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

## TL;DR

This paper introduces a parallel replica method to efficiently sample the stationary distribution of bistable stochastic reaction networks, enabling better understanding of their long-term behavior and sensitivity analysis.

## Contribution

The paper presents a novel application of the parallel replica method to stochastic reaction networks, improving sampling efficiency and integrating sensitivity analysis.

## Key findings

- Efficient sampling of rare transitions in bistable networks.
- Accurate sensitivity analysis using combined ParRep and path space bounds.
- Validated method on Schl"{o}gl model and genetic switches network.

## Abstract

Stochastic reaction networks that exhibit bistability 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 bounds for parametric sensitivity analysis. We demonstrate the efficiency and accuracy of the method by studying the Schl\"{o}gl model and the genetic switches network.