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Scale-invariance in reaction-diffusion models of spatial pattern formation.

H G Othmer·E Pate
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Abstract

We propose a reaction-diffusion model of spatial pattern formation whose solutions can exhibit scale-invariance over any desired range for suitable choices of parameters in the model. The model does not invoke preset polarity or any other ad hoc distinction between cells and provides a solution to the French flag problem without sources at the boundary. Furthermore, patterns other than the polar pattern that usually arises first in a growing one-dimensional system described by Turing's model can be obtained. Evidence is given that suggests that the model may apply in the slug stage of Dictyostelium discoideum.

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Cell DifferentiationDictyosteliumDiffusionModels, TheoreticalMorphogenesisJournal ArticleResearch Support, U.S. Gov't, P.H.S.

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BibTeXRIS

H G Othmer, E Pate. 1980. Scale-invariance in reaction-diffusion models of spatial pattern formation.. https://doi.org/10.1073/pnas.77.7.4180

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