Bistable switching asymptotics for the self regulating gene

TL;DR

This paper analyzes a stochastic model of a self-regulating gene that exhibits noise-induced bistable switching, providing an asymptotic approximation of the mean switching rate and stationary probability density.

Contribution

It introduces an improved asymptotic approximation for the mean switching rate, including the pre exponential factor, enhancing accuracy over previous models.

Findings

Derived an asymptotic approximation of the mean switching rate with pre exponential factor

Obtained a uniformly accurate approximation of the stationary probability density

Demonstrated noise-induced bistable switching in the gene regulation model

Abstract

A simple stochastic model of a self regulating gene that displays bistable switching is analyzed. While on, a gene transcribes mRNA at a constant rate. Transcription factors can bind to the DNA and affect the gene's transcription rate. Before an mRNA is degraded, it synthesizes protein, which in turn regulates gene activity by influencing the activity of transcription factors. Protein is slowly removed from the system through degradation. Depending on how the protein regulates gene activity, the protein concentration can exhibit noise induced bistable switching. An asymptotic approximation of the mean switching rate is derived that includes the pre exponential factor, which improves upon a previously reported logarithmically accurate approximation. With the improved accuracy, a uniformly accurate approximation of the stationary probability density, describing the gene, mRNA copy number, and protein concentration is also obtained.