Bursting noise in gene expression dynamics: Linking microscopic and mesoscopic models

TL;DR

This paper compares microscopic and mesoscopic models of gene expression bursting noise, showing that PDMP models outperform diffusion approximations in capturing the stochastic dynamics of short-lived mRNA.

Contribution

It introduces a PDMP-based coarse-grained model for gene expression noise, demonstrating its advantages over traditional diffusion approximations.

Findings

PDMP models better capture bursting noise in gene expression.

Diffusion approximations can fail to represent bursting dynamics.

Analytical methods for stationary distribution and switching frequencies are provided.

Abstract

The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling, and demonstrate that conventional approaches based on diffusion approximations can fail to capture bursting noise. An alternative coarse-grained model, the so-called piecewise deterministic Markov process (PDMP), is seen to outperform the diffusion approximation in biologically relevant parameter regimes. We provide a systematic embedding of the PDMP model into the landscape of existing approaches, and we present analytical methods to calculate its stationary distribution and switching frequencies.