Dynamic behavior of stochastic gene expression models in the presence of bursting

Abstract

This paper considers the behavior of discrete and continuous mathematical models for gene expression in the presence of transcriptional/translational bursting. We treat this problem in generality with respect to the distribution of the burst size as well as the frequency of bursting, and our results are applicable to both inducible and repressible expression patterns in prokaryotes and eukaryotes. We have given numerous examples of the applicability of our results, especially in the experimentally observed situation that burst size is geometrically or exponentially distributed.

22 pages

References in corpus (5)

• Analytical distributions for stochastic gene expression
• Colored extrinsic fluctuations and stochastic gene expression
• Isolating intrinsic noise sources in a stochastic genetic switch
• Substochastic semigroups and densities of piecewise deterministic Markov processes
• Stochastic single-gene auto-regulation

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• The Strassen Invariance Principle for Certain Non-stationary Markov-Feller Chains
• Exponential ergodicity in the bounded-Lipschitz distance for a subclass of piecewise-deterministic Markov processes with random switching between flows
• Efficient stochastic simulation of gene regulatory networks using hybrid models of transcriptional bursting
• On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes With State-Dependent Jump Intensity
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