Steady-state joint distribution for first-order stochastic reaction kinetics

TL;DR

This paper introduces a new method for calculating exact steady-state joint distributions in first-order stochastic reaction networks, addressing a less-explored aspect of chemical master equations with applications in gene expression modeling.

Contribution

The paper presents a novel approach for deriving exact joint distributions in steady-state for a broad class of first-order stochastic reaction systems.

Findings

Validated on four gene expression models

Successfully computed joint distributions in complex biological systems

Demonstrated effectiveness across diverse biological scenarios

Abstract

While the analytical solution for the marginal distribution of a stochastic chemical reaction network has been extensively studied, its joint distribution, i.e. the solution of a high-dimensional chemical master equation, has received much less attention. Here we develop a novel method of computing the exact joint distributions of a wide class of first-order stochastic reaction systems in steady-state conditions. The effectiveness of our method is validated by applying it to four gene expression models of biological significance, including models with 2A peptides, nascent mRNA, gene regulation, translational bursting, and alternative splicing.