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Turing Patterning in Stratified Domains.

Andrew L Krause1, Václav Klika2, Jacob Halatek3

  • 1Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK. krause@maths.ox.ac.uk.

Bulletin of Mathematical Biology
|October 15, 2020
PubMed
Summary
This summary is machine-generated.

We developed a model for bilayer reaction-diffusion systems, finding that diffusion-only layers can reduce pattern formation but also create complex instabilities. This work aids synthetic biology and developmental biology research.

Keywords:
Pattern formationStratified mediaSynthetic biologyTuring instabilities

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Area of Science:

  • Mathematical Biology
  • Chemical Kinetics
  • Developmental Biology

Background:

  • Reaction-diffusion systems drive pattern formation in diverse biological contexts.
  • Layered media present unique challenges for modeling these processes.
  • Existing models often do not fully capture the dynamics of bilayer systems.

Purpose of the Study:

  • To develop a modeling framework for bilayer reaction-diffusion systems.
  • To derive conditions for diffusion-driven instability in such systems.
  • To explore the impact of geometry and coupling on pattern formation.

Main Methods:

  • Developed a novel modeling framework for bilayer reaction-diffusion systems.
  • Derived analytical conditions for diffusion-driven instability.
  • Employed an alternative method to compute dispersion relations due to transverse coupling.
  • Validated findings with full numerical simulations.

Main Results:

  • Identified conditions for instability analogous to Turing instability.
  • Demonstrated that diffusion-only layers can inhibit pattern formation.
  • Revealed complex impacts of coupling, including non-monotonic instabilities.
  • Highlighted instabilities arising from interactions between kinetics and diffusion.

Conclusions:

  • The developed framework provides insights into pattern formation in layered media.
  • Stratified media significantly modulate reaction-diffusion dynamics.
  • Results inform synthetic engineering of patterns and understanding biological development.