Toggle Switch: Dynamics and Steady States
This Chapter aims at showing how to simulate the dynamics and analyse the steady states of the Toggle Switch with COPASI. Initially, we will build a simple model (without inducers) based on mass action kinetics in order to run both deterministic and stochastic simulations. The comparison of their results will show that the values of some kinetic parameters provoke a clear difference in the predictions of the same model if a stochastic algorithm is run instead of solving the ODE system associated with the model. This simplified model, together with the same equations as in the paper by Gardner et al.  – which we already met in Chap. 6 – will be also used to explain how to run stability analysis with COPASI. With respect to XPPAUT, COPASI offers less features for this task. However, COPASI can both calculate and determine the nature of the steady state that a synthetic gene circuit will reach, given the circuit initial conditions. Finally, we will write a more detailed model, which contains the inducer-repressor interactions, in order to show how to mimic in silico the measurements that are carried out in the wet-lab on living cells.