Coupling from the Past for the Stochastic Simulation of Chemical Reaction Networks

TL;DR

This paper introduces a perfect sampling algorithm based on Coupling from the Past for error-free simulation of stationary distributions in linear chemical reaction networks, especially when state spaces are large.

Contribution

It proposes a subset-based coupling method to efficiently generate perfect samples from the stationary distribution of stochastic CRNs, demonstrated on the Reversible Michaelis-Menten model.

Findings

The subset guarantees coupling for all states in the network.

The algorithm produces error-free samples matching analytical solutions.

Comparison shows the method's efficiency and accuracy.

Abstract

Chemical reaction networks (CRNs) are fundamental computational models used to study the behavior of chemical reactions in well-mixed solutions. They have been used extensively to model a broad range of biological systems, and are primarily used when the more traditional model of deterministic continuous mass action kinetics is invalid due to small molecular counts. We present a perfect sampling algorithm to draw error-free samples from the stationary distributions of stochastic models for coupled, linear chemical reaction networks. The state spaces of such networks are given by all permissible combinations of molecular counts for each chemical species, and thereby grow exponentially with the numbers of species in the network. To avoid simulations involving large numbers of states, we propose a subset of chemical species such that coupling of paths started from these states guarantee coupling of paths started from all states in the state space and we show for the well-known Reversible Michaelis-Menten model that the subset does in fact guarantee perfect draws from the stationary distribution of interest. We compare solutions computed in two ways with this algorithm to those found analytically using the chemical master equation and we compare the distribution of coupling times for the two simulation approaches.