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Modelling apical constriction in epithelia using elastic shell theory.

Gareth Wyn Jones1, S Jonathan Chapman

  • 1Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, Oxford, UK. gareth.wyn@gmail.com

Biomechanics and Modeling in Mechanobiology
|October 28, 2009
PubMed
Summary
This summary is machine-generated.

This study models embryonic tissue deformation via apical constriction, a key process in development. The mechanical model simulates fiber contraction within epithelial sheets, explaining tissue folding and organism shaping.

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Area of Science:

  • Biophysics
  • Developmental Biology
  • Computational Biology

Background:

  • Apical constriction is a fundamental mechanism driving embryonic tissue deformation.
  • This process involves the contraction of apical fibers in epithelial tissues, causing cell sheet invagination or folding.
  • Understanding this mechanism is crucial for comprehending organismal shape development.

Purpose of the Study:

  • To develop a mechanical model of apical constriction in embryonic epithelial tissues.
  • To incorporate the effects of fiber contraction into a shell theory framework.
  • To simulate and analyze tissue morphogenesis, including neurulation and gastrulation.

Main Methods:

  • Modeling the epithelial sheet as an elastic shell with an embedded fiber mesh.
  • Developing an enhanced shell theory that modifies stiffness and bending tensors to include fiber properties.
  • Introducing active contraction effects as body forces within the shell equilibrium equations.
  • Performing numerical simulations of plate bending, cylindrical shell deformation (neurulation), and spherical shell invagination (gastrulation).

Main Results:

  • The enhanced shell theory successfully incorporates fiber stiffness and active contraction effects.
  • Numerical examples demonstrate the model's ability to replicate key embryonic morphogenesis events.
  • The model provides insights into the mechanical basis of tissue folding and shape formation during development.

Conclusions:

  • The developed mechanical model offers a robust framework for studying apical constriction and its role in embryonic development.
  • The findings highlight the importance of mechanical forces and fiber dynamics in shaping developing organisms.
  • This approach can be extended to investigate other morphogenetic processes driven by cellular contractions.