The Mathematical Institute, University of Oxford, Eprints Archive

An analysis of one- and two-dimensional patterns in a mechanical model for morphogenesis

Maini, P. K. and Murray, J. D. and Oster, G. F. (1986) An analysis of one- and two-dimensional patterns in a mechanical model for morphogenesis. Nonlinear Oscillations in Biology and Chemistry, Proceedings 1985 Salt Lake City Conference. Lect. Notes - Biomath, 66 (n/a). Springer-Verlag, Heidelberg, Germany. ISBN n/a

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Abstract

In early embryonic development, fibroblast cells move through an extracellular matrix (ECM) exerting large traction forces which deform the ECM. We model these mechanical interactions mathematically and show that the various effects involved can combine to produce pattern in cell density. A linear analysis exhibits a wide selection of dispersion relations, suggesting a richness in pattern forming capability of the model. A nonlinear bifurcation analysis is presented for a simple version of the governing field equations. The one-dimensional analysis requires a non-standard element. The two-dimensional analysis shows the possibility of roll and hexagon pattern formation. A realistic biological application to the formation of feather germ primordia is 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:534
Deposited By:Philip Maini
Deposited On:15 Dec 2006
Last Modified:20 Jul 2009 14:22

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