression was estimated as ratio between maximal GFP expression values measured using Type I plasmids and GFP expression under repressed promoters using Type II and Type III plasmids. The CI repressor was the most effective, achieving almost 6000-fold repression of the PLs1con promoter. Furthermore, when TetR or LacI downregulated the GFP synthesis, the measured values were 100- or 20-fold smaller compared to highest recorded values for unrepressed expression. The plasmid maps and leaky GFP expression values are listed in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf).

===Demonstration of bistability===
When different genetic switches were tested for bistability, all four pTAK (pTAK117, pTAK130, pTAK131 and pTAK132) and one pIKE plasmid (pIKE107) successfully preformed switching between two stable steady states in E. coli. The only difference among vectors of the same group was the RBS sequence upstream of lacI repressor gene. Control plasmids used were Type II plasmids. These plasmids don’t contain functional genetic toggle switches because they contain only one of the two repressor genes. pTAK102 was used to determine LacI repression efficiency and can support GFP expression only when IPTG is present. This plasmid served as a positive control for IPTG transient induction and as a negative control for conditions, where IPTG is absent – including induction with heath or aTc (pTAK102 doesn’t contain genes for CI and TetR). On the other hand, pTAK106 and pTAK108 control plasmids were used as a negative control for non-induced setting and IPTG induction since they don’t express LacI repressor, and as a positive control for heat or aTc induction, respectively. The plasmid maps for control plasmids are presented in the Supplementary Information (http://www.nature.com/nature/journal/v403/n6767/extref/403339ai1.pdf). The experiment lasted for 23.5 hours from plasmid transformation into E. coli JM2.300 to final sample measurement. During the experiment, samples were washed and diluted at three time points into fresh growth medium with (or without) inducers to preform transient switching between the states. Toggle switch bearing cells were first grown for 6 h in growth media supplemented with IPTG, which set all switches in high GFP expression state. Cells were then diluted in medium without any inducer to ensure high GFP state remained stable over the course of next 5 h. As expected, the pTAK102 control plasmid didn’t support stability and it retuned to ground state. At 11 h post-transformation, the high GFP/Repressor 1 state was perturbed by heat induction at 42 °C or dilution in growth medium with aTc. After 7 h (18 h time point), the cultures were assayed for GFP fluorescence and diluted into fresh medium at 37 °C (pIKE switches) or 32 °C (pTAK switches). The induction caused switching of the toggle switches by inhibiting the repression of LacI synthesis by CI λ repressor (pTAK plasmids – induction by heath) or Tet repressor (pIKE plasmid – induction with aTc). Consequently, the GFP production was downregulated by newly formed LacI repressor protein, except for control constructs pTAK106 and pTAK108 where GFPmut3 was expressed instead of lac repressor. Finally, 23.5 h after transformation, the functioning switches retained the low GFP expression state and the controls returned to uninduced state.

This experiment provided information on switching ability of the cloned genetic circuits. All four of Cl-LacI repressor pairs (i.e. pTAK DNA constructs) conferred bistability, while only one of the two TetR-LacI mutual repressor switches (i.e. pIKE DNA constructs) supported bistablility. The authors hypothesized that pIKE105 didn’t exhibit bistability due to insufficiently balanced maximal expression rates (α in mathematical model) from Ptrc-2 – rbs B and PLtetO-1 – rbs A promoter-RBS combinations in relation to higher CI repressor efficiency compared to Tet repressor. As accurately predicted form the model, less efficient synthesis of CI repressor (lower α1) due to modified RBS sequence successfully shifted the pIKE configuration from monostability (pIKE105) to bistability (pIKE107).

===Stability of the switch===
To test if genetic toggle switch can store its information (hold its state) for longer periods of time, the CI-LacI mutual repressor switch (pTAK117) was transformed into E. coli cells and left uninduced for 28 h. In addition, one group of transformed cells was induced with IPTG in the first 6 h of the experiment. Afterward, the culture was diluted in fresh unsupplemented medium and left without any inducers for 22 h. The cultures were sampled and diluted every 6-8.5 h. Both experiment groups successfully retained their state after 6 h time point, proving that mutual repressor switch design supports long-term stability of both predicted stable states even after several cell generations (E. coli doubling time in optimal conditions is approx. 20 min).

===Toggle switch induction threshold===
According to the mathematical toggle switch model, there exist three possible steady states. Two of them are stable and one occurs between these two and is highly unstable in nature. This state also represents the threshold if induction that is characteristic for each switch. At this tipping point, the cell population divides itself (or bifurcates) into two branches: one assumes high and the other low stable state of the switch. To investigate this phenomenon, the pTAK117 switch and pTAK102 control were grown in several increasing concentrations of IPTG inducer. The control exhibited usual dose-response sigmodial curve for induction of GFP expression due to Ptrc-2 promoter derepression. On the contrary, the genetic switch jumped from its ground, or low, state to high state in almost digital fashion at 40 μM IPTG concentration in growth medium. This result is expected, as there are only two predicted stable steady states the switch can adopt. The bifurcation event wasn’t perfect (there was still gradual increase in fluorescence detected) owing to random (stochastic) nature of gene expression within individual cells, which can differ from the average transcription induction of the whole bacterial population. This variability causes slight differences in induction threshold for individual cells and can be observed as wide population distributions in flow cytometry histograms as well as divided cell populations near the induction threshold (bifurcation event). This is understandable because deterministic ODE model can predict only average population behavior and doesn’t take into account stochastic events on cellular level (1, 6).

===Switching time===
An important characteristic of a toggle switch is its switching time. For a genetic switch to be useful as a form of cellular memory, it has to have a swift switching kinetics. The well-functioning pTAK117 switch was assayed for its switching time between high and low state and vice-versa. The cells in set low state were induced with IPTG and grown for different periods of time before being diluted in fresh medium and studied with the flow cytometer at 10.25 h time point. Similarly, the cells in induced high state were first diluted in fresh medium and grown at 42 °C for 35 min to 6 h. Afterwards, the cells were diluted again and grown at standard temperature (32 °C) until the end of experiment. The results show that pTAK117 toggle switch starts switching from low to high state after 3 h of induction and that all cells complete the switching event 6 h after addition of inducer. However, switching from high to low state is significantly more rapid as the whole cell population returned to ground state after 35 min of heath induction. Observed differences in switching times are consequences of different elimination mechanisms for λ repressor and LacI. While λ repressor is quickly denatured by heath, the IPTG-bound lac repressor is gradually diluted by subsequent cell divisions. In addition, the protein production rate for new LacI from PLs1con is significantly higher than CI production, making the ground state more stable in comparison to the high, CI-dominated state. Thus, it takes more time for CI to overcome the LacI-mediated repression.

==Comment==
To conclude, the discussed work of Gardner et al. presented the first successful introduction of a genetic toggle switch network in bacteria. Their approach combined mathematical modeling with genetic engineering to construct a functioning complex genetic circuit that paved way for extensive research of artificial genetic network in the last decade. The presented genetic toggle switch functions as a device that can store epigenetic memory of transient events in cells’ past across multiple generations which could be useful in advanced cell or gene therapy, biotechnology and biocomputing (1). An identical mutual repressor switch architecture was also used in design and implementation of a bistable switch in mammalian cells by Kramer et al. in 2004 (13).

==References==
1. T. Gardner, C. Cantor, J. Collins, Nature , 339–342 (2000).
2. J. Hasty, D. McMillen, F. Isaacs, J. Collins, Nat. Rev. Genet. 2 (2001).
3. J. L. Cherry, F. R. Adler, J. Theor. Biol. 203, 117–33 (2000).
4. J. Hasty, D. McMillen, J. Collins, Nature 420 (2002).
5. J. M. Berg, J. L. Tymoczko, L. Stryer, G. J. Gatto, Biochemistry (W. H. Freeman and Company, 7th ed., 2012).
6. M. Kaern, W. J. Blake, J. J. Collins, Annu. Rev. Biomed. Eng. 5, 179–206 (2003).
7. Copy number of plasmids with ColE1 origin of - Bacteria Escherichia coli - BNID 103857 (available at http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=103857&ver=4).
8. T. Gardner, C. Cantor, J. Collins, Nature , SI (2000).
9. Part:BBa K200016 - parts.igem.org (available at http://parts.igem.org/Part:BBa_K200016).
10. A. Welman, J. Barraclough, Oncogenomics , 17–33 (2007).
11. J. B. Andersen et al., Appl. Environ. Microbiol. 64, 2240–6 (1998).
12. E. coli genotypes - OpenWetWare (available at http://openwetware.org/wiki/E._coli_genotypes#JM2.300).
13. B. P. Kramer et al., Nat. Biotechnol. 22, 867–70 (2004).

SB students resources

2014-12-29T10:42:12Z

UrbanB:

===Introduction to our students resources in Synthetic Biology===
(Marko Dolinar)

Synthetic biology made a vast progress in good 10 years since it established itself as an interdisciplinary field of research on the interface of molecular biology and engineering. University of Ljubljana Faculty of Chemistry and Chemical Technology has introduced a Synthetic Biology course as a part od Biochemistry MSc programme only in 2013/14. This is relatively late, considering a great success of Slovenian students at iGEM competitions since their first attendance in 2006. On the other hand, the field is still in its first stages if development and a complete textbook for a MSc level course is still missing. This is the reason why our students collaborated on the preparation of a Synthetic Biology textbook with the working title Synthetic Biology - A Students Textbook. It exists as a draft that is not publicly available and is actually part 1 of a (to be) 2-volumes title. Part I is subtitled Engineering Biology, while Part II (that currently doesn't exisist yet) will be subtitled Synthetic Biology Applications.

As in all highly competitive fields of science and technology, students should be following recent progress by reading articles in high quality journals. However, this is often a very difficult task, especially at the BSc level. Specificities of the scientific and technical language, push of publishers towards very short methodological chapters and limited knowledge studens might have about advanced techniques make understanding papers a very challenging task. Therefore, I decided to face MSc students with the challenge to explain selected SB articles in a manner that would make the content of these articles understandable to BSc level students and non-experts.

In 2014/15, seminars in Synthetic Biology include explanations and presentations of some of the top-cited articles from the field of Synthetic Biology. I compiled a list of 95 articles published between 2000 and 2014 having the highest number of citations according to the Web of Science database. The list ends with the paper just exceeding the 100 citations limit. Not included in the list were reviews. With 20 students enrolled in the course, the list has been further reduced to top 40 papers in the field. Students have been asked to check for content (they further eliminated 3 papers which proved to be reviews) and availabitly (they all seemed to be available as full texts with our university subscriptions). My suggestion was to avoid selecting for presentation papers with very similar content. Especially in the field of genome editing there has been a very rapid progress in the past few years resulting in a number of highly-cited articles which could appear very similar in content for a non-specialist. From the shortlist of 37 articles, students selected a topic they believed would be most interesting or easiest to explain. Presentations Will be both written (in English, which is not the mother tongue of my students) and oral (in Slovenian, to establish and maintain Slovenian terminology in the field).

===List of articles for presentation===

This is the list of top-cited papers from the broader field of Synthetic Biology that students chose for explanation in 2014/15 (sorted by year of publication):

#A synthetic oscillatory network of transcriptional regulators (2000) - Valter Bergant
#[[Construction of a genetic toggle switch in Escherichia coli]]. Gardner ''et al''., Nature, 2000 - Urban Bezeljak
#Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion (2001) - Andreja Bratovš
#Chemical synthesis of poliovirus cDNA: Generation of infectious virus in the absence of natural template (2002) - Veronika Jarc
#Combinatorial synthesis of genetic networks (2002) - Maja Remškar
#Engineering a mevalonate pathway in Escherichia coli for production of terpenoids (2003) - Ana Kapraljević
#Programmed population control by cell-cell communication and regulated killing (2004) - Alja Zottel
#Gene regulation at the single-cell level (2005) - Katarina Uršič
#A synthetic multicellular system for programmed pattern formation (2005) - Mitja Crček
#Long-term monitoring of bacteria undergoing programmed population control in a microchemostat (2005) - Jana Verbančič
#Tuning genetic control through promoter engineering (2005) - Špela Pohleven
#Production of the antimalarial drug precursor artemisinic acid in engineered yeast (2006) - Živa Marsetič
#An improved zinc-finger nuclease architecture for highly specific genome editing (2007) - Eva Knapič
#Establishment of HIV-1 resistance in CD4(+) T cells by genome editing using zinc-finger nucleases (2008) - Tamara Marić
#Synthetic protein scaffolds provide modular control over metabolic flux (2009) - Ana Dolinar
#Creation of a bacterial cell controlled by a chemically synthesized genome (2010) Eva Lucija Kozak
#A TALE nuclease architecture for efficient genome editing (2011) Jernej Mustar
#Multiplex genome engineering using CRISPR/Cas systems (2013) - Uroš Stupar
#RNA-guided human genome engineering via Cas9 (2013) - Luka Smole
#One-step generation of mice carrying mutations in multiple genes by CRISPR/Cas-mediated genome engineering (2013) - Andrej Vrankar

''Please link the title of each paper with your written seminar wiki page. Expand the citation according to the following example:
''
#Emergent bistability by a growth-modulating positive feedback circuit. Tan et al., Nature Chem. Biol., 2009

Iz induciranih pluripotentnih izvornih celic pripravljeni človeški limfociti T za terapijo raka

2014-04-11T17:28:26Z

UrbanB:

Razvoj imunoterapevtskih pristopov za zdravljenje rakavih obolenj velja za enega pomembnejših znanstvenih dosežkov v letu 2013. Zdravljenje z adoptivnim prenosom limfocitov T zahteva previden izbor donorjev celic T oz. izražanje himernih antigenskih receptorjev ([http://en.wikipedia.org/wiki/Chimeric_antigen_receptor CAR]) v bolnikovih celicah T, ki se ga doseže z genskim inženirstvom. Themeli in sod. so v svoji raziskavi združili tehnologijo CAR s tehnologijo induciranih pluripotentnih izvornih celic ([http://www.cira.kyoto-u.ac.jp/e/faq/faq2.html iPSC]), saj so želeli izkoristiti lastnosti obeh pristopov za razvoj neomejenega vira terapevstkih limfocitov T.

==Ideja==
Izražanje himernih antigenskih receptorjev s pomočjo genskega spreminjanja limfocitov T se v kliničnih študijah kaže kot obetajoč imunoterapevtski pristop za zdravljenje različnih vrst raka. Himerni antigenski receptorji so fuzijski proteini, ki vsebujejo domeno scFv izbranega monoklonskega protitelesa, transmembransko regijo in znotrajcelično signalizacijsko domeno. Vezava antigena na tako spremenjene celice T je neodvisna od kompleksa MHC, hkrati pa je dosežena aktivacija teh celic, podobno kot pri vezavi predstavljenega antigena na TCR. Themeli in sod. so uporabili CAR, ki veže antigen CD19, ki je izražen pri veliki večini levkemij in limfomov.

Uporaba iPSC namesto avtolognih ali donorskih limfocitov T je zanimiva ker teoretično predstavljajo neomejen vir željenih terapevtskih celic za zdravljenje z adoptivnim prenosom celic T. Za razliko od celic iPSC, ''in vitro'' namnožene celice T namreč niso sposobne neomejenega deljenja. V opisani raziskavi so z uporabo tehnologij CAR in iPSC želeli razviti nov pristop za adoptivno imunoterapijo, ki bi združil najboljše iz obeh svetov: od kompleksa MHC neodvisno prepoznavanje tumorskih antigenov in neomejeno razpoložljivost celic iPSC za pridobivanje terapevtskih limfocitov T.

==Rezultati==
Celice iPSC so pridobili s transdukcijo limfocitov T zdravih donorjev z retrovirusnimi vektorji, ki so nosili zapise za gene KLF4, SOX2, OCT-4 in C-MYC, ki so odgovorni za transformacijo celic v izvorne. Izbran klon tako pridobljenih celic T-iPSC so zatem transducirali še z lentivirusnim vektorjem, ki je zapisoval za CAR, ki prepoznava CD19, in rdeči fluorescenčni protein mCherry. Limfocite T so iz celic T-iPSC pridobili z ''in vitro'' diferenciacijo ob ustreznih gojitvenih pogojih in rastnih faktorjih. Med 25. in 30. dnem diferenciacije je bila večina gojenih celic CD3+ TCRαβ+ in so izražale tako željeni CAR, kot tudi enak TCR kot starševska linija T-iPSC (celice 1928z-T-iPSC-T).

Delovanje tako pridobljenih celic T so najprej preizkusili na celicah NIH-3T3, ki so izražale antigen CD19. V kokulturi so celice 1928z-T-iPSC-T prepoznale antigen in vezale celice 3T3. 24 ur po nacepitvi so celice 1928z-T-iPSC-T tvorile skupke okoli celic 3T3 in povzročile lizo celic. Celice 1928z-T-iPSC-T so ob izpostavljenosti antigenu CD19 začele izražati markerje za aktivacijo T-celic in izločati citokine IL-2, TNFα in IFNγ. S tem so potrdili, da imajo pridobljene celice nekaj lastnosti, značilnih za navadne limfocite T.

Da bi bolje razumeli naravo pridobljenih celic 1928z-T-iPSC-T, so raziskovalci izvedli ekspresijsko profiliranje teh celic na mikročipu. Rezultate so primerjali z profili izražanja mRNA naivnih celic B, CD4+ celic T, CD8+ celic T, CD3+ CD56+ celic T, γδ celic T in celic ubijalk. Izkazalo se je, da so ustvarjene celice 1928z-T-iPSC-T najbolj podobne γδ celicam T. Raziskovalci preverili še razlike v izražanju neaktiviranih in aktiviranih (prisotnost celic 3T3-CD19) celic 1928z-T-iPSC-T. Ugotovili so, da se ob aktivaciji profil izražanja genov spremeni na način, ki je značilen za odziv tipa 1, ki ga navadno usmerjajo celice Th1.

Citotoksičnost celic 1928z-T-iPSC-T so nazadnje preizkusili še ''in vitro'' na mišjih limfomskih celicah, ki so izražale človeški CD19 in ''in vivo'' na mišjem ksenogenskem tumorskem modelu. Živalski model so pripravili z injiciranjem CD19+ Raji celic človeškega Burkittovega limfoma, ki so izražale fuzijo GFP in luciferaze. Tako ''in vitro'' kot ''in vivo'' so uspeli pokazati lizo celic, ki so izražale antigen CD19. Za primerjavo so pri poskusih ''in vivo'' uporabili tudi αβ in γδ celice T, ki so izražale CAR, specifičen za CD19. Tudi ti transducirani limfociti T so bili izolirani iz istega donorja kot starševska linija celic 1928z-T-iPSC-T. Ugotovili so, da je nivo izražanja receptorja CAR pri celicah 1928z-T-iPSC-T bistveno nižji kot pri αβ in γδ celicah T, ki so jih uporabili v ''in vivo'' eksperimentu. Rezultati so pokazali, da so pridobljene celice 1928z-T-iPSC-T podobno uspešne pri omejevanju razvoja tumorja, kot γδ celice T, ki so izražale CAR. Za najuspešnejše pa so se izkazale CAR+ αβ celice T, saj je bila pri miškah, zdravljenih s temi celicami, opažena popolna regresija tumorja v 5. tednu (eksperiment je trajal 7 tednov). Avtorji članka so bili kljub temu zadovoljni z rezultatom, saj so celice 1928z-T-iPSC-T delovale enako uspešno kot njim najbolj podobni limfociti T.

==Zaključek==
Avtorjem članka je uspelo iz celic T-iPSC pripraviti celice, ki izražajo specifične receptorje CAR. Ugotovili so, da imajo tako pridobljene celice lastnosti γδ celic T, čeprav izražajo na površini poleg transduciranega receptorja CAR tudi endogeni αβ TCR. Avtorji se nameravajo posvetiti razumevanju diferenciacije celic iz izvornih celic iPSC, saj bi si želeli pripraviti tudi druge tipe limfocitov T in dodatno vplivati na njihove lastnosti.

Limfociti T, pripravljeni iz celic iPSC, katere izražajo himerni antigenski receptor, bi bili zlasti primerni za zdravljenje z adoptivnim prenosom celic pri bolnikih, ki nimajo dovolj limfocitov za izolacijo. Takšni so bolniki, okuženi z virusom HIV ter močno imunosupresirani bolniki.

=Članek=
* Themeli M, Kloss CC, Ciriello G, Fedorov VD, Perna F, ''et al''. 2013. Generation of tumor-targeted human T lymphocytes from induced pluripotent stem cells for cancer therapy. Nat. Biotechnol. 31(10):928

Iz induciranih pluripotentnih izvornih celic pripravljeni človeški limfociti T za terapijo raka

2014-04-11T17:22:34Z

UrbanB:

Razvoj imunoterapevtskih pristopov za zdravljenje rakavih obolenj velja za enega pomembnejših znanstvenih dosežkov v letu 2013. Zdravljenje z adoptivnim prenosom limfocitov T zahteva previden izbor donorjev celic T oz. izražanje himernih antigenskih receptorjev (CAR) v bolnikovih celicah T, ki se ga doseže z genskim inženirstvom. Themeli in sod. so v svoji raziskavi združili tehnologijo CAR s tehnologijo induciranih pluripotentnih izvornih celic (iPSC), saj so želeli izkoristiti lastnosti obeh pristopov za razvoj neomejenega vira terapevstkih limfocitov T.

==Ideja==
Izražanje himernih antigenskih receptorjev s pomočjo genskega spreminjanja limfocitov T se v kliničnih študijah kaže kot obetajoč imunoterapevtski pristop za zdravljenje različnih vrst raka. Himerni antigenski receptorji so fuzijski proteini, ki vsebujejo domeno scFv izbranega monoklonskega protitelesa, transmembransko regijo in znotrajcelično signalizacijsko domeno. Vezava antigena na tako spremenjene celice T je neodvisna od kompleksa MHC, hkrati pa je dosežena aktivacija teh celic, podobno kot pri vezavi predstavljenega antigena na TCR. Themeli in sod. so uporabili CAR, ki veže antigen CD19, ki je izražen pri veliki večini levkemij in limfomov.

Uporaba iPSC namesto avtolognih ali donorskih limfocitov T je zanimiva ker teoretično predstavljajo neomejen vir željenih terapevtskih celic za zdravljenje z adoptivnim prenosom celic T. Za razliko od celic iPSC, ''in vitro'' namnožene celice T namreč niso sposobne neomejenega deljenja. V opisani raziskavi so z uporabo tehnologij CAR in iPSC želeli razviti nov pristop za adoptivno imunoterapijo, ki bi združil najboljše iz obeh svetov: od kompleksa MHC neodvisno prepoznavanje tumorskih antigenov in neomejeno razpoložljivost celic iPSC za pridobivanje terapevtskih limfocitov T.

==Rezultati==
Celice iPSC so pridobili s transdukcijo limfocitov T zdravih donorjev z retrovirusnimi vektorji, ki so nosili zapise za gene KLF4, SOX2, OCT-4 in C-MYC, ki so odgovorni za transformacijo celic v izvorne. Izbran klon tako pridobljenih celic T-iPSC so zatem transducirali še z lentivirusnim vektorjem, ki je zapisoval za CAR, ki prepoznava CD19, in rdeči fluorescenčni protein mCherry. Limfocite T so iz celic T-iPSC pridobili z ''in vitro'' diferenciacijo ob ustreznih gojitvenih pogojih in rastnih faktorjih. Med 25. in 30. dnem diferenciacije je bila večina gojenih celic CD3+ TCRαβ+ in so izražale tako željeni CAR, kot tudi enak TCR kot starševska linija T-iPSC (celice 1928z-T-iPSC-T).

Delovanje tako pridobljenih celic T so najprej preizkusili na celicah NIH-3T3, ki so izražale antigen CD19. V kokulturi so celice 1928z-T-iPSC-T prepoznale antigen in vezale celice 3T3. 24 ur po nacepitvi so celice 1928z-T-iPSC-T tvorile skupke okoli celic 3T3 in povzročile lizo celic. Celice 1928z-T-iPSC-T so ob izpostavljenosti antigenu CD19 začele izražati markerje za aktivacijo T-celic in izločati citokine IL-2, TNFα in IFNγ. S tem so potrdili, da imajo pridobljene celice nekaj lastnosti, značilnih za navadne limfocite T.

Da bi bolje razumeli naravo pridobljenih celic 1928z-T-iPSC-T, so raziskovalci izvedli ekspresijsko profiliranje teh celic na mikročipu. Rezultate so primerjali z profili izražanja mRNA naivnih celic B, CD4+ celic T, CD8+ celic T, CD3+ CD56+ celic T, γδ celic T in celic ubijalk. Izkazalo se je, da so ustvarjene celice 1928z-T-iPSC-T najbolj podobne γδ celicam T. Raziskovalci preverili še razlike v izražanju neaktiviranih in aktiviranih (prisotnost celic 3T3-CD19) celic 1928z-T-iPSC-T. Ugotovili so, da se ob aktivaciji profil izražanja genov spremeni na način, ki je značilen za odziv tipa 1, ki ga navadno usmerjajo celice Th1.

Citotoksičnost celic 1928z-T-iPSC-T so nazadnje preizkusili še ''in vitro'' na mišjih limfomskih celicah, ki so izražale človeški CD19 in ''in vivo'' na mišjem ksenogenskem tumorskem modelu. Živalski model so pripravili z injiciranjem CD19+ Raji celic človeškega Burkittovega limfoma, ki so izražale fuzijo GFP in luciferaze. Tako ''in vitro'' kot ''in vivo'' so uspeli pokazati lizo celic, ki so izražale antigen CD19. Za primerjavo so pri poskusih ''in vivo'' uporabili tudi αβ in γδ celice T, ki so izražale CAR, specifičen za CD19. Tudi ti transducirani limfociti T so bili izolirani iz istega donorja kot starševska linija celic 1928z-T-iPSC-T. Ugotovili so, da je nivo izražanja receptorja CAR pri celicah 1928z-T-iPSC-T bistveno nižji kot pri αβ in γδ celicah T, ki so jih uporabili v ''in vivo'' eksperimentu. Rezultati so pokazali, da so pridobljene celice 1928z-T-iPSC-T podobno uspešne pri omejevanju razvoja tumorja, kot γδ celice T, ki so izražale CAR. Za najuspešnejše pa so se izkazale CAR+ αβ celice T, saj je bila pri miškah, zdravljenih s temi celicami, opažena popolna regresija tumorja v 5. tednu (eksperiment je trajal 7 tednov). Avtorji članka so bili kljub temu zadovoljni z rezultatom, saj so celice 1928z-T-iPSC-T delovale enako uspešno kot njim najbolj podobni limfociti T.

==Zaključek==
Avtorjem članka je uspelo iz celic T-iPSC pripraviti celice, ki izražajo specifične receptorje CAR. Ugotovili so, da imajo tako pridobljene celice lastnosti γδ celic T, čeprav izražajo na površini poleg transduciranega receptorja CAR tudi endogeni αβ TCR. Avtorji se nameravajo posvetiti razumevanju diferenciacije celic iz izvornih celic iPSC, saj bi si želeli pripraviti tudi druge tipe limfocitov T in dodatno vplivati na njihove lastnosti.

Limfociti T, pripravljeni iz celic iPSC, katere izražajo himerni antigenski receptor, bi bili zlasti primerni za zdravljenje z adoptivnim prenosom celic pri bolnikih, ki nimajo dovolj limfocitov za izolacijo. Takšni so bolniki, okuženi z virusom HIV ter močno imunosupresirani bolniki.

=Članek=
* Themeli M, Kloss CC, Ciriello G, Fedorov VD, Perna F, ''et al''. 2013. Generation of tumor-targeted human T lymphocytes from induced pluripotent stem cells for cancer therapy. Nat. Biotechnol. 31(10):928

Iz induciranih pluripotentnih izvornih celic pripravljeni človeški limfociti T za terapijo raka

2014-04-11T17:17:03Z

UrbanB: New page: Razvoj imunoterapevtskih pristopov za zdravljenje rakavih obolenj velja za enega pomembnejših znanstvenih dosežkov v letu 2013. Zdravljenje z adoptivnim prenosom limfocitov T zahteva pre...

Razvoj imunoterapevtskih pristopov za zdravljenje rakavih obolenj velja za enega pomembnejših znanstvenih dosežkov v letu 2013. Zdravljenje z adoptivnim prenosom limfocitov T zahteva previden izbor donorjev celic T oz. izražanje himernih antigenskih receptorjev (CAR) v bolnikovih celicah T, ki se ga doseže z genskim inženirstvom. Themeli in sod. so v svoji raziskavi združili tehnologijo CAR s tehnologijo induciranih pluripotentnih izvornih celic (iPSC), saj so želeli izkoristiti lastnosti obeh pristopov za razvoj neomejenega vira terapevstkih limfocitov T.

==Ideja==
Izražanje himernih antigenskih receptorjev s pomočjo genskega spreminjanja limfocitov T se v kliničnih študijah kaže kot obetajoč imunoterapevtski pristop za zdravljenje različnih vrst raka. Himerni antigenski receptorji so fuzijski proteini, ki vsebujejo domeno scFv izbranega monoklonskega protitelesa, transmembransko regijo in znotrajcelično signalizacijsko domeno. Vezava antigena na tako spremenjene celice T je neodvisna od kompleksa MHC, hkrati pa je dosežena aktivacija teh celic, podobno kot pri vezavi predstavljenega antigena na TCR. Themeli in sod. so uporabili CAR, ki veže antigen CD19, ki je izražen pri veliki večini levkemij in limfomov.

Uporaba iPSC namesto avtolognih ali donorskih limfocitov T je zanimiva ker teoretično predstavljajo neomejen vir željenih terapevtskih celic za zdravljenje z adoptivnim prenosom celic T. Za razliko od celic iPSC, in vitro namnožene celice T namreč niso sposobne neomejenega deljenja. V opisani raziskavi so z uporabo tehnologij CAR in iPSC želeli razviti nov pristop za adoptivno imunoterapijo, ki bi združil najboljše iz obeh svetov: od kompleksa MHC neodvisno prepoznavanje tumorskih antigenov in neomejeno razpoložljivost celic iPSC za pridobivanje terapevtskih limfocitov T.

==Rezultati==
Celice iPSC so pridobili s transdukcijo limfocitov T zdravih donorjev z retrovirusnimi vektorji, ki so nosili zapise za gene KLF4, SOX2, OCT-4 in C-MYC, ki so odgovorni za transformacijo celic v izvorne. Izbran klon tako pridobljenih celic T-iPSC so zatem transducirali še z lentivirusnim vektorjem, ki je zapisoval za CAR, ki prepoznava CD19, in rdeči fluorescenčni protein mCherry. Limfocite T so iz celic T-iPSC pridobili z in vitro diferenciacijo ob ustreznih gojitvenih pogojih in rastnih faktorjih. Med 25. in 30. dnem diferenciacije je bila večina gojenih celic CD3+ TCRαβ+ in so izražale tako željeni CAR, kot tudi enak TCR kot starševska linija T-iPSC (celice 1928z-T-iPSC-T).

Delovanje tako pridobljenih celic T so najprej preizkusili na celicah NIH-3T3, ki so izražale antigen CD19. V kokulturi so celice 1928z-T-iPSC-T prepoznale antigen in vezale celice 3T3. 24 ur po nacepitvi so celice 1928z-T-iPSC-T tvorile skupke okoli celic 3T3 in povzročile lizo celic. Celice 1928z-T-iPSC-T so ob izpostavljenosti antigenu CD19 začele izražati markerje za aktivacijo T-celic in izločati citokine IL-2, TNFα in IFNγ. S tem so potrdili, da imajo pridobljene celice nekaj lastnosti, značilnih za navadne limfocite T.

Da bi bolje razumeli naravo pridobljenih celic 1928z-T-iPSC-T, so raziskovalci izvedli ekspresijsko profiliranje teh celic na mikročipu. Rezultate so primerjali z profili izražanja mRNA naivnih celic B, CD4+ celic T, CD8+ celic T, CD3+ CD56+ celic T, γδ celic T in celic ubijalk. Izkazalo se je, da so ustvarjene celice 1928z-T-iPSC-T najbolj podobne γδ celicam T. Raziskovalci preverili še razlike v izražanju neaktiviranih in aktiviranih (prisotnost celic 3T3-CD19) celic 1928z-T-iPSC-T. Ugotovili so, da se ob aktivaciji profil izražanja genov spremeni na način, ki je značilen za odziv tipa 1, ki ga navadno usmerjajo celice Th1.

Citotoksičnost celic 1928z-T-iPSC-T so nazadnje preizkusili še in vitro na mišjih limfomskih celicah, ki so izražale človeški CD19 in in vivo na mišjem ksenogenskem tumorskem modelu. Živalski model so pripravili z injiciranjem CD19+ Raji celic človeškega Burkittovega limfoma, ki so izražale fuzijo GFP in luciferaze. Tako in vitro kot in vivo so uspeli pokazati lizo celic, ki so izražale antigen CD19. Za primerjavo so pri poskusih in vivo uporabili tudi αβ in γδ celice T, ki so izražale CAR, specifičen za CD19. Tudi ti transducirani limfociti T so bili izolirani iz istega donorja kot starševska linija celic 1928z-T-iPSC-T. Ugotovili so, da je nivo izražanja receptorja CAR pri celicah 1928z-T-iPSC-T bistveno nižji kot pri αβ in γδ celicah T, ki so jih uporabili v in vivo eksperimentu. Rezultati so pokazali, da so pridobljene celice 1928z-T-iPSC-T podobno uspešne pri omejevanju razvoja tumorja, kot γδ celice T, ki so izražale CAR. Za najuspešnejše pa so se izkazale CAR+ αβ celice T, saj je bila pri miškah, zdravljenih s temi celicami, opažena popolna regresija tumorja v 5. tednu (eksperiment je trajal 7 tednov). Avtorji članka so bili kljub temu zadovoljni z rezultatom, saj so celice 1928z-T-iPSC-T delovale enako uspešno kot njim najbolj podobni limfociti T.

==Zaključek==
Avtorjem članka je uspelo iz celic T-iPSC pripraviti celice, ki izražajo specifične receptorje CAR. Ugotovili so, da imajo tako pridobljene celice lastnosti γδ celic T, čeprav izražajo na površini poleg transduciranega receptorja CAR tudi endogeni αβ TCR. Avtorji se nameravajo posvetiti razumevanju diferenciacije celic iz izvornih celic iPSC, saj bi si želeli pripraviti tudi druge tipe limfocitov T in dodatno vplivati na njihove lastnosti.

Limfociti T, pripravljeni iz celic iPSC, katere izražajo himerni antigenski receptor, bi bili zlasti primerni za zdravljenje z adoptivnim prenosom celic pri bolnikih, ki nimajo dovolj limfocitov za izolacijo. Takšni so bolniki, okuženi z virusom HIV ter močno imunosupresirani bolniki.

=Članek=
* Themeli M, Kloss CC, Ciriello G, Fedorov VD, Perna F, et al. 2013. Generation of tumor-targeted human T lymphocytes from induced pluripotent stem cells for cancer therapy. Nat. Biotechnol. 31(10):928

MBT seminarji 2014

2014-03-03T21:08:21Z

UrbanB:

'''Seznam seminarjev iz Molekularne biotehnologije v študijskem letu 2013/14'''

V študijskem letu 13/14 izvajamo predmet Molekularna biotehnologija (in s tem tudi seminarje) prvič.
Tabela za razpored po tednih bo objavljena v spletni učilnici, vanjo pa se vpišite tudi za kratke predstavitve novic (5 min). Na tej strani bo samo seznam odobrenih člankov za seminar in povezave do člankov in do povzetkov, ki jih morate objaviti najkasneje tri dni pred predstavitvijo (petek).

Način vnosa:

# The importance of ''Arabidopsis'' glutathione peroxidase 8 for protecting ''Arabidopsis'' plant and ''E. coli'' cells against oxidative stress (A. Gaber; GM Crops & Food 5(1), 2014; http://dx.doi.org/10.4161/gmcr.26979) Pomen glutation peroksidaze 8 iz repnjakovca za zaščito rastline ''Arabidopsis thaliana'' in bakterije ''Escherichia coli'' pred oksidativnim stresom. Janez Novak, 15. marca 2014
(slovenski naslov povežete z novo stranjo, na kateri bo povzetek)

Naslovi odobrenih člankov:

# Generation of protective immune response against anthrax by oral immunization with protective antigen plant-based vaccine. Sabina Kolar
# Influence of valine and other amino acids on total diacetyl and 2,3-pentanedione levels during fermentation of brewer’s wort. Jernej Mustar
# Development of influenza H7N9 virus like particle (VLP) vaccine: Homologous A/Anhui/1/2013 (H7N9) protection and heterologous A/chicken/Jalisco/CPA1/2012 (H7N3) cross-protection in vaccinated mice challenged with H7N9 virus. Ana Dolinar
# Generation of tumor-targeted human T lymphocytes from induced pluripotent stem cells for cancer therapy (M. Themeli ''et al.''; Nature Biotechnology 31, 928–933, 2013; http://www.nature.com/nbt/journal/v31/n10/full/nbt.2678.html). [[Iz induciranih pluripotentnih izvornih celic pripravljeni človeški limfociti T za terapijo raka]]. Urban Bezeljak

MBT seminarji 2014

2014-03-03T21:05:14Z

UrbanB:

'''Seznam seminarjev iz Molekularne biotehnologije v študijskem letu 2013/14'''

V študijskem letu 13/14 izvajamo predmet Molekularna biotehnologija (in s tem tudi seminarje) prvič.
Tabela za razpored po tednih bo objavljena v spletni učilnici, vanjo pa se vpišite tudi za kratke predstavitve novic (5 min). Na tej strani bo samo seznam odobrenih člankov za seminar in povezave do člankov in do povzetkov, ki jih morate objaviti najkasneje tri dni pred predstavitvijo (petek).

Način vnosa:

# The importance of ''Arabidopsis'' glutathione peroxidase 8 for protecting ''Arabidopsis'' plant and ''E. coli'' cells against oxidative stress (A. Gaber; GM Crops & Food 5(1), 2014; http://dx.doi.org/10.4161/gmcr.26979) Pomen glutation peroksidaze 8 iz repnjakovca za zaščito rastline ''Arabidopsis thaliana'' in bakterije ''Escherichia coli'' pred oksidativnim stresom. Janez Novak, 15. marca 2014
(slovenski naslov povežete z novo stranjo, na kateri bo povzetek)

Naslovi odobrenih člankov:

# Generation of protective immune response against anthrax by oral immunization with protective antigen plant-based vaccine. Sabina Kolar
# Influence of valine and other amino acids on total diacetyl and 2,3-pentanedione levels during fermentation of brewer’s wort. Jernej Mustar
# Development of influenza H7N9 virus like particle (VLP) vaccine: Homologous A/Anhui/1/2013 (H7N9) protection and heterologous A/chicken/Jalisco/CPA1/2012 (H7N3) cross-protection in vaccinated mice challenged with H7N9 virus. Ana Dolinar
# Generation of tumor-targeted human T lymphocytes from induced pluripotent stem cells for cancer therapy (M. Themeli ''et al.''; Nature Biotechnology 31, 928–933, 2013; http://www.nature.com/nbt/journal/v31/n10/full/nbt.2678.html). [[Priprava človeških limfocitov T iz induciranih pluripotentnih izvornih celic za terapijo raka]]. Urban Bezeljak

CRISPR/Cas9

2013-10-14T21:51:20Z

UrbanB:

= Spreminjanje genomske DNA s pomočjo sistema CRISPR/Cas9 =
== Uvod ==

Bakterije in arheje so za obrambo pred virusnimi okužbami razvile poseben od RNA odvisen sistem pridobljene imunosti, imenovan CRISPR/Cas (angl. clustered regularly interspaced short palindromic repeats/CRISPR-associated), ki specifično prepozna in reže tujo tarčno DNA. To se lahko s pridom izkoristi pri genomskem inženirstvu. To hitro razvijajoče področje raziskav sega vse od bazične znanosti do biotehnoloških aplikacij. Do sedaj znana orodja modificiranja genomske DNA so npr. nukleaze s cinkovimi prsti ([http://en.wikipedia.org/wiki/Zinc_finger_nuclease ZFN]) in nukleaze TAL efektorjev ([http://en.wikipedia.org/wiki/Transcription_activator-like_effector_nuclease TALEN]). Delovanje teh specifičnih endonukleaz sproži željene spremembe v genomski DNA z izrabljanjem celičnih popravljalnih mehanizmov: združevanja nehomolognih koncev ([http://en.wikipedia.org/wiki/NHEJ NHEJ]) in popravljanje s [http://en.wikipedia.org/wiki/Homologous_recombination homologno rekombinacijo]. V primerjavi s ZFN in TALEN se CRISPR/Cas9 sistem kaže kot bistveno enostavnejše in zanesljivejše orodje za spreminjanje genomske DNA, saj lahko protein Cas9 veže poljubno vodečo RNA (gRNA), katera je komplementarna tarčnemu zaporedju. Kompleks Cas9-gRNA prepozna vezavno mesto na genomski DNA, ki je definirano z najmanj 13 nt dolgim komplementarnim odsekom med gRNA in tarčno DNA navzgor od motiva PAM, kateri je nujno potreben za vezavo kompleksa in ima pri uporabljenemu sistemu iz ''Streptococcus pyogenes'' obliko NGG. Cepitev poteče 3 nt navzgor od tega zaporedja.

== Povzetek rezultatov in metod ==
Mali in sod. so kot prvi uporabili sistem CRISPR/Cas9 za spreminjanje človeške genomske DNA v različnih celičnih linijah. Z različnimi eksperimentalnimi pristopi so pokazali, da je sistem CRISPR/Cas9 enako ali celo bolj učinkovit kot ZFN in TALEN pri induciranju popravljalnih mehanizmov DNA, na katerih temelji genomski inženiring.

=== Konstrukcija plazmidov ===
Za izražanje proteina Cas9 v jedru človeških celic so genu optimizirali kodone in dodali zapis za NLS iz virusa SV40 na 3' konec gena. Gen so s hierarhičnim združevanjem s PCR sestavili iz 9 kosov 500 bp dolge sintetične dsDNA ([http://eu.idtdna.com/pages/products/genes?c=EU gBlocks]) in ga prenesli v plazmid, ki je prilagojen izražanju v sesalskih celicah. Za izražanje gRNA so naročili sintetične 455 bp dolge fragmente DNA, ki so vsebovali celotno ekspresijsko kaseto – promotor, zapis za gRNA in poli (T) - ki so jih vnesli v vektor, ki se ga lahko uporablja v človeških celicah. Gen za Cas9 je bil tako pod kontrolo konstitutivnega promotorja iz virusa CMV, gRNA pa se je izražala s pomočjo človeškega promotorja U6 za RNA polimerazo III, ki je bil vključen v naročeni sintetični fragment.

=== Spremljanje homologne rekombinacije ===
Delovanje sistema so v celicah HEK293T preizkusili z domiselnim ekperimentom, kjer so v stabilni celični liniji s pomočjo homologne rekombinacije in ustrezno homologno donorsko DNA, popravili gen za GFP, ki je bil prekinjen s stop kodonom in 68 bp dolgim insertom iz genomskega lokusa AAVS1. Uspešnost homologne rekombinacije (»poprave« gena za GFP – celice so pričele izražati GFP) so lahko spremljali s pretočno citometrijo (ločevanje fluorescenčno označenih celic; FACS) in konfokalno mikroskopijo. Za tarčenje so preizkusili 2 različni gRNA, ki sta bili komplementarni vstavljenemu lokusu AAVS1 (T1 in T2). V eksperimentu so primerjali uspešnost homologne rekombinacije z nukleazama TALEN, ki sta vezali isto sekvenco. S pomočjo FACS so pokazali, da je bilo z uporabo sistema CRISPR/Cas9 z T1 gRNA GFP pozitivnih 3 %, z T2 pa kar 8 % celic. S TALEN so dosegli zgolj 0,5 % uspešnost rekombinacije.

=== Spremljanje NHEJ ===
Sistem so preizkusili tudi na nativnem lokusu AAVS1 (znan »varni pristan« za vstavljanje genov). Učinkovitost sistema CRISPR/Cas9, da preko NHEJ sproži insercije oz. delecije na tem lokusu, so spremljali s sekvenatorjem nove generacije ([http://en.wikipedia.org/wiki/DNA_sequencing#Illumina_.28Solexa.29_sequencing Illumina MiSeq Personal Sequencer]). Z uporabo T1 oz. T2 gRNA so na celicah HEK293T dosegli insercije ali delecije v 10 % oz. 25 % branj s sekvenatorjem.

== Zaključek ==
Študija Mali in sod. služi kot pomemben dokaz principa uporabe sistema CRISPR/Cas9 za uvajanje sprememb v genom sesalskih celic. Ostalim raziskovalcem so utrli pot za uporabo tega novega orodja za modificiranje genomov v človeškem sistemu. Opisali so uspešnost delovanja v različnih celičnih linijah in primerjali učinkovitost z uveljavljenimi metodami. Razvili so osnovne protokole, ki se jih lahko uporabi za aplikativne in bazične študije s pomočjo genomskega inženirstva. Številne objave uporabe tega sistema v zadnjem letu so dokaz pomembnosti tega pionirskega dela.

== Članek ==
* Mali, P., ''et al''. 2013. RNA-guided human genome engineering via Cas9. ''Science''. 339(6121):823