Transcriptional bursting in gene expression: analytical results for general stochastic models

TL;DR

This paper develops analytical tools for understanding gene expression variability by modeling transcriptional bursting with general stochastic processes, moving beyond traditional assumptions of geometric burst sizes and Poisson arrival times.

Contribution

It introduces a mapping between gene expression models and queueing theory, providing exact formulas for moments and conditions to detect deviations from classical assumptions.

Findings

Derived explicit conditions for non-geometric burst distributions.

Provided methods for estimating burst parameters from experimental data.

Established a framework for analyzing complex burst arrival processes.

Abstract

Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Bursting in gene expression is known to impact cell-fate in diverse systems ranging from latency in HIV-1 viral infections to cellular differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for more general stochastic models. To address this issue, we invoke a mapping between general models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These moments are then used to derive explicit conditions, based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters.