ArticleJournal of mathematical biology2010
Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes.
Article in Journal of mathematical biology, 2010. 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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Who cites it
3 citing papers in PubMed.
- Analytic solutions for stochastic hybrid models of gene regulatory networks.Journal of mathematical biology · 2021Article
- A stochastic and dynamical view of pluripotency in mouse embryonic stem cells.PLoS computational biology · 2018Article
- Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models.Journal of the Royal Society, Interface · 2016Article
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Authors and funding
3 authors.
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Abstract
In the present work we propose an alternative approach to model autocatalytic networks, called piecewise-deterministic Markov processes. These were originally introduced by Davis in 1984. Such a model allows for random transitions between the active and inactive state of a gene, whereas subsequent transcription and translation processes are modeled in a deterministic manner. We consider three types of autoregulated networks, each based on a positive feedback loop. It is shown that if the densities of the stationary distributions exist, they are the solutions of a system of equations for a one-dimensional correlated random walk. These stationary distributions are determined analytically. Further, the distributions are analyzed for different simulation periods and different initial concentration values by numerical means. We show that, depending on the network structure, beside a binary response also a graded response is observable.
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Registered trials
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