Mathematical Modeling of Bistable Toggle Switch

Kinetic Model of Bistable System

Following Gardner's Work...

intro to gardner's work

equation (Ref gardner paper)

explain bifurcation

figure (bifurcation) figure (trajectory)

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

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

explain

show values for variables like degradation rate

Results from Our Kinetic Model

show graph

explain

show nullcline

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