  Stochasticity in gene expression can give rise to fluctuations in protein
levels and lead to phenotypic variation across a population of genetically
identical cells. Recent experiments indicate that bursting and feedback
mechanisms play important roles in controlling noise in gene expression and
phenotypic variation. A quantitative understanding of the impact of these
factors requires analysis of the corresponding stochastic models. However, for
stochastic models of gene expression with feedback and bursting, exact
analytical results for protein distributions have not been obtained so far.
Here, we analyze a model of gene expression with bursting and feedback
regulation and obtain exact results for the corresponding protein steady-state
distribution. The results obtained provide new insights into the role of
bursting and feedback in noise regulation and optimization. Furthermore, for a
specific choice of parameters, the system studied maps on to a two-state
biochemical switch driven by a bursty input noise source. The analytical
results derived thus provide quantitative insights into diverse cellular
processes involving noise in gene expression and biochemical switching.
