PT  - JOURNAL ARTICLE
AU  - Pavol Bokes
TI  - Heavy-tailed distributions in a stochastic gene autoregulation model
AID  - 10.1101/2021.06.02.446860
DP  - 2021 Jan 01
TA  - bioRxiv
PG  - 2021.06.02.446860
4099  - http://biorxiv.org/content/early/2021/10/22/2021.06.02.446860.short
4100  - http://biorxiv.org/content/early/2021/10/22/2021.06.02.446860.full
AB  - 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 2020 92C40; 60J76, 45D05, 41A60Competing Interest StatementThe authors have declared no competing interest.