The Mathematical Institute, University of Oxford, Eprints Archive

The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems

Seirin Lee, S and Gaffney, E. A. and Monk, N. A. M. (2010) The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems. Bulletin of Mathematical Biology, 72 (8). pp. 2139-2160.

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Abstract

There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens.

Item Type:Article
Uncontrolled Keywords:Time delays - Gierer–Meinhardt system - Gene expression - Turing pattern formation
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1369
Deposited By:Eamonn Gaffney
Deposited On:13 Aug 2011 10:04
Last Modified:13 Aug 2011 10:04

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