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Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction-Diffusion and Chemotaxis.

Camile Fraga Delfino Kunz1, Alf Gerisch2, James Glover3

  • 1Frankfurt Institute for Advanced Studies and Department of Computer Science and Mathematics, Goethe-University Frankfurt, Ruth-Moufang-Str. 1, 60438, Frankfurt, Germany.

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|December 1, 2023
PubMed
Summary

This study models how chemotaxis and reaction-diffusion systems interact to create biological patterns. Coupling these systems enhances pattern formation robustness and can even enable patterning where neither system works alone.

Keywords:
Biological developmentChemotaxisMorphogenesisReaction–diffusion

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Area of Science:

  • Mathematical Biology
  • Developmental Biology
  • Pattern Formation

Background:

  • Experimental studies suggest a link between Turing-type diffusion instability and chemotaxis in morphogenesis.
  • Both reaction-diffusion systems and chemotaxis can independently generate spatial patterns.

Purpose of the Study:

  • To develop and analyze a mathematical model coupling chemotaxis with a reaction-diffusion system.
  • To investigate how this coupling affects pattern formation stability, parameter space, geometry, and dynamics.

Main Methods:

  • Classical linear stability analysis.
  • Numerical analysis of the coupled system.
  • Exploration of different model structures.

Main Results:

  • Coupling reaction-diffusion and chemotaxis generally increases pattern formation robustness by expanding the parameter space.
  • Increased chemosensitivity can accelerate patterning but may reduce spatial regularity.
  • Pattern formation is possible even when individual systems do not generate patterns.
  • Coupling can also inhibit pattern formation under certain parameter settings.

Conclusions:

  • The coupled model provides theoretical support for experimental findings in morphogenesis.
  • This work highlights the potential for pattern formation through the interplay of diffusion-driven instability and chemotaxis.
  • Findings guide future experimental research and offer insights into coupling pattern formation systems from a parameter space perspective.