Nonlinear pattern selection in a mechanical model for morphogenesis.

A S Perelson; P K Maini; J D Murray; J M Hyman; G F Oster

doi:10.1007/bf00275682

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Nonlinear pattern selection in a mechanical model for morphogenesis.

A S Perelson·P K Maini·J D Murray·J M Hyman·G F Oster

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Abstract

We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.

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Animals Cells Mathematics Models, Biological Morphogenesis Comparative Study Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S.

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A S Perelson, P K Maini, J D Murray, J M Hyman, G F Oster. 1986. Nonlinear pattern selection in a mechanical model for morphogenesis.. https://doi.org/10.1007/bf00275682

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