Improved estimations of stochastic chemical kinetics by finite state expansion

TL;DR

This paper introduces finite state expansion (FSE), a novel analytical method that improves stochastic chemical kinetics estimations by bridging microscopic and macroscopic models, effectively handling complex dynamics like noise and multi-stability.

Contribution

The paper presents FSE, an innovative approach that couples the master equation with the deterministic rate equation to enhance accuracy in stochastic reaction network analysis.

Findings

FSE exactly preserves stochastic dynamics in expanded networks.

FSE improves estimations in models with intrinsic noise and multi-stability.

FSE outperforms existing techniques in challenging stochastic models.

Abstract

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations, and multi-stability.