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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 möglich sobald Postprint bei der ZB eingereicht worden ist.
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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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Discrete stochastic process; Delay; Stochastic simulation; Somitogenesis; Delta-Notch pathway
ISSN (print) / ISBN 0303-6812
e-ISSN 1432-1416
Zeitschrift Journal of Mathematical Biology
Quellenangaben Band: 57, Heft: 5, Seiten: 613-648 Artikelnummer: , Supplement: ,
Verlag Springer
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biomathematics and Biometry (IBB)