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Related Experiment Videos

Complex pattern formation by a self-destabilization of established patterns: chemotactic orientation and phyllotaxis

Hans Meinhardt1

  • 1Max-Planck-Institut für Entwicklungsbiologie, Spemannstrasse 35 IV, Dept. Evolutionsbiologie, 72076 Tübingen, Germany. hans.meinhardt@tuebingen.mpg.de

Comptes Rendus Biologies
|May 21, 2003
PubMed
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Molecular interactions create stable or dynamic patterns. Dynamic patterns, like traveling waves, emerge from destabilized maxima and exhibit unique properties, explaining biological phenomena.

Area of Science:

  • Pattern formation
  • Theoretical biology
  • Mathematical modeling

Background:

  • Molecular interactions with local self-enhancement and long-range inhibition can generate stable patterns.
  • Highly dynamic patterns arise when these maxima are destabilized by a second, local, long-lasting antagonistic reaction.

Purpose of the Study:

  • To explain the generation of dynamic patterns, including traveling waves, through molecular interactions.
  • To connect theoretical models of pattern formation to observed phenomena in biological systems.

Main Methods:

  • Modeling molecular interactions with competing reaction-diffusion processes.
  • Analyzing the behavior of maxima destabilization leading to dynamic pattern formation.
  • Investigating properties of traveling waves, such as penetration without annihilation.

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Main Results:

  • Destabilization of maxima leads to patterns where maxima disappear and reappear or form traveling waves.
  • Traveling waves can exhibit non-annihilative mutual penetration.
  • The model explains patterns observed in cell chemotaxis, phyllotaxis (golden angle leaf initiation), and seashell patterns.

Conclusions:

  • A reaction-diffusion model with local enhancement and long-range inhibition, coupled with a local destabilizing reaction, can generate diverse dynamic biological patterns.
  • The model provides a unified explanation for phenomena like cell orientation, leaf arrangement, and seashell markings.
  • Animated simulations of these models are available for further study.