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

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.

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• Intrinsic noise in stochastic models of gene expression with molecular memory and bursting
• Applications of Little's Law to stochastic models of gene expression
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• Transcriptional bursts in a non-equilibrium model for gene regulation by supercoiling
• A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits
• Queues with resetting: a perspective
• Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution
• Kinetic foundation of the zero-inflated negative binomial model for single-cell RNA sequencing data
• Transport equations and perturbations of boundary conditions
• The Role of RNA Condensation in Reducing Gene Expression Noise
• Most probable dynamics of a genetic regulatory network under stable Lévy noise
• Most Probable Evolution Trajectories in a Genetic Regulatory System Excited by Stable Lévy Noise
• Gene expression noise is affected differentially by feedback in burst frequency and burst size
• Decomposing variability in protein levels from noisy expression, genome duplication and partitioning errors during cell-divisions