ArticleJournal of mathematical biology2020
Limit theorems for generalized density-dependent Markov chains and bursty stochastic gene regulatory networks.
Article in Journal of mathematical biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks.Journal of the Royal Society, Interface · 2023Article
- Inference on autoregulation in gene expression with variance-to-mean ratio.Journal of mathematical biology · 2023Article
- Analytic solutions for stochastic hybrid models of gene regulatory networks.Journal of mathematical biology · 2021Article
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2 authors.
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Abstract
Stochastic gene regulatory networks with bursting dynamics can be modeled mesocopically as a generalized density-dependent Markov chain (GDDMC) or macroscopically as a piecewise deterministic Markov process (PDMP). Here we prove a limit theorem showing that each family of GDDMCs will converge to a PDMP as the system size tends to infinity. Moreover, under a simple dissipative condition, we prove the existence and uniqueness of the stationary distribution and the exponential ergodicity for the PDMP limit via the coupling method. Further extensions and applications to single-cell stochastic gene expression kinetics and bursty stochastic gene regulatory networks are also discussed and the convergence of the stationary distribution of the GDDMC model to that of the PDMP model is also proved.
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