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Turing pattern with proportion preservation.

Shuji Ishihara1, Kunihiko Kaneko

  • 1Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan. shuji@complex.c.u-tokyo.ac.jp

Journal of Theoretical Biology
|August 16, 2005
PubMed
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Turing patterns can now maintain proportionality across different system sizes by incorporating a catalytic chemical. This breakthrough addresses limitations in standard models, enhancing pattern formation relevance for biological morphogenesis.

Area of Science:

  • Chemical kinetics
  • Developmental biology
  • Pattern formation

Background:

  • The standard Turing model for pattern formation exhibits scale-dependent stripe numbers due to invariant wavelength.
  • This invariance prevents the preservation of pattern proportionality (wavelength to system size ratio), a key feature in biological morphogenesis.

Purpose of the Study:

  • To propose and validate a modified Turing model that preserves pattern proportionality across varying system sizes.
  • To introduce a mechanism for achieving size-dependent chemical concentrations within the Turing model.

Main Methods:

  • Theoretical modeling of Turing patterns with a size-dependent catalytic chemical.
  • Analysis of two specific models demonstrating proportionality preservation.
  • Discussion of plausible mechanisms for achieving size-dependent concentrations.

Related Experiment Videos

Main Results:

  • Demonstrated that introducing a catalytic chemical with size-dependent concentration allows Turing patterns to maintain proportionality.
  • Showcased two models where Turing patterns successfully preserve this proportionality.
  • Identified general principles for achieving size-dependent concentrations.

Conclusions:

  • The modified Turing model offers a solution to the proportionality problem in pattern formation.
  • This approach enhances the relevance of Turing patterns for understanding biological morphogenesis due to its generality, robustness, and evolutionary accessibility.