Transcriptional pulsing and consequent stochasticity in gene expression

TL;DR

This paper provides an exact solution to the Master equation for transcriptional pulsing, revealing how different rate constants produce diverse mRNA and protein distributions, including bimodal and power-law behaviors, impacting cellular variability understanding.

Contribution

It offers the first exact time-dependent analysis of mRNA distributions in transcriptional pulsing models, linking mRNA variability to protein distribution regimes.

Findings

Bimodal and long-tailed distributions occur at steady state.

Time evolution of distributions shows non-steady state behaviors.

Protein distributions can mirror or deviate from mRNA distributions depending on rate constants.

Abstract

Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell to cell variability of protein and mRNA numbers. The issue is how the time constants associated with episodes of transcriptional bursting impact cellular mRNA and protein distributions and reciprocally, to what extent experimentally observed distributions can be attributed to transcriptional pulsing. We address these questions by investigating the exact time-dependent solution of the Master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results: we show that, among others, bimodal and long-tailed (power law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state distributions may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is essentially determined by proteins, we investigate the effect of the different mRNA distributions on the corresponding protein distributions. We delineate the regimes of rate constants for which the protein distribution mimics the mRNA distribution and those for which the protein distribution deviates significantly from the mRNA distribution.