Gene expression dynamics with stochastic bursts: exact results for a coarse-grained model

TL;DR

This paper develops an exact theoretical framework for gene expression dynamics with stochastic bursts, deriving a reduced model that accurately predicts protein distribution and timing, outperforming traditional diffusion models.

Contribution

It introduces a novel coarse-grained model that simplifies the system while fully capturing mRNA effects, providing exact stationary and first-passage time distributions.

Findings

Exact stationary distribution derived for the protein population.

Model accurately predicts first-passage times.

Diffusion-type models fail to capture key dynamics.

Abstract

We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose a novel expansion of the master equation for the joint process. The resulting coarse-grained model reduces the dimensionality of the system, describing only the protein population while fully accounting for the effects of discrete and fluctuating mRNA population. Closed form expressions for the stationary distribution of the protein population and mean first-passage times of the coarse-grained model are derived and large-scale Monte Carlo simulations show that the analysis accurately describes the individual-based process accounting for mRNA population, in contrast to the failure of commonly proposed diffusion-type models.