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bioRxiv · 10.1101/2021.06.02.446860

Heavy-tailed distributions in a stochastic gene autoregulation model

Bokes, P.
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Abstract

Synthesis of gene products in bursts of multiple molecular copies is an important source of gene expression variability. This paper studies large deviations in a Markovian drift-jump process that combines exponentially distributed bursts with deterministic degradation. Large deviations occur as a cumulative effect of many bursts (as in diffusion) or, if the model includes negative feedback in burst size, in a single big jump. The latter possibility requires a modification in the WKB solution in the tail region. The main result of the paper is the construction, via a modified WKB scheme, of matched asymptotic approximations to the stationary distribution of the drift-jump process. The stationary distribution possesses a heavier tail than predicted by a routine application of the scheme. MSC 202092C40; 60J76, 45D05, 41A60

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Bokes, P.. 2021-06-03. Heavy-tailed distributions in a stochastic gene autoregulation model. https://doi.org/10.1101/2021.06.02.446860

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