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Stochasticity in gene expression can give rise to fluctuations in proteinlevels and lead to phenotypic variation across a population of geneticallyidentical cells. Recent experiments indicate that bursting and feedbackmechanisms play important roles in controlling noise in gene expression andphenotypic variation. A quantitative understanding of the impact of thesefactors requires analysis of the corresponding stochastic models. However, forstochastic models of gene expression with feedback and bursting, exactanalytical results for protein distributions have not been obtained so far.Here, we analyze a model of gene expression with bursting and feedbackregulation and obtain exact results for the corresponding protein steady-statedistribution. The results obtained provide new insights into the role ofbursting and feedback in noise regulation and optimization. Furthermore, for aspecific choice of parameters, the system studied maps on to a two-statebiochemical switch driven by a bursty input noise source. The analyticalresults derived thus provide quantitative insights into diverse cellularprocesses involving noise in gene expression and biochemical switching.

Exact distributions for stochastic gene expression models with bursting and feedback