A stochastic model for post-transcriptional regulation of rare events in gene expression

Post-transcriptional regulation of gene expression is often a critical component of cellular processes involved in cell-fate decisions. Correspondingly, considerable efforts have focused on modeling post-transcriptional regulation of stochastic gene expression and on quantifying its impact on the mean and variance of protein levels. However, the impact of post-transcriptional regulation on rare events corresponding to large deviations in gene expression is less well understood. Here, we study a simple model involving post-transcriptional control of gene expression and characterize the impact of regulation on large deviations in activity fluctuations. We derive analytical results for the large deviation function for protein production rate and for the corresponding driven process which characterizes system fluctuations conditional on the rare event. Our results suggest that fluctuations in burst size rather than frequency play a dominant role in controlling rare events. The results derived also provide insight into how post-transcriptional regulation can be used to fine-tune the probability of rare fluctuations and to thereby control phenotypic variation in a population of cells.