Team:Duke/Modeling/3

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Contents

Mathematical Modeling of Bistable Toggle Switch

Kinetic Model of Bistable System

Following Gardner's Work...

Tim Gardner from Jim Collins' Lab of Boston Univeristy published one of the first major papers on genetic toggle switch. In his work, he used a kinetic approach to model the stability of a genetic toggle switch. His equations involved two equations expressing the change in the level of two mutually repressive repressors with respect to time.

Gardner model.png
Figure 1. Equation Used in Gardner's Model



Gardner variables.png
Figure 2. Equation Used in Gardner's Model




explain bifurcation


Gardner trajectory.png
Figure 3. Nullclines for Gardner's Model


figure (trajectory)


Gardner bifurcation.png
Figure 4. Gardner's Bifurcation Region Plots


figure (bifurcation)


explain the effect of changing hill coeff on bifurcation region. explain nullcline

reproduce nullcline and trajectory (explain trajectory)

Kinetic nullcine.png
Figure 5. Bifurcation Region and Trajectory


Development of Our Kinetic Model

moving on, we have developed another kinetic model using the results of the thermodynamic model. gardner = effect of hill coeff on bistability of a system (bifurcation region) new model = effect of various parameters on bistability (highlight and number Kd, pr_Str, basal rate.

as mentioned before, key assumption is is (du/dt , dv/dt = proportional to p_bound)

show equation

Thermo rates.png
Figure 6. Our Kinetic Model


explain

show values for variables like degradation rate

Results from Our Kinetic Model

show graph

Thermo prstrength.png
Figure 7. Bifurcation Region with Different Promoter Strengths


Thermo binding.png
Figure 8. Bifurcation Region with Different Repressor Binding Strengths


Thermo leaky.png
Figure 9. Bifurcation Region with Different Basal Transcription Rate


explain



show nullcline

Thermo nullcline.png
Figure 10. Nullcines and Trajectories Using Our Model



confirm bistability of the system (thermodynamic model incorporated into kinetic model)

References

  1. Gardener, T. et al. Construction of a genetic toggle switch in Escherichia coli. Nature. 403, 339-342 (2000).




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