Product-form stationary distributions for deficiency zero networks with non-mass action kinetics

TL;DR

This paper derives explicit product-form stationary distributions for a class of continuous-time Markov chain models of biochemical systems with non-mass action kinetics, under certain network constraints, aiding statistical analysis in multiscale modeling.

Contribution

It introduces a novel class of biochemical network models with non-mass action kinetics that admit explicit product-form stationary distributions under specific conditions.

Findings

Stationary distributions can be explicitly computed in product form.

Applicable to biochemical systems with non-mass action kinetics.

Facilitates analysis of multiscale biochemical models.

Abstract

In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form.