Stochastic models and numerical algorithms for a class of regulatory gene networks

TL;DR

This paper develops numerical algorithms to analyze steady state distributions in self-regulated gene networks, combining stochastic modeling with mean-field approaches and establishing convergence for certain feedback systems.

Contribution

It introduces efficient numerical methods for steady state analysis and studies convergence in time-delayed mean-field models of regulatory gene networks.

Findings

Numerical algorithms accurately compute steady state distributions.

Convergence of Markov chains is proven for specific feedback network models.

Application to synthetic biology and gene therapy networks.

Abstract

Regulatory gene networks contain generic modules like those involving feedback loops, which are essential for the regulation of many biological functions. We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady state distributions of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in synthetic biology and in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops