Modeling the skin pattern of fishes

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 3, 2009, Pages

  Barrio, Rafael A ^a,b   Baker, Ruth E ^a   Vaughan, Benjamin ^a   Tribuzy, Karla ^c   De Carvalho, Marcelo R ^d   Bassanezi, Rodney ^e   Maini, Philip K ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^c FEDERAL UNIVERSITY OF AMAZONAS   (Brazil)

^d UNIVERSITY OF SÃO PAULO   (Brazil)

^e UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC IDEAS; BIOLOGICAL MECHANISMS; DIFFERENT LENGTH SCALE; INDEPENDENT SYSTEMS; MORPHOGENS; PIGMENTATION PATTERNS; REACTION-DIFFUSION SYSTEMS; SPATIAL SCALE; TRAVELING WAVE FRONTS; TURING PATTERNS; TURING SYSTEMS;

EID: 64349087272     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.031908     Document Type: Article

References (37)

1. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952). 10.1098/rstb.1952.0012
2. S. Sick, S. Reinker, J. Timmer, and T. Schlake, Science 314, 1447 (2006). 10.1126/science.1130088
3. S. Kondo and R. Asai, Nature (London) 376, 765 (1995). 10.1038/376765a0
4. J. L. Aragón, C. Varea, R. A. Barrio, and P. K. Maini, Forma 13, 213 (1998).
5. K. J. Painter, P. K. Maini, and H. G. Othmer, Proc. Natl. Acad. Sci. U.S.A. 96, 5549 (1999). 10.1073/pnas.96.10.5549
6. T. Nakamura, N. Mine, E. Nakaguchi, A. Mochizuki, M. Yamamoto, K. Yashiro, C. Meno, and H. Hamada, Dev. Cell 11, 495 (2006). 10.1016/j.devcel. 2006.08.002
7. A. J. Koch and H. Meinhardt, Rev. Mod. Phys. 66, 1481 (1994). 10.1103/RevModPhys.66.1481
8. H. Meinhardt, P. Prusinkiewicz, and D. R. Fowler, The Algorithmic Beauty of Sea Shells (Springer-Verlag, Berlin, 2003).
9. H. Meinhardt, Dev. Biol. 157, 321 (1993). 10.1006/dbio.1993.1138
10. R. A. Barrio, C. Varea, J. L. Aragón, and P. K. Maini, Bull. Math. Biol. 61, 483 (1999). 10.1006/bulm.1998.0093
11. L. Yang, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. Lett. 88, 208303 (2002). 10.1103/PhysRevLett.88.208303
12. L. Yang and I. R. Epstein, Phys. Rev. Lett. 90, 178303 (2003). 10.1103/PhysRevLett.90.178303
13. L. Yang and I. R. Epstein, Phys. Rev. E 69, 026211 (2004). 10.1103/PhysRevE.69.026211
14. I. Berenstein, M. Dolnik, L. Yang, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. E 70, 046219 (2004). 10.1103/PhysRevE.70.046219
15. K. Kyttä, K. Kaski, and R. A. Barrio, Physica A 385, 105 (2007). 10.1016/j.physa.2007.06.034
16. L. Wolpert, R. Beddington, T. Jessell, P. Lawrence, E. Meyerowitz, and J. Smith, Principles of Development, 3rd edition (Oxford University Press, New York, 2006).
17. C-M. Chuong, Molecular Basis of Epithelial Appendage Morphogenesis (Landes Bioscience, Austin, Tx, 1998).
18. R. B. Widelitz, T.-J. Jiang, A. Noveen, C.-W. J. Chen, and C.-M. Chuong, J. Invest. Dermatol. 107, 797 (1996). 10.1111/1523-1747.ep12330553
19. J. D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 2003).
20. J. D. Murray, P. K. Maini, and R. T. Tranquillo, Phys. Rep. 171, 59 (1988). 10.1016/0370-1573(88)90003-8
21. J. D. Murray, G. F. Oster, and A. K. Harris, J. Math. Biol. 17, 125 (1983). 10.1007/BF00276117
22. G. F. Oster, J. D. Murray, and A. K. Harris, J. Embryol. Exp. Morphol. 78, 83 (1983).
23. M. R. de Carvalho, N. R. Lovejoy, and R. S. Rosa, Checklist of the Freshwater Fishes of South and Central America, Family Potamotrygonidae (River Stingrays), Porto Alegre, 2003, pp. 22-28.
24. T. Leppänen, Ph.D. thesis, Helsinki University of Technology, Helsinki, 2004.
25. C. Varea, D. Hernández, and R. A. Barrio, J. Math. Biol. 54, 797 (2007). 10.1007/s00285-007-0071-0
26. D. Gomila, P. Colet, G.-L. Oppo, and M. S. Miguel, Phys. Rev. Lett. 87, 194101 (2001). 10.1103/PhysRevLett.87.194101
27. D. Gomila, Ph.D. thesis, Universitat de les Illes Balears, 2003.
28. R. A. Barrio, Turning Systems: A General Model for Complex Patterns In Nature In Physics of Emergence and Organization, edited by, I. Licata, and, A. J. Sakaji, (World Scientific, Singapore, 2007), 267 - 296.
29. B. Ermentrout, Proc. R. Soc. London, Ser. A 434, 413 (1991). 10.1098/rspa.1991.0100
30. J. L. Aragón, M. Torres, D. Gil, R. A. Barrio, and P. K. Maini, Phys. Rev. E 65, 051913 (2002). 10.1103/PhysRevE.65.051913
31. K. M. Page, P. K. Maini, and A. M. Monk, Physica D 202, 95 (2005). 10.1016/j.physd.2005.01.022
32. B. N. Nagorcka and J. R. Mooney, J. Theor. Biol. 98, 575 (1982). 10.1016/0022-5193(82)90139-4
33. G. C. Cruywagen, P. K. Maini, and J. D. Murray, IMA J. Math. Appl. Med. Biol. 9, 227 (1992). 10.1093/imammb/9.4.227
34. G. C. Cruywagen, P. K. Maini, and J. D. Murray, SIAM J. Appl. Math. 61, 213 (2000). 10.1137/S003613999732857X
35. Traité de Zoologique. Tome XIII. Agnathes et Poissons, Anatomie, Ithologie, Systématique, Premier Fascicule, edited by, P. P. Grassé, (Masson & Cie, Paris, 1958), Chap., pp. 433-458.
36. J. J. Nordlund, R. E. Boissy, V. J. Hearing, R. A. King, and J.-P. Ortonne, The Pigmentary System: Physiology and Pathophysiology (Oxford University Press, Oxford, 1998), Chap., pp. 9-40.
37. See EPAPS Document No. E-PLEEE8-79-044903 for supplementory movies. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.