Stochastic delay differential equations for genetic regulatory networks

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

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Tian, Dr Tianhai
• Authors: Tian, T., Burrage, K., Burrage, P.M., and Carletti, M.
• Subjects: Q Science > QH Natural history > QH345 Biochemistry
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Computational and Applied Mathematics
• ISSN: 0377-0427
• Published Online: 07 August 2006