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Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes.
J. Math. Biol. 60, 207-246 (2010)
DOI Verlagsversion bestellen
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Autocatalytic network; Markov process; Stationary distributions; Correlated random walk
ISSN (print) / ISBN 0303-6812
Zeitschrift Journal of Mathematical Biology
Quellenangaben Band: 60, Heft: 2, Seiten: 207-246
Verlagsort New York, NY
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biomathematics and Biometry (IBB)