Asymptotic and numerical methods for metastable events in stochastic gene networks

TL;DR

This paper develops asymptotic and numerical methods to analyze rare metastable transitions in stochastic gene networks with self regulation, providing a more accurate framework than traditional approximations.

Contribution

It introduces a large deviation principle for stochastic gene models that accounts for gene switching without relying on adiabatic or diffusion approximations.

Findings

Derivation of a large deviation principle for gene switching

Application of quasi stationary analysis to metastability

Enhanced analysis of gene network transitions

Abstract

A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating when the proteins they produce affect the rate of switching between regulatory states. Under weak noise conditions, the deterministic forces are much stronger than fluctuations from gene switching and protein synthesis. Metastable transitions, such as bistable switching, can occur under weak noise conditions, causing dramatic shifts in the expression of a gene. A general tool used to describe metastability is the quasi stationary analysis (QSA). A large deviation principle is derived so that the QSA can explicitly account for random gene switching without using an adiabatic limit or diffusion approximation, which are unreliable and inaccurate for metastable events.This allows the existing asymptotic and numerical methods that have been developed for continuous Markov processes to be used to analyze the full model.