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Understanding Cerebellar Pattern Formation
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Extending the Mathematical Palette for Developmental Pattern Formation: Piebaldism.

Michaël Dougoud1, Christian Mazza1, Beat Schwaller2

  • 1Department of Mathematics, University of Fribourg, Chemin du Musée 23, 1700, Fribourg, Switzerland.

Bulletin of Mathematical Biology
|January 29, 2019
PubMed
Summary

This study explores reaction-diffusion models for animal coat patterns. It reveals how a cell-autonomous factor can generate diverse patterns, including piebaldism, by influencing system bistability.

Keywords:
PiebaldismSkin pattern developmentTuring pattern

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Area of Science:

  • Developmental Biology
  • Theoretical Biology
  • Mathematical Modeling

Background:

  • Animal coat patterns, such as spots and stripes, are often explained by Turing's reaction-diffusion theory.
  • Piebaldism, characterized by unpigmented areas, presents a pattern distinct from classical Turing patterns.

Purpose of the Study:

  • To investigate theoretical models for generating diverse animal fur patterns.
  • To explore the role of diffusing factors and a cell-autonomous transcription factor in pattern formation.
  • To elucidate the mechanisms underlying piebald pattern development.

Main Methods:

  • Theoretical investigation using reaction-diffusion equations.
  • Incorporation of two diffusing factors and one cell-autonomous transcription factor.
  • Numerical simulations to analyze pattern formation under different feedback mechanisms.

Main Results:

  • Replication of classical Turing patterns (spots, labyrinths) with specific factor combinations.
  • Observation of homogeneous color tones in a third scenario.
  • Demonstration of piebald patterns arising from transient dynamics and system bistability, influenced by the cell-autonomous factor.
  • Expansion of pattern formation parameter space and capabilities due to the cell-autonomous factor.

Conclusions:

  • Reaction-diffusion systems with specific feedback mechanisms can generate diverse coat patterns.
  • A cell-autonomous factor is crucial for generating piebald patterns, which are transient and rely on bistability.
  • The model provides insights into developmental mechanisms and extends understanding of pattern formation in biological systems.