A generalized work theorem for stopped stochastic chemical reaction networks

TL;DR

This paper develops a generalized work theorem for stochastic chemical reaction networks, extending nonequilibrium relations to stopped processes and validating them through simulations, with applications in biological systems.

Contribution

It introduces a martingale-based generalized work theorem for CRNs, applicable to various initial conditions and stopping times, without requiring detailed balance.

Findings

Validated the theorem with stochastic simulations.

Demonstrated applicability to biological circuits.

Showed independence from detailed balance assumptions.

Abstract

We establish a generalized work theorem for stochastic chemical reaction networks (CRNs). By using a compensated Poisson jump process, we identify a martingale structure in a generalized entropy defined relative to an auxiliary backward process and extend nonequilibrium work relations to processes stopped at bounded arbitrary times. Our results apply to discrete, mesoscopic chemical reaction networks and remain valid for singular initial conditions and state-dependent termination events. We show how martingale properties emerge directly from the structure of reaction propensities without assuming detailed balance. Stochastic simulations of a simple chemical kinetic proofreading network are used to explore the dependence of the exponentiated entropy production on initial conditions and model parameters, validating our new work theorem relationships. Our results provide new quantitative tools for analyzing biological circuits ranging from metabolic to gene regulation pathways.