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2004 | 14 | 3 | 351-361
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
14
Numer
3
Strony
351-361
Opis fizyczny
Daty
wydano
2004
otrzymano
2004-03-01
poprawiono
2004-06-01
Twórcy
  • Department of Applied Mathematics, Faculty of Biological Sciences, Complutense University of Madrid, Madrid 28040, Spain
  • Department of Applied Mathematics, Faculty of Biological Sciences Complutense University of Madrid, Madrid 28040, Spain
Bibliografia
  • Ball P. (1999): The Self-Made Tapstry: Pattern Formation in Nature. — Oxford: Oxford University Press.
  • Bard J.B.L. (1977): A unity underlying the different zebra striping patterns.- J. Zool. Vol. 183, pp. 527–539.
  • Bard J.B.L. (1981): A model for generating aspects of zebra and other mammalian coat patterns. — J. Theoret. Biol., Vol. 93, pp. 363–385.
  • Bentley K. (2002): Evolving asynchronous adaptive systems for an exploration of aesthetic pattern formation. — EASy M.Sc. thesis, Computer Science Department, University College of London.
  • Blickle T. and Thiele L. (1995): A mathematical analysis of tournament selection. — Proc. 6-th Int. Conf. Genetic Algorithms, Pittsburgh, USA, pp. 9–16.
  • Corno F., Sonza Reorda M. and Squillero G. (2000): Evolving cellular automata for self-testing hardware. — 3-rd Int. Conf. Evolvable Systems: From Biology to Hardware (ICES2000), Edinburgh, UK, pp. 31–39.
  • Culik II K., Hurd L.P. and Yu S. (1990): Computation theoretic aspects of cellular automata. — Physica D, Vol. 45, pp. 357–378.
  • Davis L. (Ed.). (1991): Handbook of Genetic Algorithms. — New York: Van Nostrand Reinhold.
  • Fersht A. (1985): Enzyme Structure and Mechanism. — San Francisco, CA: W.H. Freeman.
  • Gibson G. (2002): Developmental evolution: Getting robust about robustness. — Current Biol., Vol. 12, pp. R347– R349.
  • Gierer A. and Meinhardt H. (1972): A theory of biological pattern formation. — Kybernetic, Vol. 12, pp. 30–39.
  • Gillespie D.T. (1976): A general method for numerically simulating the stochastic time evolution of coupled chemical reactions.— J. Comp. Phys., Vol. 22, pp. 403–434.
  • Gillespie D.T. (1977): Exact stochastic simulation of coupled chemical reactions. — J. Phys. Chem., Vol. 81, pp. 2340– 2361.
  • Goldberg D.E. (1989): Genetic Algorithms in Search, Optimization, and Machine Learning. — Reading, MA: Addison- Wesley.
  • Hamahashi S. and Kitano H. (1999): Parameter optimization in hierarchical structures. — Proc. 5-th Europ. Conf. Artificial Life (ECAL), Lausanne, Switzerland, pp. 461–471.
  • Inghe O. (1989): Genet and ramet survivorship under different mortality regimes — A cellular automata model. — J. Theor. Biol., Vol. 138, pp. 257–270.
  • Kerszberg M. (1996): Accurate reading of morphogen concentrations by nuclear receptors: A formal model of complex transduction pathways.— J. Theor. Biol., Vol. 183, pp. 95– 104.
  • Kipling R. (1908): Just So Stories. — London: Macmillan.
  • Kitano H. (1994): Evolution of metabolism for morphogenesis, In: Artificial Life IV. Proc. Workshop Artificial Life (R. Brooks and P. Maes, Eds.). — Cambridge, MA: MIT Press, pp. 49–58.
  • Kitano H. (1995): A simple model of neurogenesis and cell differentiation based on evolutionary large-scale chaos. — Artificial Life, Vol. 2, pp. 79–99.
  • Kondo A. and Asai R. (1995): A reaction-diffusion wave on the marine angelfish Pomacanthus. — Nature, Vol. 376, pp. 765–768.
  • Lahoz-Beltra R. (1997): Molecular automata assembly: principles and simulation of bacterial membrane construction. — BioSyst., Vol. 44, pp. 209–229.
  • Lahoz-Beltra R. (1998): Molecular automata modeling in structural biology.— Adv. Struct. Biol., Vol. 5, pp. 85–101.
  • Lahoz-Beltra R. (2001): Evolving hardware as model of enzyme evolution. — BioSyst., Vol. 61, pp. 15–25.
  • Lahoz-Beltra R., Recio Rincón C. and Di Paola V. (2002): Autómatas moleculares evolutivos: algoritmo SDS y sus aplicaciones. — Actas del Primer Congreso Espa˜nol de Algoritmos Evolutivos y Bioinspirados (AEB02), pp. 333–340.
  • Mitchell M., Hraber P.T. and Crutchfield J.T. (1993): Revisiting the edge of chaos: Evolving cellular automata to perform computations. — Complex Syst., Vol. 7, pp. 89–130.
  • Murray J.D. (1981): A pre-patterns formation mechanism for animal coat markings.— J. Theor. Biol., Vol. 88, pp. 161– 199.
  • Murray J.D. (1989): Mathematical Biology. — New York: Springer.
  • Nelson D.R. and Shnerb N.M. (1998): Non-Hermitian localization and population biology. — Physical Review E, Vol. 58, pp. 1383–1403.
  • Omohundro S. (1984): Modelling cellular automata with partial differential equations.— Physica D, Vol. 10, pp. 128–134.
  • Painter K.J., Maini P.K. and Othmer H.G. (1999): Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis. — Proc. Nat. Acad. Sci. USA, Vol. 96, pp. 5549–5554.
  • Pearson J.E. (1993): Complex patterns in a simple system. — Science, Vol. 261, pp. 189–192.
  • Price N.E. and Stevens L. (1996): Fundamentals of Enzymology. — London: Oxford University Press.
  • Prusinkiewicz P. (1993): Modeling and visualization of biological structures. — Proc. Conf. Graphics Interface’93, Toronto, Canada, pp. 128–137.
  • Rohlf T. and Bornholdt S. (2003): Self-organized pattern formation and noise-induced control from particle computation. — Available at: http://www.arxiv.org/abs/cond-mat/0312366
  • Savill N.J. and Hogeweg P. (1997): Modelling morphogenesis: From single cells to crawling slugs. — J. Theor. Biol., Vol. 184, pp. 229–235.
  • Schreckenberg M., Schadschneider A., Nagel K. and Ito N. (1995): Discrete stochastic models for traffic flow. — Physical Rev. E, Vol. 51, pp. 2939.
  • Shoji H. and Iwasa Y. (2003): Pattern selection and the direction of stripes in two-dimensional Turing systems for skin pattern formation of fishes. — Forma, Vol. 18, pp. 3–18.
  • Srinivasan S., Rashka K.E. and Bier E. (2002): Creation of a sog morphogen gradient in Drosophila embryo. — Developmental Cell, Vol. 2, pp. 91–101.
  • The I. and Perrimon N. (2000): Morphogen diffusion: The case of the Wingless protein. — Nature Cell Biol., Vol. 2, pp. 79–82.
  • Toffoli T. (1984): Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. — Physica D, Vol. 10, pp. 117–127.
  • Toffoli T. and Margolus N. (1987): Cellular Automata Machines. — Cambridge, MA: The MIT Press.
  • Turing A. (1952): The chemical basis of morphogenesis.— Philos. Trans. Roy. Soc. London B, Vol. 237, pp. 37–52.
  • Varea A., Aragon J.L. and Barrui R.A. (1999): Turing patterns on a sphere. — Physical Review E, Vol. 60, No. 4, pp. 4588–4592.
  • Weimar J.R. (1997): Cellular automata for reaction-diffusion systems. — Parallel Comput., Vol. 23, pp. 1699–1715.
  • Werfel J., Mitchell M. Crutchfield J.P. (2000): Resource sharing and coevolution in evolving cellular automata. — IEEE Trans. Evolut. Comput., Vol. 4, pp. 388–393.
  • Wolfram S. (1983): Statistical mechanics of cellular automata. — Rev. Mod. Phys., Vol. 55, No. 3, pp. 601–644.
  • Wolfram S. (1984a): Cellular automata as models of complexity. — Nature, Vol. 311, pp. 419–424.
  • Wolfram S. (1984b): Universality and complexity in cellular automata. — Physica D, Vol. 10, pp. 1–35.
  • Xia Y. and Levitt M. (2002): Roles of mutation and recombination in the evolution of protein thermodynamics. — Proc. Nat. Acad. Sci., Vol. 99, pp. 10382–10387.
  • Young D.A. (1984): A local activator-inhibitor model of vertebrate skin patterns. — Math. Biosci., Vol. 72, pp. 51–58.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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