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Generation of biological pattern and form.

J D Murray1, G F Oster

  • 1Centre for Mathematical Biology, University of Oxford.

IMA Journal of Mathematics Applied in Medicine and Biology
|January 1, 1984
PubMed
Summary

We present two models for early embryogenesis pattern formation. One model explains mesenchymal cell patterns influenced by extracellular matrix deformation, while the other describes epithelial sheet patterns using viscoelastic field equations.

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Area of Science:

  • Developmental biology
  • Mathematical biology
  • Cell biology

Background:

  • Pattern formation is crucial for embryonic development.
  • Understanding the biophysical mechanisms driving these patterns is essential.

Purpose of the Study:

  • To propose and analyze two novel biophysical models for pattern formation in early embryogenesis.
  • To apply these models to specific developmental phenomena.

Main Methods:

  • Formulation and analysis of field equations for mesenchymal cell patterns.
  • Development of viscoelastic field equations with a calcium-controlled contraction trigger for epithelial patterns.
  • Application of models to skin-organ primordia and limb bone development.

Main Results:

  • The mesenchymal model explains how cell-exerted tractions on the extracellular matrix influence cell motion and pattern formation.
  • The epithelial model, incorporating a calcium-controlled contraction trigger, shows potential for generating traveling wave solutions.

Conclusions:

  • The proposed models offer a biophysical framework for understanding pattern formation in different embryonic contexts.
  • Further analysis of the epithelial model may reveal mechanisms for dynamic pattern generation during development.

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