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

Authored by Yen Ting Lin, Charles R Doering

Date Published: 2016

DOI: 10.1103/physreve.93.022409

Sponsors: United Kingdom Engineering and Physical Sciences Research Council (EPSRC) United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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 an 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.

Tags

differentiation noise systems potential landscape stability Cells Jump markov processes 1st-passage times Switches