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. SIGNIFICANCE:Activation 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.

Inferring transcriptional bursting kinetics from single-cell snapshot data using a generalized telegraph model

“…Finally, we consider two specific cases of the GTM. First, if the ON-state dwell time is exponential, i.e., , the GTM and corresponding results reduce to the previous conclusions(Shi, et al, 2020) (see Supplementary Note 3.1). Further, if the OFF-state dwell time is also exponential, i.e.,…”

Silent transcription intervals and translational bursting lead to diverse phenotypic switching

“…Note that this model is an extension of previously studied models. 59, 60 In addition, if f off ( t ) and f on ( t ) are exponentially distributed, then the gene model described by Eq. 1 reduces to a two-state model with translational bursting.…”

“…58 Shi et al derived the analytical distribution of gene product in a two-state model with non-exponentially distributed inactive periods. 59 Latter, Zhang et al extended this model to double activation pathways (i.e., crosstalk), and derived the exact expressions for steady-state mRNA distribution and noise. 60 The analysis of these models is mainly confined to steady-state moments and noise of protein counts, but the precise role of silent transcription times regulating the transition among the phenotypic states in a single cell is not understood.…”

“…derived the analytical distribution of gene product in a two-state model with non-exponentially distributed inactive periods. 59 Latter, Zhang et al . extended this model to double activation pathways (i.e., crosstalk), and derived the exact expressions for steady-state mRNA distribution and noise.…”

Kinetic characteristics of transcriptional bursting in a complex gene model with cyclic promoter structure

“…Of these models, the most widely 3 used model is the two-state model [17,[36][37][38][39], where the promoter is assumed to switch between transcriptionally active (ON) and inactive (OFF) states with constant switching rates. Queuing models have also been proposed to analyze the impact of transcription regulation on bursting kinetics [31,[40][41][42], where waiting-time distributions are general (either exponential or non-exponential). For example, Schwabe et al used Erlang-distributed times to model ON-phase and transcription ignition, and found that burst sizes peaked distribution [43].…”