Heavy-tailed distributions in a stochastic gene autoregulation model

Bokes, Pavol

doi:10.1101/2021.06.02.446860

Cited by 2 publications

(1 citation statement)

References 78 publications

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“…As an example, they state that 63% of financial returns of half a century can be associated with only 10 trading days. While many authors are aware of non-negligible stochastic effects and use this to their advantage to adequately model for instance bursty gene expression (2)(3)(4), expectations remain the instrument of choice to describe stochastic processes in various scientific fields. The Chemical Master Equation (CME) is a standard approach to describe the time evolution of CRNs (see e.g.…”

Section: Introductionmentioning

confidence: 99%

The impossible challenge of estimating non-existent moments of the Chemical Master Equation

Wagner

Radde

2023

Preprint

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Motivation: The Chemical Master Equation is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge are moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter heavy-tailedness and hence do not possess statistical moments. Results: We show that estimation via Stochastic Simulation Algorithm trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the Method of Moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution's heavy-tailedness on SSA run times and explain inherent difficulties. While moment estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment estimation techniques themselves reliably indicate the potential heavy-tailedness of the CME's solution.

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Section: Introductionmentioning

confidence: 99%

The impossible challenge of estimating non-existent moments of the Chemical Master Equation

Wagner

Radde

2023

Preprint

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Exact and WKB-approximate distributions in a gene expression model with feedback in burst frequency, burst size, and protein stability

Bokes

2020

Preprint

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The expression of individual genes into functional protein molecules is a noisy dynamical process. Here we model the protein concentration as a jump--drift process which combines discrete stochastic production bursts (jumps) with continuous deterministic decay (drift). We allow the drift rate, the jump rate, and the jump size to depend on the current protein level in an arbitrary fashion to implement feedback in protein stability, burst frequency, and burst size. Two versions of feedback in burst size are considered: in the ``infinitesimally delayed'' version, only those molecules of protein that have been present before a burst started can regulate the size of the burst; in the ``undelayed'' version, newly produced molecules also partake in the regulation of the further growth of a burst. Excluding the infinitesimal delay in burst size, the model is explicitly solvable. With the inclusion of the infinitesimal delay, an exact distribution to the model is no longer available, but we are able to construct a WKB approximation that applies in the asymptotic regime of small but frequent bursts. Comparing the asymptotic behaviour of the two model versions, we report that they yield the same WKB quasi-potential but a different exponential prefactor. We illustrate the difference on the case of a bimodal protein distribution sustained by a sigmoid feedback in burst size: we show that the omission of the infinitesimal delay overestimates the weight of the upper mode of the protein distribution. The analytic results are supported by kinetic Monte-Carlo simulations.

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Heavy-tailed distributions in a stochastic gene autoregulation model

Cited by 2 publications

References 78 publications

The impossible challenge of estimating non-existent moments of the Chemical Master Equation

The impossible challenge of estimating non-existent moments of the Chemical Master Equation

Exact and WKB-approximate distributions in a gene expression model with feedback in burst frequency, burst size, and protein stability

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