Team:ETH Zurich/Modeling/Switch Circuit



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


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


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)


(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