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Schlicht, R. ; Winkler, G.

A delay stochastic process with applications in molecular biology.

J. Math. Biol. 57, 613-648 (2008)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
Molecular processes of cell differentiation often involve reactions with delays. We develop a mathematical model that provides a basis for a rigorous theoretical analysis of these processes as well as for direct simulation. A discrete, stochastic approach is adopted because several molecules appear in small numbers only. Our model is a non-Markovian stochastic process. The main theoretical results include a constructive proof of the existence of the process and a derivation of the rates for initiation and completion of reactions with delays. These results guarantee that the stochastic process is a consistent and realistic description of the molecular system. They also serve as a theoretical justification of recent work on delay stochastic simulation. We apply our model to an important process in developmental biology, the formation of somites in the vertebrate embryo. Simulation of the molecular oscillator controlling this process reveals major differences between stochastic and deterministic models.
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Publication type Article: Journal article
Document type Scientific Article
Corresponding Author
Keywords Discrete stochastic process; Delay; Stochastic simulation; Somitogenesis; Delta-Notch pathway
ISSN (print) / ISBN 0303-6812
e-ISSN 1432-1416
Journal Journal of Mathematical Biology
Quellenangaben Volume: 57, Issue: 5, Pages: 613-648 Article Number: , Supplement: ,
Publisher Springer
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)