Bistable switching asymptotics for the self regulating gene

Abstract

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