Stochastic delay differential equations for genetic regulatory networks

Tian, Tianhai, Burrage, Kevin, Burrage, Pamela M. and Carletti, Margherita (2007) Stochastic delay differential equations for genetic regulatory networks. Journal of Computational and Applied Mathematics, 205 2: 696-707. doi:10.1016/j.cam.2006.02.063


Author Tian, Tianhai
Burrage, Kevin
Burrage, Pamela M.
Carletti, Margherita
Title Stochastic delay differential equations for genetic regulatory networks
Journal name Journal of Computational and Applied Mathematics   Check publisher's open access policy
ISSN 0377-0427
Publication date 2007-08-15
Sub-type Article (original research)
DOI 10.1016/j.cam.2006.02.063
Volume 205
Issue 2
Start page 696
End page 707
Total pages 12
Editor Brenner
Goovaerts
Mitsui
Ng
Sommeijer
Wuytack
Place of publication Amsterdam
Publisher Elsevier BV
Collection year 2006
Language eng
Subject C1
230116 Numerical Analysis
239901 Biological Mathematics
780101 Mathematical sciences
Abstract Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.
Keyword Mathematics, Applied
stochastic delay differential equations
genetic regulatory networks
chemical Langevin equation
stochastic simulation algorithm
Oscillatory Expression
Chemical-kinetics
Systems
Hes1
Approximation
Simulation
Noise
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 10:54:21 EST