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

Bistable switching asymptotics for the self regulating gene