Queuing models of gene expression: Analytical distributions and beyond

Abstract

Activation of a gene is a multistep biochemical process, involving recruitments of transcription factors and histone kinases as well as modification of histones. Many of these intermediate reaction steps would have been unspecified by experiments. Therefore, classical two-state models of gene expression established based on the memoryless (or Markovian) assumption would not well describe the reality in gene expression. In fact, recent experimental data have indicated that the inactive phases of gene promoters are differently distributed, showing strong memory. Here, we use a non-exponential waiting-time distribution to model the complex activation process of a gene, and analyze a queuing model of stochastic transcription. We successfully derive the analytical expression for the mRNA distribution, which provides insight into the effect of molecular memory created by complex activating events on the mRNA expression. We find that the reduction in the waiting-time noise may result in the increase in the mRNA noise, contrary to the previous conclusion. Based on the derived distribution, we also develop a method to infer the waiting-time distribution from a known mRNA distribution. Data analysis on a realistic example verifies the validity of this method. SIGNIFICANCEActivation of a gene is a complex biochemical process and involve several intermediate reaction steps, many of which have been unspecified by experiments. Stochastic models of gene expression that were previously established based on the constant reaction rates would not well reflect the reality in gene expression. To this end, we study a queuing model of stochastic transcription which assume that the reaction waiting time follows a general distribution and derive the analytical expression for mRNA distribution. Our results provide insight into the role of molecular memory in fine-tuning the gene expression noise, and can be used to infer the underlying molecular mechanism.