Evolving morphogenetic fields in the zebra skin pattern based on Turing's morphogen hypothesis

Carlos Graván; Rafael Lahoz-Beltra

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 3, page 351-361
  • ISSN: 1641-876X

Abstract

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One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular automaton: a discrete version of the reaction-diffusion equations proposed by Turing in 1952. In the simulation experiments we searched for proper parameter values of two hypothetical proteins playing the role of activator and inhibitor morphogens. Our results show that on molecular and cellular levels recombination is the genetic mechanism that plays the key role in morphogen evolution, obtaining similar results in the presence or absence of mutation. However, spot patterns appear more often than stripe patterns on the simulated skin of zebras. Even when simulation results are consistent with the general picture of pattern modeling and simulation based on the Turing reaction-diffusion, we conclude that the stripe pattern of zebras may be a result of other biological features (i.e., genetic interactions, the Kipling hypothesis) not included in the present model.

How to cite

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Graván, Carlos, and Lahoz-Beltra, Rafael. "Evolving morphogenetic fields in the zebra skin pattern based on Turing's morphogen hypothesis." International Journal of Applied Mathematics and Computer Science 14.3 (2004): 351-361. <http://eudml.org/doc/207702>.

@article{Graván2004,
abstract = {One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular automaton: a discrete version of the reaction-diffusion equations proposed by Turing in 1952. In the simulation experiments we searched for proper parameter values of two hypothetical proteins playing the role of activator and inhibitor morphogens. Our results show that on molecular and cellular levels recombination is the genetic mechanism that plays the key role in morphogen evolution, obtaining similar results in the presence or absence of mutation. However, spot patterns appear more often than stripe patterns on the simulated skin of zebras. Even when simulation results are consistent with the general picture of pattern modeling and simulation based on the Turing reaction-diffusion, we conclude that the stripe pattern of zebras may be a result of other biological features (i.e., genetic interactions, the Kipling hypothesis) not included in the present model.},
author = {Graván, Carlos, Lahoz-Beltra, Rafael},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {modeling biological structures; developmental models; evolving cellular automata; mammalian coat pattern; morphogenetic field; Turing reaction-diffusion},
language = {eng},
number = {3},
pages = {351-361},
title = {Evolving morphogenetic fields in the zebra skin pattern based on Turing's morphogen hypothesis},
url = {http://eudml.org/doc/207702},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Graván, Carlos
AU - Lahoz-Beltra, Rafael
TI - Evolving morphogenetic fields in the zebra skin pattern based on Turing's morphogen hypothesis
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 3
SP - 351
EP - 361
AB - One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm to the Young cellular automaton: a discrete version of the reaction-diffusion equations proposed by Turing in 1952. In the simulation experiments we searched for proper parameter values of two hypothetical proteins playing the role of activator and inhibitor morphogens. Our results show that on molecular and cellular levels recombination is the genetic mechanism that plays the key role in morphogen evolution, obtaining similar results in the presence or absence of mutation. However, spot patterns appear more often than stripe patterns on the simulated skin of zebras. Even when simulation results are consistent with the general picture of pattern modeling and simulation based on the Turing reaction-diffusion, we conclude that the stripe pattern of zebras may be a result of other biological features (i.e., genetic interactions, the Kipling hypothesis) not included in the present model.
LA - eng
KW - modeling biological structures; developmental models; evolving cellular automata; mammalian coat pattern; morphogenetic field; Turing reaction-diffusion
UR - http://eudml.org/doc/207702
ER -

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