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

Othmer, H. G. and Pate, E. (1980) Scale-invariance in reaction-diffusion models of spatial pattern formation. Proceedings of the National Academy of Sciences of the United States of America, 77 (7). pp. 4180-4184. ISSN 0027-8424.

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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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Additional Information:© 1980 by the National Academy of Sciences. Communicated by John Ross, April 2, 1980. This research was partially supported by Grant GM21558 from the National Institutes of Health. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Subject Keywords:development; regulation; morphallaxis
Issue or Number:7
Record Number:CaltechAUTHORS:OTHpnas80
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9162
Deposited By: Tony Diaz
Deposited On:08 Nov 2007
Last Modified:02 Oct 2019 23:57

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