Models of stochastic gene expression

Gene expression is an inherently stochastic process: Genes are activated and inactivated by random association and dissociation events, transcription is typically rare, and many proteins are present in low numbers per cell. The last few years have seen an explosion in the stochastic modeling of these processes, predicting protein fluctuations in terms of the frequencies of the probabilistic events. Here I discuss commonalities between theoretical descriptions, focusing on a gene-mRNA-protein model that includes most published studies as special cases. I also show how expression bursts can be explained as simplistic time-averaging, and how generic approximations can allow for concrete interpretations without requiring concrete assumptions. Measures and nomenclature are discussed to some extent and the modeling literature is briefly reviewed.