Weighted next reaction method and parameter selection for efficient simulation of rare events in biochemical reaction systems

Zhouyi Xu,Xiaodong Cai

doi:10.1186/1687-4153-2011-797251

Abstract

The weighted stochastic simulation algorithm (wSSA) recently developed by Kuwahara and Mura and the refined wSSA proposed by Gillespie et al. based on the importance sampling technique open the door for efficient estimation of the probability of rare events in biochemical reaction systems. In this paper, we first apply the importance sampling technique to the next reaction method (NRM) of the stochastic simulation algorithm and develop a weighted NRM (wNRM). We then develop a systematic method for selecting the values of importance sampling parameters, which can be applied to both the wSSA and the wNRM. Numerical results demonstrate that our parameter selection method can substantially improve the performance of the wSSA and the wNRM in terms of simulation efficiency and accuracy.

Highlights

Biochemical reaction systems in living cells exhibit significant stochastic fluctuations due to a small number of molecules involved in processes such as the transcription and translation of genes [1]
We develop a systematic method for selecting optimal values for importance sampling parameters that can be incorporated into both the weighted stochastic simulation algorithm (wSSA) and the weighted NRM (wNRM)
We developed an alternative wNRM for estimating the probability of the rave event

Summary

Introduction

Biochemical reaction systems in living cells exhibit significant stochastic fluctuations due to a small number of molecules involved in processes such as the transcription and translation of genes [1]. The weighted stochastic simulation algorithm (wSSA) recently developed by Kuwahara and Mura [22] based on the importance sampling technique enables one to efficiently estimate the probability of a rare event. We first apply the importance sampling technique to the reaction method (NRM) of the SSA [4] and develop a weighted NRM (wNRM) as an alternative to the wSSA. We develop a systematic method for selecting optimal values for importance sampling parameters that can be incorporated into both the wSSA and the wNRM.

Weighted stochastic simulation algorithms

Parameter selection for wSSA and wNRM

Systems with dimerization reactions

Findings

Conclusion