The Mathematical Institute, University of Oxford, Eprints Archive

Size dependent symmetry breaking in models for morphogenesis

Barrio, R. A. and Maini, P. K. and Aragón, J. L. and Torres, M. (2002) Size dependent symmetry breaking in models for morphogenesis. Physica D, 168-169 (1). pp. 61-72.

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Abstract

A general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed very frequently in all kinds of real systems, including the development of shape in living organisms. Many nonlinear dynamical systems present a wide variety of patterns with different shapes and symmetries. This fact restricts the applicability of these models to morphogenesis, since one often finds a surprisingly small variation in the shapes of living organisms. For instance, all individuals in the Phylum Echinodermata share a persistent radial fivefold symmetry. In this paper, we investigate in detail the symmetry-breaking properties of a Turing reaction–diffusion system confined in a small disk in two dimensions. It is shown that the symmetry of the resulting pattern depends only on the size of the disk, regardless of the boundary conditions and of the differences in the parameters that differentiate the interior of the domain from the outer space. This study suggests that additional regulatory mechanisms to control the size of the system are of crucial importance in morphogenesis.

Item Type:Article
Uncontrolled Keywords:Pattern formation; Reaction–diffusion system; Morphogenesis; Mathematical biology
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:389
Deposited By:Philip Maini
Deposited On:20 Nov 2006
Last Modified:20 Jul 2009 14:20

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