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Journal of Mathematical Biology

, Volume 24, Issue 5, pp 525–541 | Cite as

Nonlinear pattern selection in a mechanical model for morphogenesis

  • A. S. Perelson
  • P. K. Maini
  • J. D. Murray
  • J. M. Hyman
  • G. F. Oster
Article

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.

Keywords

Stochastic Process Dispersion Relation Mechanical Model Mathematical Biology Matrix Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • A. S. Perelson
    • 1
  • P. K. Maini
    • 2
  • J. D. Murray
    • 2
  • J. M. Hyman
    • 1
  • G. F. Oster
    • 3
  1. 1.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK
  3. 3.Departments of Biophysics and EntomologyUniversity of CaliforniaBerkeleyUSA

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