Silent transcription intervals and translational bursting lead to diverse phenotypic switching

Abstract

Bimodality of gene expression, as a mechanism generating phenotypic diversity, enhances the survival of cells in a fluctuating environment. Growing experimental evidence suggests that silent transcription intervals and translational bursting play important roles in regulating phenotypic switching. Characterizing these kinetics is challenging. Here, we develop an interpretable and tractable model, the generalized telegraph model (GTM), which considers silent transcription intervals described by a general waiting-time distribution and translational bursting characterized by an arbitrary distribution. Using methods of queuing theory, we derive analytical expressions of all moment statistics and distribution of protein counts. We show that non-exponential inactive times and translational bursting can lead to two nonzero bimodalities that cannot be captured in the classical telegraph model (CTM). In addition, we find that both silent-intervals noise and translational burst-size noise can amplify gene expression noise, as well as induce diverse dynamic expressions. Our results not only provide an alternative mechanism for phenotypic switching driven by silent transcription intervals and translational bursting, but also can be used to infer complex promoter structures based on experimental data. SIGNIFICANCEUnderstanding how phenotypic diversity arises among isogenic cell populations is a fundamental problem in biology. Previous studies have shown that the bimodality of gene expression contributing to phenotypic variations is mostly caused by the intrinsic or extrinsic regulations of underlying systems. It is unclear whether bimodality occurs in the absence of these regulations. The CTM has made great success in interpreting many experimental phenomena, but it cannot capture the bimodal distributions with two nonzero peaks that have been demonstrated in experiments. In particular, recent single-cell studies have shown non-exponential inactive periods and non-geometric translational bursting in gene expression. How to model these kinetics is challenging. We develop a stochastic gene model, namely the GTM, to model the silent transcription intervals by a general waiting-time distribution and translational bursting by an arbitrary distribution. By mapping the GTM into a queuing model, we derive the steady-state distribution of gene products that can be used for analyzing phenotypic switching. We find that non-exponential inactive times and translational bursting can lead to two nonzero bimodalities that cannot be captured in the CTM. These results indicate that both silent transcription intervals and translational bursting have important roles in controlling cell phenotypic variations in fluctuating environments.