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- W3037647549 abstract "Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a formal asymptotic approach, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable fixed point of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable fixed points; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation." @default.
- W3037647549 created "2020-07-02" @default.
- W3037647549 creator A5004790111 @default.
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- W3037647549 date "2020-06-24" @default.
- W3037647549 modified "2023-10-04" @default.
- W3037647549 title "Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach" @default.
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- W3037647549 doi "https://doi.org/10.1007/s00285-020-01512-y" @default.
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