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A model of morphogenetic pattern formation.

F W Cummings1

  • 1Department of Physics, University of California, Riverside 92521.

Journal of Theoretical Biology
|June 21, 1990
PubMed
Summary
This summary is machine-generated.

This study proposes a mathematical model for cellular morphogenesis, where morphogen distribution influences surface geometry and vice versa. The model demonstrates inherent size invariance, crucial for biological regulation.

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Area of Science:

  • Developmental Biology
  • Mathematical Modeling
  • Cell Biology

Background:

  • Morphogenetic movements are fundamental to embryonic development.
  • Understanding the interplay between cellular behavior and tissue shape is crucial.

Purpose of the Study:

  • To propose a novel mathematical model for morphogenetic movement in cellular monolayers.
  • To investigate the relationship between morphogen distribution and surface geometry.
  • To demonstrate the property of size invariance (regulation) in the proposed model.

Main Methods:

  • Development of coupled non-linear equations for surface metric and morphogen distribution.
  • Self-consistent solution of these equations based on cell deformation functions.
  • Numerical integration under conditions of axial symmetry.

Main Results:

  • The model establishes a feedback loop where surface geometry dictates morphogen distribution, which in turn affects geometry.
  • Demonstrated size invariance, meaning the model regulates size without external parameters.
  • Numerical results presented for specific cell deformation scenarios.

Conclusions:

  • The proposed model provides a framework for understanding size-invariant morphogenetic movements.
  • The model's principles are applicable to early embryonic development, such as gastrulation in holoblastic eggs.
  • The model can be extended to include multiple morphogens while retaining regulation properties.