Team:ETH Zurich/Modeling/Switch Circuit

From 2008.igem.org

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==Switch Circuit==
==Switch Circuit==
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We designed a novel switching circuit consisting of two inputs and one output – a start signal initiates the synthesis of a specific protein, and a terminating signalswitches gene expression off. The goal of this system is the controlled expression of a restriction enzyme to delete genome fragments in vivo.
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The designed switching circuit is driven by  two input signals – a start signal initiates the synthesis of a specific protein and a terminating signal switches gene expression off. The goal of this system is to control expression of restriction enzymes in order to delete genome fragments ''in vivo''.
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In order to do some preliminary experiments, the restriction enzyme has been substitued by a fluorescent protein.<br>
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In order to do some preliminary experiments, the restriction enzyme has been substituted by a fluorescent protein.<br>
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The basic idea of the how the system should work is as follows :  
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The detailed mechanism is described [[Team:ETH_Zurich/Wetlab/Switch_Circuit#Switch_Circuit| here]]. It follows a summarized version of it's mode of operation:<br>
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Fluorescent protein gene expression is under the control of LacI and can be induced by the addition of IPTG. In order to stop gene expression, the IPTG-sensitive LacI is replaced by IPTG-insensitive LacIS, which shuts restriction enzyme gene expression off again. The synthesis of LacIS is started by the addition of Tetracyclin to the system, which binds to the tet repressor TetR and thus de-represses the expression of the lacIs gene. The fluorescent protein is tagged, so that it is degraded faster by the Clp protease and vanishes faster from the system as its expression has been stopped.<br>
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Fluorescent protein gene expression is under control of LacI and can be induced by the addition of IPTG. In order to stop gene expression, the IPTG-sensitive LacI is replaced by IPTG-insensitive LacIIs, which shuts off fluorescent gene expression again. The synthesis of LacIIs is started by the addition of Tetracyclin (tet) to the system, which binds to the tet repressor TetR and thus de-represses the expression of the LacIIs gene. The fluorescent protein is tagged, so that it is degraded faster by the Clp protease and vanishes faster from the system as its expression is stopped.<br>
[[Image:Circuit model.JPG|center|600px]]
[[Image:Circuit model.JPG|center|600px]]
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This switching circuit is described by a set of 64 chemical reactions and XX molecular species. (see "Detailed Model")
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This switching circuit is described by a set of 64 chemical reactions and 41 molecular species.
In order to do a computational analysis of the circuit, this model has been simplified and implemented in MATLAB. Then the system has been simulated using ODE and stochastic solvers.
In order to do a computational analysis of the circuit, this model has been simplified and implemented in MATLAB. Then the system has been simulated using ODE and stochastic solvers.
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=== Implementation ===
=== Implementation ===
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For the implementation, different steps having no significant effects on the aspired results have been neglected for the sake of simplicity. In the transcriptions the additional step involving the RNA-Polymerase and in the translations the step involving the ribosomes have not been taken into account. Furthermore, the effects of the dimerization of TetR as well as the impacts of dimerization and tetramerization of LacI and LacIIs have not been considered in the final implementation. <br>
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In the implementation, some minor parts that do not have significant effects on the aspired results have been neglected for the sake of simplicity. In the MATLAB-model of the different protein-expressions, the RNA-polymerase and the ribosomes have not been taken into account, in the transcription and translation respectively. Furthermore, the effects of the dimerization of TetR as well as the impacts of dimerization and tetramerization of LacI and LacIIs [https://2008.igem.org/Team:ETH_Zurich/Modeling/Switch_Circuit#References (4)] have not been considered in the final implementation. <br>
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This simplified model still comprises more than 20 different species and over 30 kinetic reactions and has been implemented by using the Simbiology Toolbox in MATLAB.<br>
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This simplified model still comprises more than 20 different molecular species and over 30 kinetic reactions and was implemented by using the SimBiology Toolbox in MATLAB.<br>
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[[Image:model.PNG|thumb|center|600px|diagram view of the model]]
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[[Image:model.PNG|thumb|center|900px|diagram view of the model]]
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To get any useful results form the model, we performed deterministic and stochastic simulations based on the Mass-Action-Kinetics. The stochastic simulations turned out to be computationally very exhaustive but generated no further significant information compared to the deterministic simulations.<br>
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We performed deterministic and stochastic simulations based on Mass Action Kinetics. The stochastic simulations turned out to be computationally very exhaustive but generated no further significant information compared to the deterministic simulations.<br>
=== Simulation Results ===
=== Simulation Results ===
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[[Image:Induction2.JPG|thumb|left|400px|Input signals: Start signal (Induction with IPTG) at t=0 and Stop signal (induction with tet) at t=600]]
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[[Image:Induction2.JPG|thumb|left|420px|Input signals: Start signal (Induction with IPTG) and Stop signal (induction with tet) after 10 min]]
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[[Image:pulse.JPG|thumb|right|400px|Output signal: expression of GFP and GFP_mRNA as a response to the input signals on the left]]
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[[Image:pulse.JPG|thumb|right|428px|Output signal: expression of GFP and GFP_mRNA as a response to the input signals on the left]]
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 +
The simulations show that our system actually should create a nice pulse-shaped expression of the fluorescent protein (GFP). This expression can be initiated by inducing with IPTG and stopped by subsequent addition of tet into the medium. By tagging the protein it will be degraded much faster by the Clp protease, so that the overall concentration is bounded and, after activating the stop-signal, the remaining proteins disappear quickly.<br>
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The simulations show that our system actually should create a nice pulse-shaped expression of the fluorescent protein (FP). This expression can be started by inducing with IPTG and stopped by subsequent addition of tet into the medium. By tagging the protein it will be degraded much faster by the Clp protease, so that the overall concentration is bounded and, after activating the stop-signal, the remaining proteins disappear quickly.<br>
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Another fact that the simulations showed is that in order to get one single pulse the tet-concentration inside, the medium must not reach zero before all the IPTG is degraded too. Otherwise there would still be IPTG in the system inhibiting the binding of LacI to the GFP-promoter and leading to an unwanted expression of our protein of interest as the LacIIs degrades.<br>
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Another fact, our simulations show, is that in order to get one single pulse, the tet-concentration inside the medium must not reach zero before all the IPTG has degraded too. Otherwise, there would still be IPTG in the system inhibiting the binding of LacI to the FP-promotor and leading to an unwanted expression of our protein of interest as the LacIIs degrades.<br>
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One way to overcome this problem is by simply inducing with a much higher quantity of tet than IPTG, so that it simply takes longer for it to completely degrade or being washed away. Still another way would be to wait a bit longer after the induction with IPTG so that it has already partly vanished until switching off the GFP-expression by inducing with tet.
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One way to overcome this problem is simply by inducing a much higher quantity of tet than IPTG, so that it takes longer for it to completely degrade or being washed away. Another way would be to wait a bit longer after the induction with IPTG, so that it has already partly vanished until stopping the FP-expression with tet.
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=== Sensitivity Analysis ===
=== Sensitivity Analysis ===
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We define the sensitivity as the change of the production of the desired fluorescence protein - which is the output of our system - depending on the change of the paramters.
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We define the sensitivity as the change of the production of the desired fluorescence protein - which is the output of our system - depending on the change of the  
 +
[[Team:ETH_Zurich/Modeling/Switch_Circuit#Parameters|parameters]].
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[[Image:sensitivities.JPG|thumb|center|600px|Sensitivity analysis]]
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[[Image:sensitivities.JPG|thumb|center|600px|Sensitivity analysis - change in the GFP concentration depending on the change of the kinetic parameters]]
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The sensitivity analysis shows, that the concentration of the fluorescent protein strongly depends on its decay rate (paramter 13) the decay rate of its mRNA (paramter 10) and of course the transcription and translation rates of the protein (paramters 29 and 27), which is no surprise.
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The sensitivity analysis shows, that the concentration of the fluorescent protein strongly depends on its decay rate (parameter 13) the decay rate of its mRNA (parameter 10) and of course the transcription and translation rates of the protein (parameters 29 and 27), which is no surprise.
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We can also see that the decay rate of LacIIs (paramter 9) and the transcription rate of LacIIs (paramter 31) have an influence on the expression of the fluorescent protein.
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We can also see that the decay rates of LacIIs (parameter 9) and LacIIs_mRNA (parameter 12) and the transcription rate of LacIIs (parameter 31) have an influence on the expression of the fluorescent protein.
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== Detailed Model ==
== Detailed Model ==
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In order to switch on the circuit, we induce with IPTG. When IPTG is added into the medium it diffuses reversibly between the medium and the cells, where it is slowly degraded. In a chemostat extracellular IPTG is washed away.<br>
In order to switch on the circuit, we induce with IPTG. When IPTG is added into the medium it diffuses reversibly between the medium and the cells, where it is slowly degraded. In a chemostat extracellular IPTG is washed away.<br>
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<html><table border=0> <colgroup>
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=== diffusion of tet ===
=== diffusion of tet ===
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The second inducer which is used in our system is tet. This one also diffuses into the cell when it is added into the medium and degrades slowly.<br>
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The second inducer which is used in our system is tet. This one also diffuses reversibly between the medium and the cells, where it is slowly degraded and is washed away in the medium.
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<html><table border=0> <colgroup>
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=== binding of TetR to LacIIs-promotor ===
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=== binding of IPTG to LacI ===
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The first inducer IPTG can bind to the tetramerized LacI [https://2008.igem.org/Team:ETH_Zurich/Modeling/Switch_Circuit#References (4)].<br>
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TetR is constitutively expressed and binds to the LacIIs promotor, inhibiting its expression.<br>
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<html><table border=0> <colgroup>
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<html><table border=1> <colgroup>
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     <col width="250">
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<tr width="950px"><td></html>[[Image:Circuit_LacI_LacIIs_Pgfp.JPG|thumb|250px]]<html></td><td></html>
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<tr width="950px"><td></html>[[Image:Circuit_IPTG_LacI.JPG|thumb|250px]]<html></td><td></html>
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[[Image:binding_tetR_to_LacIIs.JPG|left]]
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[[Image:binding_IPTG_to_LacI.JPG|left]]
<html></td></tr></table></html>
<html></td></tr></table></html>
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=== binding of LacI and LacIIs to GFP-promotor ===
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=== binding of tet to TetR ===
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LacI which is constitutively expressed and LacIIs which is under the control of a tet repressor both can bind to the GFP promotor.<br>
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The second inducer tet can bind to TetR.<br>
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<html><table border=1> <colgroup>
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<html><table border=0> <colgroup>
     <col width="250">
     <col width="250">
     <col width="*">
     <col width="*">
   </colgroup>
   </colgroup>
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<tr width="950px"><td></html>[[Image:Circuit_TetR_PLacIIs.JPG|thumb|250px]]<html></td><td></html>
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<tr width="950px"><td></html>[[Image:Circuit_tet_tetR.JPG|thumb|250px]]<html></td><td></html>
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[[Image:binding_LacIIs_to_Pgfp.JPG|left]]
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[[Image:binding_tet_to_tetR.JPG|left]]
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[[Image:binding_LacI_to_Pgfp.JPG|left]]
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<html></td></tr></table></html>
<html></td></tr></table></html>
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=== binding of tet to TetR ===
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=== binding of TetR to LacIIs-promoter ===
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TetR is constitutively expressed and binds to the LacIIs promoter, inhibiting its expression.<br>
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<html><table border=1> <colgroup>
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<html><table border=0> <colgroup>
     <col width="250">
     <col width="250">
     <col width="*">
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   </colgroup>
   </colgroup>
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<tr width="950px"><td></html>[[Image:Circuit_tet_tetR.JPG|thumb|250px]]<html></td><td></html>
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<tr width="950px"><td></html>[[Image:Circuit_TetR_PLacIIs.JPG|thumb|250px]]<html></td><td></html>
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[[Image:binding_tet_to_tetR.JPG|left]]
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[[Image:binding_tetR_to_LacIIs.JPG|left]]
<html></td></tr></table></html>
<html></td></tr></table></html>
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=== binding of IPTG to LacI ===
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=== binding of LacI and LacIIs to GFP-promoter ===
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LacI which is constitutively expressed and LacIIs which is under the control of a tet repressor can bind both to the GFP promotor.<br>
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<html><table border=1> <colgroup>
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<html><table border=0> <colgroup>
     <col width="250">
     <col width="250">
     <col width="*">
     <col width="*">
   </colgroup>
   </colgroup>
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<tr width="950px"><td></html>[[Image:Circuit_IPTG_LacI.JPG|thumb|250px]]<html></td><td></html>
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<tr width="950px"><td></html>[[Image:Circuit_LacI_LacIIs_Pgfp.JPG|thumb|250px]]<html></td><td></html>
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[[Image:binding_IPTG_to_LacI.JPG|left]]
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[[Image:binding_LacIIs_to_Pgfp.JPG|left]]
 +
[[Image:binding_LacI_to_Pgfp.JPG|left]]
<html></td></tr></table></html>
<html></td></tr></table></html>
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=== transcription and translation of LacI ===
=== transcription and translation of LacI ===
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* RNA polymerase binds to the LacI-promoter and transcribes it into LacI-mRNA
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<html><table border=1> <colgroup>
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* RNA polymerase detaches from the LacI-mRNA
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* degradation of LacI-mRNA
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* ribosome binds to LacI-mRNA and translates it into LacI
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* ribosome detaches from LacI
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* degradation of LacI
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<html><table border=0> <colgroup>
     <col width="250">
     <col width="250">
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     <col width="*">
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=== transcription and translation of LacIIs ===
=== transcription and translation of LacIIs ===
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* RNA polymerase binds to the LacIIs-promoter and transcribes it into LacIIs-mRNA
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<html><table border=1> <colgroup>
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* RNA polymerase detaches from the LacIIs-mRNA
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* degradation of LacIIs-mRNA
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* ribosome binds to LacIIs-mRNA and translates it into LacIIs
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* ribosome detaches from LacIIs
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* degradation of LacIIs
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<html><table border=0> <colgroup>
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     <col width="250">
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     <col width="*">
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=== transcription and translation of TetR ===
=== transcription and translation of TetR ===
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* RNA polymerase binds to the TetR-promoter and transcribes it into TetR-mRNA
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<html><table border=1> <colgroup>
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* RNA polymerase detaches from the TetR-mRNA
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* degradation of TetR-mRNA
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* ribosome binds to TetR-mRNA and translates it into TetR
 +
* ribosome detaches from TetR
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* degradation of TetR
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<html><table border=0> <colgroup>
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=== transcription and translation of GFP ===
=== transcription and translation of GFP ===
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<html><img src="https://static.igem.org/mediawiki/2008/b/b3/Circuit_gfp_expression.JPG" alt="Grafik" width="30%"></img></html>
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* RNA polymerase binds to the GFP-promoter and transcribes it into GFP-mRNA
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[[Image:transcription_of_gfp.JPG|left width=30%]]
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* RNA polymerase detaches from the GFP-mRNA
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[[Image:translation_of_gfp.JPG|left]]<br clear="all" >
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* degradation of GFP-mRNA
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* ribosome binds to TGFP-mRNA and translates it into GFP
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=== dimerization of tetR ===
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* ribosome detaches from GFP
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[[Image:dimerization_of_tetR.JPG|left]]<br clear="all" >
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* degradation of GFP
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<html><table border=0> <colgroup>
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    <col width="250">
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    <col width="*">
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  </colgroup>
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<tr width="950px"><td></html>[[Image:Circuit_gfp_expression.JPG|thumb|250px]]<html></td><td></html>
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[[Image:transcription_of_gfp.JPG|left]]
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[[Image:translation_of_gfp.JPG|left]]
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<html></td></tr></table></html>
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=== dimerization and tetramerization of LacI and LacIIs ===
=== dimerization and tetramerization of LacI and LacIIs ===
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[[Image:dimerization_of_LacI.JPG|left]]<br clear="all" >
 
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[[Image:dimerization_of_LacIIs.JPG|left]]<br clear="all" >
 
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[[Image:tetramerization_of_LacI.JPG|left]]<br clear="all" >
 
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[[Image:tetramerization_of_LacIIs.JPG|left]]<br clear="all" >
 
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<html><table border=0> <colgroup>
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<tr width="950px"><td></html>[[Image:Dimtet_LacI_Is.JPG|thumb|250px]]<html></td><td></html>
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[[Image:dimerization_of_LacI.JPG|left]]
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[[Image:dimerization_of_LacIIs.JPG|left]]
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[[Image:tetramerization_of_LacI.JPG|left]]
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[[Image:tetramerization_of_LacIIs.JPG|left]]
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<html></td></tr></table></html>
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=== dimerization of tetR ===
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<html><table border=0> <colgroup>
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    <col width="250">
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    <col width="*">
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  </colgroup>
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<tr width="950px"><td></html>[[Image:Dim_TetR.JPG‎ |thumb|250px]]<html></td><td></html>
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[[Image:dimerization_of_tetR.JPG|left]]
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<html></td></tr></table></html>
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== Parameters ==
== Parameters ==
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In this section you can find all the parameters used in the simulation.
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In this section you can find all the parameters used in the simulation.<br>
 +
 
 +
Because many of the in vivo rates of the biochemical reactions we simulated are unknown or could not be found in the literature, the kinetic parameters were mainly obtained from estimates [https://2008.igem.org/Team:ETH_Zurich/Modeling/Switch_Circuit#References (2)] based on the values found in the supporting text to [https://2008.igem.org/Team:ETH_Zurich/Modeling/Switch_Circuit#References (1)].<br>
{| border="1"
{| border="1"
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|-
|-
! 1
! 1
-
| k_assoc(IPTG_LacI) || 5.0 || 1/(mole*second) || X
+
| k_assoc(IPTG_LacI) || 5.0 || 1/(mole*second) || Estimate
|-
|-
! 2
! 2
-
| k_assoc(LacI) || 5.0 || 1/(mole*second) || X
+
| k_assoc(LacI) || 5.0 || 1/(mole*second) || Estimate
|-
|-
! 3
! 3
-
| k_assoc(LacIs) || 5.0 || 1/(mole*second) || X
+
| k_assoc(LacIIs) || 5.0 || 1/(mole*second) || Estimate
|-
|-
! 4
! 4
-
| k_assoc(tet) || 5.0 || 1/(mole*second) || X
+
| k_assoc(tet) || 5.0 || 1/(mole*second) || Estimate
|-
|-
! 5
! 5
-
| k_assoc(tetR) || 5.0 || 1/(mole*second) || X
+
| k_assoc(tetR) || 5.0 || 1/(mole*second) || Estimate
|-
|-
! 6
! 6
-
| k_dec(IPTG) || 0.0002 || 1/second || X
+
| k_dec(IPTG) || 0.0002 || 1/second || Estimate
|-
|-
! 7
! 7
-
| k_dec(IPTG_ext) || 0.001 || 1/second || X
+
| k_dec(IPTG_ext) || 0.001 || 1/second || [*]
|-
|-
! 8
! 8
-
| k_dec(LacI) || 0.05 || 1/second || X
+
| k_dec(LacI) || 0.05 || 1/second || Estimate
|-
|-
! 9
! 9
-
| k_dec(LacIs) || 0.05 || 1/second || X
+
| k_dec(LacIIs) || 0.05 || 1/second || Estimate
|-
|-
! 10
! 10
-
| k_dec(gfp) || 0.25 || 1/second || X
+
| k_dec(gfp) || 0.25 || 1/second || [**]
|-
|-
! 11
! 11
-
| k_dec(mRNA_LacI) || 0.05 || 1/second || X
+
| k_dec(mRNA_LacI) || 0.05 || 1/second || Estimate
|-
|-
! 12
! 12
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| k_dec(mRNA_LacIs) || 0.05 || 1/second || X
+
| k_dec(mRNA_LacIIs) || 0.05 || 1/second || Estimate
|-
|-
! 13
! 13
-
| k_dec(mRNA_gfp) || 0.1 || 1/second || X
+
| k_dec(mRNA_gfp) || 0.1 || 1/second || [**]
|-
|-
! 14
! 14
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| k_dec(mRNA_tetR) || 0.05 || 1/second || X
+
| k_dec(mRNA_tetR) || 0.05 || 1/second || Estimate
|-
|-
! 15
! 15
-
| k_dec(tetR) || 0.05 || 1/second || X
+
| k_dec(tetR) || 0.05 || 1/second || Estimate
|-
|-
! 16
! 16
-
| k_dec(tet) || 0.0002 || 1/second || X
+
| k_dec(tet) || 0.0002 || 1/second || Estimate
|-
|-
! 17
! 17
-
| k_dec(tet_ext) || 0.001 || 1/second || X
+
| k_dec(tet_ext) || 0.001 || 1/second || [*]
|-
|-
! 18
! 18
-
| k_diff(IPTG) || 0.1 || 1/second || X
+
| k_diff(IPTG) || 0.1 || 1/second || (1)
|-
|-
! 19
! 19
-
| k_diff(tet) || 0.1 || 1/second || X
+
| k_diff(tet) || 0.1 || 1/second || (1)
|-
|-
! 20
! 20
-
| k_dissoc(IPTG_LacI) || 1.0 || 1/second || X
+
| k_dissoc(IPTG_LacI) || 1.0 || 1/second || Estimate
|-
|-
! 21
! 21
-
| k_dissoc(LacI) || 1.0 || 1/second || X
+
| k_dissoc(LacI) || 1.0 || 1/second || Estimate
|-  
|-  
! 22
! 22
-
| k_dissoc(LacIs) || 1.0 || 1/second || X
+
| k_dissoc(LacIIs) || 1.0 || 1/second || Estimate
|-
|-
! 23
! 23
-
| k_dissoc(tet) || 1.0 || 1/second || X
+
| k_dissoc(tet) || 1.0 || 1/second || Estimate
|-
|-
! 24
! 24
-
| k_dissoc(tetR) || 1.0 || 1/second || X
+
| k_dissoc(tetR) || 1.0 || 1/second || Estimate
|-
|-
! 25
! 25
-
| k_tl(LacI) || 5.0 || 1/second || X
+
| k_tl(LacI) || 5.0 || 1/second || Estimate
|-
|-
! 26
! 26
-
| k_tl(LacIs) || 5.0 || 1/second || X
+
| k_tl(LacIIs) || 5.0 || 1/second || Estimate
|-
|-
! 27
! 27
-
| k_tl(gfp) || 5.0 || 1/second || X
+
| k_tl(gfp) || 5.0 || 1/second || (1)
|-
|-
! 28
! 28
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| k_tl(tetR) || 5.0 || 1/second || X
+
| k_tl(tetR) || 5.0 || 1/second || Estimate
|-
|-
! 29
! 29
-
| k_tr(gfp) || 1.0 || 1/second || X
+
| k_tr(gfp) || 1.0 || 1/second || (1)
|-
|-
! 30
! 30
-
| k_tr(LacI) || 0.1 || 1/second || X
+
| k_tr(LacI) || 0.1 || 1/second || [***]
|-
|-
! 31
! 31
-
| k_tr(LacIs) || 0.1 || 1/second || X
+
| k_tr(LacIIs) || 0.1 || 1/second || [***]
|-
|-
! 32
! 32
-
| k_tr(tetR) || 1.0 || 1/second || X
+
| k_tr(tetR) || 1.0 || 1/second || Estimate
|}
|}
 +
 +
[*]  the degradation constants of the two inducers are bigger outside the cell, the effect that they are washed away in the chemostat is taken into account in those parameters<br>
 +
[**]  degradation rates of gfp are higher because of the tagging <br>
 +
[***] need to be that high to account for the autorepression of LacI / in order to get a low steady state concentration of LacI of about 50 proteins (3)
== References ==
== References ==

Latest revision as of 05:32, 30 October 2008

Contents

Switch Circuit

The designed switching circuit is driven by two input signals – a start signal initiates the synthesis of a specific protein and a terminating signal switches gene expression off. The goal of this system is to control expression of restriction enzymes in order to delete genome fragments in vivo. In order to do some preliminary experiments, the restriction enzyme has been substituted by a fluorescent protein.

The detailed mechanism is described here. It follows a summarized version of it's mode of operation:
Fluorescent protein gene expression is under control of LacI and can be induced by the addition of IPTG. In order to stop gene expression, the IPTG-sensitive LacI is replaced by IPTG-insensitive LacIIs, which shuts off fluorescent gene expression again. The synthesis of LacIIs is started by the addition of Tetracyclin (tet) to the system, which binds to the tet repressor TetR and thus de-represses the expression of the LacIIs gene. The fluorescent protein is tagged, so that it is degraded faster by the Clp protease and vanishes faster from the system as its expression is stopped.

Circuit model.JPG

This switching circuit is described by a set of 64 chemical reactions and 41 molecular species. In order to do a computational analysis of the circuit, this model has been simplified and implemented in MATLAB. Then the system has been simulated using ODE and stochastic solvers.

Implementation and Simulation

Implementation

In the implementation, some minor parts that do not have significant effects on the aspired results have been neglected for the sake of simplicity. In the MATLAB-model of the different protein-expressions, the RNA-polymerase and the ribosomes have not been taken into account, in the transcription and translation respectively. Furthermore, the effects of the dimerization of TetR as well as the impacts of dimerization and tetramerization of LacI and LacIIs (4) have not been considered in the final implementation.

This simplified model still comprises more than 20 different molecular species and over 30 kinetic reactions and was implemented by using the SimBiology Toolbox in MATLAB.

diagram view of the model

We performed deterministic and stochastic simulations based on Mass Action Kinetics. The stochastic simulations turned out to be computationally very exhaustive but generated no further significant information compared to the deterministic simulations.

Simulation Results

Input signals: Start signal (Induction with IPTG) and Stop signal (induction with tet) after 10 min
Output signal: expression of GFP and GFP_mRNA as a response to the input signals on the left


The simulations show that our system actually should create a nice pulse-shaped expression of the fluorescent protein (GFP). This expression can be initiated by inducing with IPTG and stopped by subsequent addition of tet into the medium. By tagging the protein it will be degraded much faster by the Clp protease, so that the overall concentration is bounded and, after activating the stop-signal, the remaining proteins disappear quickly.

Another fact that the simulations showed is that in order to get one single pulse the tet-concentration inside, the medium must not reach zero before all the IPTG is degraded too. Otherwise there would still be IPTG in the system inhibiting the binding of LacI to the GFP-promoter and leading to an unwanted expression of our protein of interest as the LacIIs degrades.

One way to overcome this problem is by simply inducing with a much higher quantity of tet than IPTG, so that it simply takes longer for it to completely degrade or being washed away. Still another way would be to wait a bit longer after the induction with IPTG so that it has already partly vanished until switching off the GFP-expression by inducing with tet.

Sensitivity Analysis

We define the sensitivity as the change of the production of the desired fluorescence protein - which is the output of our system - depending on the change of the parameters.

Sensitivity analysis - change in the GFP concentration depending on the change of the kinetic parameters


The sensitivity analysis shows, that the concentration of the fluorescent protein strongly depends on its decay rate (parameter 13) the decay rate of its mRNA (parameter 10) and of course the transcription and translation rates of the protein (parameters 29 and 27), which is no surprise. We can also see that the decay rates of LacIIs (parameter 9) and LacIIs_mRNA (parameter 12) and the transcription rate of LacIIs (parameter 31) have an influence on the expression of the fluorescent protein.

Detailed Model

diffusion of IPTG

In order to switch on the circuit, we induce with IPTG. When IPTG is added into the medium it diffuses reversibly between the medium and the cells, where it is slowly degraded. In a chemostat extracellular IPTG is washed away.

Circuit iptg diff.JPG
Diffusion iptg.JPG


diffusion of tet

The second inducer which is used in our system is tet. This one also diffuses reversibly between the medium and the cells, where it is slowly degraded and is washed away in the medium.

Circuit tet diff.JPG
Diffusion tet.JPG


binding of IPTG to LacI

The first inducer IPTG can bind to the tetramerized LacI (4).

Circuit IPTG LacI.JPG
Binding IPTG to LacI.JPG


binding of tet to TetR

The second inducer tet can bind to TetR.

Circuit tet tetR.JPG
Binding tet to tetR.JPG


binding of TetR to LacIIs-promoter

TetR is constitutively expressed and binds to the LacIIs promoter, inhibiting its expression.

Circuit TetR PLacIIs.JPG
Binding tetR to LacIIs.JPG


binding of LacI and LacIIs to GFP-promoter

LacI which is constitutively expressed and LacIIs which is under the control of a tet repressor can bind both to the GFP promotor.

Circuit LacI LacIIs Pgfp.JPG
Binding LacIIs to Pgfp.JPG
Binding LacI to Pgfp.JPG


transcription and translation of LacI

  • RNA polymerase binds to the LacI-promoter and transcribes it into LacI-mRNA
  • RNA polymerase detaches from the LacI-mRNA
  • degradation of LacI-mRNA
  • ribosome binds to LacI-mRNA and translates it into LacI
  • ribosome detaches from LacI
  • degradation of LacI
Circuit LacI expression.JPG
Transcription of LacI.JPG
Translation of LacI.JPG


transcription and translation of LacIIs

  • RNA polymerase binds to the LacIIs-promoter and transcribes it into LacIIs-mRNA
  • RNA polymerase detaches from the LacIIs-mRNA
  • degradation of LacIIs-mRNA
  • ribosome binds to LacIIs-mRNA and translates it into LacIIs
  • ribosome detaches from LacIIs
  • degradation of LacIIs
Circuit LacIIs expression.JPG
Transcription of LacIIs.JPG
Translation of LacIIs.JPG


transcription and translation of TetR

  • RNA polymerase binds to the TetR-promoter and transcribes it into TetR-mRNA
  • RNA polymerase detaches from the TetR-mRNA
  • degradation of TetR-mRNA
  • ribosome binds to TetR-mRNA and translates it into TetR
  • ribosome detaches from TetR
  • degradation of TetR
Circuit tetR expression.JPG
Transcription of tetR.JPG
Translation of tetR.JPG


transcription and translation of GFP

  • RNA polymerase binds to the GFP-promoter and transcribes it into GFP-mRNA
  • RNA polymerase detaches from the GFP-mRNA
  • degradation of GFP-mRNA
  • ribosome binds to TGFP-mRNA and translates it into GFP
  • ribosome detaches from GFP
  • degradation of GFP
Circuit gfp expression.JPG
Transcription of gfp.JPG
Translation of gfp.JPG


dimerization and tetramerization of LacI and LacIIs

Dimtet LacI Is.JPG
Dimerization of LacI.JPG
Dimerization of LacIIs.JPG
Tetramerization of LacI.JPG
Tetramerization of LacIIs.JPG


dimerization of tetR

Dim TetR.JPG
Dimerization of tetR.JPG


Parameters

In this section you can find all the parameters used in the simulation.

Because many of the in vivo rates of the biochemical reactions we simulated are unknown or could not be found in the literature, the kinetic parameters were mainly obtained from estimates (2) based on the values found in the supporting text to (1).

# Parameter name Value Units Reference/Comment
1 k_assoc(IPTG_LacI) 5.0 1/(mole*second) Estimate
2 k_assoc(LacI) 5.0 1/(mole*second) Estimate
3 k_assoc(LacIIs) 5.0 1/(mole*second) Estimate
4 k_assoc(tet) 5.0 1/(mole*second) Estimate
5 k_assoc(tetR) 5.0 1/(mole*second) Estimate
6 k_dec(IPTG) 0.0002 1/second Estimate
7 k_dec(IPTG_ext) 0.001 1/second [*]
8 k_dec(LacI) 0.05 1/second Estimate
9 k_dec(LacIIs) 0.05 1/second Estimate
10 k_dec(gfp) 0.25 1/second [**]
11 k_dec(mRNA_LacI) 0.05 1/second Estimate
12 k_dec(mRNA_LacIIs) 0.05 1/second Estimate
13 k_dec(mRNA_gfp) 0.1 1/second [**]
14 k_dec(mRNA_tetR) 0.05 1/second Estimate
15 k_dec(tetR) 0.05 1/second Estimate
16 k_dec(tet) 0.0002 1/second Estimate
17 k_dec(tet_ext) 0.001 1/second [*]
18 k_diff(IPTG) 0.1 1/second (1)
19 k_diff(tet) 0.1 1/second (1)
20 k_dissoc(IPTG_LacI) 1.0 1/second Estimate
21 k_dissoc(LacI) 1.0 1/second Estimate
22 k_dissoc(LacIIs) 1.0 1/second Estimate
23 k_dissoc(tet) 1.0 1/second Estimate
24 k_dissoc(tetR) 1.0 1/second Estimate
25 k_tl(LacI) 5.0 1/second Estimate
26 k_tl(LacIIs) 5.0 1/second Estimate
27 k_tl(gfp) 5.0 1/second (1)
28 k_tl(tetR) 5.0 1/second Estimate
29 k_tr(gfp) 1.0 1/second (1)
30 k_tr(LacI) 0.1 1/second [***]
31 k_tr(LacIIs) 0.1 1/second [***]
32 k_tr(tetR) 1.0 1/second Estimate

[*] the degradation constants of the two inducers are bigger outside the cell, the effect that they are washed away in the chemostat is taken into account in those parameters
[**] degradation rates of gfp are higher because of the tagging
[***] need to be that high to account for the autorepression of LacI / in order to get a low steady state concentration of LacI of about 50 proteins (3)

References

(1) "Spatiotemporal control of gene expression with pulse-generating networks", Basu et al., PNAS, 2004

(2) "Genetic circuit building blocks for cellular computation, communications, and signal processing", Weiss et al., Natural Computing, 2003

(3) "Predicting stochastic gene expression dynamics in single cells", Mettetal et al., PNAS, 2006

(4) "Engineered gene circuits", Hasty et al., Nature, 2002

Retrieved from "http://2008.igem.org/Team:ETH_Zurich/Modeling/Switch_Circuit"