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Models for contact-mediated pattern formation: cells that form parallel arrays.

L Edelstein-Keshet1, G B Ermentrout

  • 1Mathematics Department, University of British Columbia, Vancouver, Canada.

Journal of Mathematical Biology
|January 1, 1990
PubMed
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Cellular models show how cell movement and neighbor interactions create ordered patterns. Changes in cell behavior parameters can shift populations from uniform states to aligned arrays.

Area of Science:

  • Mathematical modeling
  • Cellular dynamics
  • Biophysics

Background:

  • Understanding collective cell behavior is crucial in developmental biology and tissue engineering.
  • Existing models often simplify cell-cell interactions and movement dynamics.

Purpose of the Study:

  • To develop kinetic continuum models for crawling cells on a 2D substrate.
  • To investigate how cell orientation distribution changes due to random reorientation and contact-induced turning.

Main Methods:

  • Derivation of integro-partial differential equations.
  • Linear stability analysis.
  • Numerical simulations.
  • Cellular automata simulations.

Main Results:

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  • Model behavior depends on parameters like total mass, motility, adherence, and sloughing rates.
  • A bifurcation point was identified where the uniform (isotropic) state loses stability.
  • The system transitions to an anisotropic patterned state with cells aligned in parallel arrays.

Conclusions:

  • Kinetic continuum models effectively capture the emergence of collective cell patterning.
  • Cell-cell contact responses and motility parameters significantly influence pattern formation.
  • The findings provide insights into self-organization mechanisms in cellular populations.