Modeling the skin pattern of fishes

Rafael A. Barrio, Ruth E. Baker, Benjamin Vaughan, Jr., Karla Tribuzy, Marcelo R. de Carvalho, Rodney Bassanezi, and Philip K. Maini
Phys. Rev. E 79, 031908 – Published 18 March 2009
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Abstract

Complicated patterns showing various spatial scales have been obtained in the past by coupling Turing systems in such a way that the scales of the independent systems resonate. This produces superimposed patterns with different length scales. Here we propose a model consisting of two identical reaction-diffusion systems coupled together in such a way that one of them produces a simple Turing pattern of spots or stripes, and the other traveling wave fronts that eventually become stationary. The basic idea is to assume that one of the systems becomes fixed after some time and serves as a source of morphogens for the other system. This mechanism produces patterns very similar to the pigmentation patterns observed in different species of stingrays and other fishes. The biological mechanisms that support the realization of this model are discussed.

    • Received 1 September 2008

    DOI:https://doi.org/10.1103/PhysRevE.79.031908

    ©2009 American Physical Society

    Authors & Affiliations

    Rafael A. Barrio1,2, Ruth E. Baker1,*, Benjamin Vaughan, Jr.1, Karla Tribuzy3, Marcelo R. de Carvalho4, Rodney Bassanezi5, and Philip K. Maini1,6

    • 1Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford OX1 3LB, United Kingdom
    • 2Instituto de Fisica, Universidad Nacional Autónoma de México (UNAM), Apartado Postal 20-364 01000 México, D.F., Mexico
    • 3Universidade Federal do Amazonas-UFAM/ICE, Av. Gen. Rodrigo Otavio Jordão Ramos 3000, CEP.: 69077-000 Manaus, AM, Brasil
    • 4Universidade de São Paulo, USP-Departamento de Zoologia, Instituto de Biociências, Rua do Matão, Trav. 14, no. 101, São Paulo, CEP 05508-900, Brasil
    • 5Universidade Estadual de Campinas-UNICAMP/IMECC, Cidade Universitária Zeferino Vaz, Barão Geraldo, CEP.: 13083-970 Campinas, SP, Brasil
    • 6Oxford Centre for Integrative Systems Biology, Department of Biochemistry, South Parks Road, Oxford OX1 3QU, United Kingdom

    • *Corresponding author.

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    Issue

    Vol. 79, Iss. 3 — March 2009

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