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Article
Interaction of Turing Patterns with an External Linear Morphogen Gradient
Nonlinearity (2009)
  • Tilmann Glimm, Western Washington University
  • Jianying Zhang
  • Yun-Qui Shen
Abstract
We investigate a simple generic model of a reaction–diffusion system consisting of an activator and an inhibitor molecule in the presence of a linear morphogen gradient. We assume that this morphogen gradient is established independently of the reaction–diffusion system and acts by increasing the production of the activator proportional to the morphogen concentration. The model is motivated by several existing models in developmental biology in which a Turing patterning mechanism is proposed and various chemical gradients are known to be important for development. Mathematically, this leads to reaction–diffusion equations with explicit spatial dependence. We investigate how the Turing pattern is affected, if it exists. We also show that in the parameter range where a Turing pattern is not possible, the system may nevertheless produce 'Turing-like' patterns.
Keywords
  • Linear morphogen gradient,
  • Turing patterns,
  • Turing-like patterns
Disciplines
Publication Date
September 10, 2009
Publisher Statement
2009 IOP Publishing Ltd and London Mathematical Society
Citation Information
Tilmann Glimm, Jianying Zhang and Yun-Qui Shen. "Interaction of Turing Patterns with an External Linear Morphogen Gradient" Nonlinearity Vol. 22 Iss. 10 (2009)
Available at: http://works.bepress.com/tilmann_glimm/16/