Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Ting Wang, Petr Plechac

Abstract:

Stochastic reaction networks that exhibit bi-stable behavior are common in many fields such as systems biology
and materials science. Sampling of the stationary distribution is crucial for understanding and characterizing
the long term dynamics of bistable stochastic dynamical systems. However, this is normally hindered by the
insufficient sampling of the rare transitions between the two metastable regions. In this paper, we apply the
parallel replica (ParRep) method for continuous time Markov chain to accelerate the stationary distribution
sampling of bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate
the sampling of rare transitions and it is very easy to implement. We combine ParRep with the path space
information bounds13 for parametric sensitivity analysis. We demonstrate the efficiency and accuracy of the
method by studying the Schl¨ogl model and the genetic switch network.