Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments

TL;DR

This paper introduces a mathematical framework to decouple stochastic reaction networks from fluctuating environments, simplifying analysis and simulation of cellular processes affected by extrinsic noise.

Contribution

The authors develop a novel method to marginalize extrinsic environmental factors, enabling easier analysis of stochastic reaction networks in fluctuating conditions.

Findings

Framework successfully decouples networks from environments

Derivation of process and master equations for the decoupled model

Application to protein translation in fluctuating environments

Abstract

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach. For instance, we exemplarily formulate and solve a marginal master equation describing the protein translation and degradation in a fluctuating environment.