ArticleJournal of mathematical biology2021
Analytic solutions for stochastic hybrid models of gene regulatory networks.
Article in Journal of mathematical biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed.
- Translation regulation by RNA stem-loops can reduce gene expression noise.BMC bioinformatics · 2024Article
- Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks.Journal of the Royal Society, Interface · 2023Article
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Authors and funding
3 authors.
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Abstract
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have become a popular alternative. The evolution of the corresponding probability density functions is given by a coupled system of hyperbolic PDEs. This system has Markovian nature but its hyperbolic structure makes it difficult to apply standard functional analytical methods. We are able to prove convergence towards the stationary solution and determine such equilibrium explicitly by combining abstract methods from the theory of positive operators and elementary ideas from potential analysis.
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