Stochastic delay differential equations for genetic regulatory networks

Authors:
Tianhai Tian;Kevin Burrage;Pamela M. Burrage;Margherita Carletti
Affiliations:
Advanced Computational Modelling Centre, The University of Queensland, Australia;Advanced Computational Modelling Centre, The University of Queensland, Australia;Advanced Computational Modelling Centre, The University of Queensland, Australia;Institute of Biomathematics, University of Urbino, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 4
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A derivative-free explicit method with order 1.0 for solving stochastic delay differential equations

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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 master equation 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.