Quantifying noise in general stochastic models of post-transcriptional regulation of gene expression

Short Abstract — Gene expression is an stochastic process, and fluctuations in protein levels are often critical for generating phenotypic heterogeneity within a population of isogenic cells. There is thus considerable interest in quantifying how fluctuations (noise) in gene expression are impacted by cellular control mechanisms such as post-transcriptional regulation. In previous work, a general framework for promoter-based regulation has been developed [1], which leads to exact results for the moments of mRNA distributions. However, a similar framework for protein statistics in models with post-transcriptional regulation is currently lacking. In this work we develop an analytical framework that maps a general class of models of post-transcriptional regulation into models with promoter-based regulation, leading to exact analytical results for the moments of protein distributions. This mapping is based on the partitioning of Poisson arrivals (PPA) approach developed in recent work [2]. The proposed framework can be used to model complex schemes of post-transcriptional regulation and to evaluate its effects on variability in protein distributions.