The Mathematical Institute, University of Oxford, Eprints Archive

A mechanical model for biological pattern formation: A nonlinear bifurcation analysis

Maini, P. K. and Murray, J. D. and Oster, G. F. (1985) A mechanical model for biological pattern formation: A nonlinear bifurcation analysis. Ordinary and Partial Differential Equations, Proceedings 1984 Dundee Conference. Lecture Notes - Mathematics 1151, n/a (n/a). Springer-Verlag, Heidelberg, Germany. ISBN 0075-8434

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Abstract

We present a mechanical model for cell aggregation in embryonic development. The model is based on the large traction forces exerted by fibroblast cells which deform the extracellular matrix (ECM) on which they move. It is shown that the subsequent changes in the cell environment can combine to produce pattern. A linear analysis is carried out for this model. This reveals a wide spectrum of different types of dispersion relations. A non-linear bifurcation analysis is presented for a simple version of the field equations: a non-standard element is required. Biological applications are briefly discussed.

Item Type:Book
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:536
Deposited By:Philip Maini
Deposited On:15 Dec 2006
Last Modified:20 Jul 2009 14:22

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