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Poisson distributions in stochastic dynamics of gene expression: What events do they count?

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  • Lee, Julian

Abstract

The Poisson distribution is the probability distribution of the number of independent events in a given period. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as time-dependent distributions and stationary distributions, underlying independent events that give rise to such distributions have not been clear, especially in the presence of the degradation of gene products, which is not a Poisson process. I show that the variable following the Poisson distribution is the number of independent events where biomolecules are created, destined to survive until the end of a given time duration. This new viewpoint enables me to rederive the Poisson distribution as a time-dependent probability distribution for molecule numbers in various monomolecular reaction models of stochastic gene dynamics. Additionally, it allows me to derive an analytic form of the time-dependent probability distribution for multispecies monomolecular reaction models with species whose lifetimes follow nonexponential distributions, which is the convolution of the Poisson distribution with the multinomial distribution. This distribution is then utilized for deriving a novel series expansion form of a time-dependent distribution for a model with a stochastic production rate.

Suggested Citation

  • Lee, Julian, 2023. "Poisson distributions in stochastic dynamics of gene expression: What events do they count?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
  • Handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123007562
    DOI: 10.1016/j.physa.2023.129201
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    1. Long Cai & Nir Friedman & X. Sunney Xie, 2006. "Stochastic protein expression in individual cells at the single molecule level," Nature, Nature, vol. 440(7082), pages 358-362, March.
    2. Stirzaker, David, 2005. "Stochastic Processes and Models," OUP Catalogue, Oxford University Press, number 9780198568148.
    3. Avigdor Eldar & Michael B. Elowitz, 2010. "Functional roles for noise in genetic circuits," Nature, Nature, vol. 467(7312), pages 167-173, September.
    4. John R. S. Newman & Sina Ghaemmaghami & Jan Ihmels & David K. Breslow & Matthew Noble & Joseph L. DeRisi & Jonathan S. Weissman, 2006. "Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise," Nature, Nature, vol. 441(7095), pages 840-846, June.
    5. Cappelletti, Daniele & Pal Majumder, Abhishek & Wiuf, Carsten, 2021. "The dynamics of stochastic mono-molecular reaction systems in stochastic environments," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 106-148.
    6. Johan Paulsson, 2004. "Summing up the noise in gene networks," Nature, Nature, vol. 427(6973), pages 415-418, January.
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