Post-transcriptional Regulation of Stochastic Gene Expression Conditioned on Large Deviations

Gene expression is a stochastic process that gives rise to large fluctuations in protein levels leading to phenotypic heterogeneity in clonal cell populations; post-transcriptional regulation plays a crucial role in controlling the level of phenotypic variability within a population, which is directly tied to cell-fate decisions. As such, substantial efforts have been directed towards quantitatively modeling the effects of various post-transcriptional mechanisms on the strength of fluctuations in protein levels (noise). However, the corresponding effects of post-transcriptional regulation on the occurrence of rare events corresponding to large deviations are far less explored and have only been considered for a special model. Here, we take a general model of post-transcriptional regulation and apply the partitioning of Poisson arrivals (PPA) framework to map it onto a model that resembles promoter-based regulation of transcription, leading to a general framework to obtain objects of interest in large deviations (i.e. large deviation rate function for quantifying the likelihood of observing rare protein production rates and the corresponding driven process that characterizes the system dynamics conditional on the rare event) for models of post-transcriptional regulation directly from prior results for promoter-based models. The results derived create new avenues to analyze rare events in general models of post-transcriptional regulation pertaining to various different biological settings.