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Related Experiment Videos

Size adaptation of Turing prepatterns.

A Hunding1, P G Sørensen

  • 1Panum Institute, Department of Chemistry, University of Copenhagen, Denmark.

Journal of Mathematical Biology
|January 1, 1988
PubMed
Summary
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Biological systems can form patterns using reaction-diffusion equations. This study shows how apparent diffusion can adapt Turing prepatterns to size variations in cells and embryos.

Area of Science:

  • Biophysics
  • Developmental Biology
  • Mathematical Biology

Background:

  • Spontaneous pattern formation is crucial in biological systems.
  • Turing prepatterns, arising from reaction-diffusion equations, depend on a specific ratio of diffusion coefficient to characteristic length squared (D/R²).
  • Biological systems, like embryos, vary significantly in size, challenging the stability of prepattern geometry.

Purpose of the Study:

  • To investigate how biological systems maintain Turing prepattern geometry despite size variations.
  • To explore the role of apparent diffusion (Dapp) in adapting pattern formation.
  • To demonstrate the adaptability of Turing structures in both single cells and larger systems.

Main Methods:

  • Analysis of nonlinear parabolic partial differential equations governing chemical reaction-diffusion systems.

Related Experiment Videos

  • Modeling of biochemical control systems that can vary apparent diffusion (Dapp).
  • Mathematical analysis of how Dapp/R² variations influence pattern stability across different scales.

    • Main Results:

    • Turing prepatterns require a limited interval for D/R² to maintain geometry.
    • Biochemical control systems can vary Dapp/R², where Dapp is an enzyme-regulated apparent diffusion constant.
    • This variation allows Turing structures to adapt to size changes exceeding three orders of magnitude.

    Conclusions:

    • Biochemical systems possess inherent mechanisms to adjust apparent diffusion, enabling robust pattern formation.
    • Turing structures can adapt to significant size variations, crucial for processes in cleaving eggs and embryos.
    • The findings extend the understanding of pattern formation beyond fixed-geometry models to dynamic biological contexts.