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Open Access Green as soon as Postprint is submitted to ZB.
Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes.
J. Math. Biol. 60, 207-246 (2010)
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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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Autocatalytic network; Markov process; Stationary distributions; Correlated random walk
ISSN (print) / ISBN
0303-6812
e-ISSN
1432-1416
Journal
Journal of Mathematical Biology
Quellenangaben
Volume: 60,
Issue: 2,
Pages: 207-246
Publisher
Springer
Publishing Place
New York, NY
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)