The Mathematical Institute, University of Oxford, Eprints Archive

Gene expression time delays & Turing pattern formation systems

Gaffney, E. A. and Monk, N. A. M. (2006) Gene expression time delays & Turing pattern formation systems. Bulletin of Mathematical Biology, 68 (1). pp. 99-130.

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Abstract

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning.

Item Type:Article
Uncontrolled Keywords:Time delays - Reaction diffusion equations
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:885
Deposited By:Eamonn Gaffney
Deposited On:15 Jan 2010 07:46
Last Modified:15 Jan 2010 07:46

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