Spatial pattern formation in chemical and biological systems

Journal of the Chemical Society - Faraday Transactions

Volumn 93, Issue 20, 1997, Pages 3601-3610

  Maini, Philip K ^a   Painter, Kevin J ^a   Chau, Helene Nguyen Phong ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b PSL RESEARCH UNIVERSITY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748737797     PISSN: 09565000     EISSN: None     Source Type: Journal    
DOI: 10.1039/a702602a     Document Type: Article

References (114)

1. A. M. Turing, Philos. Trans. R. Soc. London, Sect. B, 1952, 327, 37.
2. J. Schnakenberg, J. Theor. Biol., 1979, 81, 389.
3. P. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, Springer-Verlag, Berlin, Heidelberg, New York, 1979, vol. 28.
4. J. D. Murray, Mathematical Biology, Springer-Verlag, Berlin, Heidelberg, New York, 1993.
5. H. Meinhardt, Models of Biological Pattern Formation, Academic Press, London, 1982.
6. L. Edelstein-Keshet, Mathematical Models in Biology, Random House, New York, 1988.
7. N. F. Britton, Reaction-Diffusion Equations and Their Applications to Biology, Academic Press, London, 1986.
8. L. A. Segel, Modeling Dynamic Phenomena in Molecular and Cell Biology, Cambridge University Press, 1989.
9. L. A. Segel and J. L. Jackson, J. Theor. Biol., 1972, 37, 545.
10. Y. I. Balkarei, A. V. Grigor'Yants, Y. A. Rzhanov and M. I. Elinson, Opt. Commun., 1988, 66, 16.
11. Self-Organization, Auto-Waves and Structures Far From Equilibrium, ed. V. I. Krinski, Springer, Berlin, 1984.
12. D. Walgraef and N. M. Ghoniem, Phys. Rev. B, 1990, 13, 8867.
13. D. B. White, J. Fluid Mech., 1988, 191, 247.
14. T. Nozakura and S. Ikeuchi, Astrophys. J., 1984, 279, 40.
15. M. Maruyama, Am. Sci., 1963, 51, 164.
16. B. P. Belousov, in Oscillations and Travelling Waves in Chemical Systems, ed. R. J. Field and M. Burger, Wiley, New York, 1985, p. 605.
17. Oscillations and Travelling Waves in Chemical Systems, ed. R. J. Field and M. Burger, Wiley, New York, 1985.
18. B. R. Johnson and S. K. Scott, Chem. Soc. Rev., 1996, 265.
19. R. J. Field, E. Körös and R. M. Noyes, J. Am. Chem. Soc., 1972, 94, 8649.
20. R. J. Field and R. M. Noyes, J. Chem. Phys., 1974, 60, 1877.
21. J. J. Tyson, The Belousov-Zhabotinskii Reaction, Lecture Notes in Biomathematics, Springer-Verlag, Berlin, Heidelberg, New York, 1976, vol. 10.
22. J. J. Tyson, in Oscillations and Travelling Waves in Chemical Systems, ed. R. J. Field and M. Burger, Wiley, New York, 1985, p. 92.
23. S. K. Scott, Chemical Chaos, Oxford University Press, 1991.
24. A. N. Zaikin and A. M. Zhabotinskii, Nature (London), 1970, 225, 535.
25. A. T. Winfree, Science, 1972, 175, 634.
26. A. T. Winfree, Science, 1973, 181, 937.
27. A. T. Winfree, SIAM-AMS Proc., 1974, 8, 13.
28. A. T. Winfree, Theor. Chem., 1978, 4, 1.
29. S. C. Müller, T. Plesser and B. Hess, Science, 1985, 230, 661.
30. B. J. Welsh, J. Gomatam and A. E. Burgess, Nature (London), 1983, 304, 611.
31. A. B. Rovinskii, J. Chem. Phys., 1987, 91, 4606.
32. G. Nicolis and I. Progogine, Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977.
33. J. Pearson and W. Horsthemcke, J. Chem. Phys., 1989, 90, 1588.
34. V. Castets, E. Dulos, J. Boissonade and P. De Kepper, Phys. Rev. Lett., 1990, 64, 2953.
35. P. De Kepper, V. Castets, E. Dulos and J. Boissonade. Physica D, 1991, 49, 161.
36. P. De Kepper, I. R. Epstein, K. Kustin and M. Orbán, J. Phys. Chem., 1982, 86, 170.
37. Q. Ouyang and H. L. Swinney, Nature (London), 1991, 352, 610.
38. Q. Ouyang and H. L. Swinney, Chaos, 1991, 1, 411.
39. D. Walgraef, G. Dewel and P. Borckmans, Adv. Chem. Phys., 1982, 49, 311.
40. Q. Ouyang, Z. Noszticius and H. L. Swinney, J. Phys. Chem., 1992, 96, 6773.
41. G. H. Gunaratne, Q. Ouyang and H. L. Swinney, Phys. Rev. E, 1994, 50, 2802.
42. M. Watzl and A. F. Münster, Chem. Phys. Lett., 1995, 242, 273.
43. M. Burger and R. J. Field, Nature (London), 1984, 307, 720.
44. P. Resch, R. J. Field and F. W. Schneider, J. Phys. Chem., 1989, 93, 2783.
45. Y. X. Zhang and R. J. Field, J. Phys. Chem., 1991, 95, 723.
46. K. Lee, W. D. McCormick, Q. Ouyang and H. L. Swinney, Science, 1993, 261, 192.
47. K. Lee, W. D. McCormick, J. E. Pearson and H. L. Swinney, Nature (London), 1994.
48. W. N. Reynolds, J. E. Pearson and S. Ponce-Dawson, Phys. Rev. Lett., 1994, 72, 2797.
49. P. Gray and S. K. Scott, Chem. Eng. Sci., 1983, 38, 29.
50. P. Gray and S. K. Scott, Chem. Eng. Sci., 1984, 39, 1087.
51. P. Gray and S. K. Scott, J. Phys. Chem., 1985, 89, 22.
52. D. Haim, G. Li, Q. Ouyang, W. D. McCormick, H. L. Swinney, A. Hagberg and E. Meron, Phys. Rev. Lett., 1996, 77, 190.
53. I. Lengyel and I. R. Epstein, Proc. Natl. Acad. Sci. USA, 1992, 89, 3977.
54. I. R. Epstein and I. Lengyel, Physica D, 1995, 84, 1.
55. A. Gierer and H. Meinhardt, Kybernetik, 1972, 12, 30.
56. D. Thomas, in Analysis and Control of Immobilized Enzyme Systems, ed. D. Thomas and J.-P. Kernevez, Springer, Berlin, Heidelberg, New York, 1975, p. 115.
57. V. Dufiet and J. Boissonade, Physica A, 1992, 188, 158.
58. I. Lengyel, G. Rabai and I. R. Epstein, J. Am. Chem. Soc., 1990, 112, 4606.
59. I. Lengyel, G. Rabai and I. R. Epstein, J. Am. Chem. Soc., 1990, 112, 9104.
60. I. Lengyel and I. R. Epstein, Science, 1991, 251, 650.
61. I. Lengyel and I. R. Epstein, Acc. Chem. Res., 1993, 26, 235.
62. O. Jensen, E. Mesekilded, P. Borckmans and G. Dewel, Phys. Scr., 1996, 53, 243.
63. K. Lee, W. D. McCormick, H. L. Swinney and Z. J. Noszticius, J. Chem. Phys., 1992, 95, 4048.
64. K. Agladze, E. Dulos and P. De Kepper, J. Phys. Chem., 1992, 96, 2400.
65. Z. Noszticius, Q. Ouyang, W. D. McCormick and H. L. Swinney, J. Phys. Chem., 1992, 96, 6302.
66. J. J. Perraud, A. De Wit, E. Dulos, P. De Kepper, G. Dewel and P. Borckmans, Phys. Rev. Lett., 1993, 71, 1272.
67. R. Kapral, Physica D, 1995, 86, 149.
68. Q. Ouyang, R. Li, G. Li and H. L. Swinney, J. Chem. Phys., 1995, 102, 2551.
69. J. E. Pearson, Science, 1993, 261, 189.
70. E. E. Selkov, Eur. J. Biochem., 1968, 4, 79.
71. V. Gaspar and K. Showalter, J. Am. Chem. Soc., 1987, 109, 4876.
72. V. Gaspar and K. Showalter, J. Phys. Chem., 1990, 94, 4973.
73. K. Lee and H. L. Swinney, Phys. Rev. E, 1995, 51, 1899.
74. V. Dufiet and J. Boissonade, J. Chem. Phys., 1992, 96, 664.
75. J. Guslander and R. J. Field, J. Phys. Chem., 1992, 96, 10575.
76. H. G. Othmer and L. E. Scriven, Ind. Eng. Chem. Fundam., 1969, 8, 302.
77. L. Wolpert, J. Theor. Biol., 1969, 25, 1.
78. B. N. Nagorcka, J. Theor. Biol., 1989, 137, 127.
79. G. F. Oster, J. D. Murray and A. K. Harris, J. Embryol. Exp. Morphol., 1983, 78, 83.
80. J. D. Murray and G. F. Oster, IMA J. Math. Appl. Med. Biol., 1984, 1, 51.
81. J. D. Murray and G. F. Oster, J. Math. Biol., 1984, 19, 265.
82. G. F. Oster, J. D. Murray and P. K. Maini, J. Embryol. Exp. Morphol., 1985, 89, 93.
83. P. K. Maini, M. R. Myerscough, J. D. Murray, K. H. Winters, Bull. Math. Biol., 1991, 53, 701.
84. J. D. Murray, D. C. Deeming and M. W. J. Ferguson, Proc. R. Soc. London, Ser. B, 1990, 239, 1990.
85. J. D. Murray and M. R. Myerscough, J. Theor. Biol., 1991, 149, 339.
86. C. Thaller and G. Eichele, Nature (London), 1987, 327, 625.
87. P. K. Maini and M. Solursh, Int. Rev. Cytol., 1991, 129, 91.
88. S. A. Kauffman, R. Shymko and K. Trabert, Science, 1978, 199, 259.
89. S. A. Kauffman, Philos. Trans. R. Soc. London B, 1981, 295, 567.
90. T. C. Lacalli, D. A. Wilkinson and L. G. Harrison, Development, 1988, 103, 105.
91. T. C. Lacalli, J. Theor. Biol., 1990, 144, 171.
92. H. Meinhardt, J. Cell Sci., 1977, 23, 117.
93. H. Meinhardt, J. Cell Sci. Suppl., 1986, 4, 357.
94. B. Bunow, J.-P. Kernevez, G. Joly and D. Thomas, J. Theor. Biol., 1980, 84, 629.
95. J. Bard and I. Lauder, J. Theor. Biol., 1974, 45, 501.
96. R. Dillon, P. K. Maini and H. G. Othmer, J. Math. Biol., 1994, 32, 345.
97. L. Wolpert and A. Hornbruch, Development, 1990, 109, 961.
98. P. K. Maini, D. L. Benson and J. A. Sherratt, IMA J. Math. Appl. Med. Biol., 1992, 9, 197.
99. P. K. Maini, J. Biol. Syst., 1995, 3, 987.
100. F. Brümmer, G. Zempel, P. Buhle, J.-C. Stein and D. F. Hulser, Exp. Cell Res., 1991, 196, 158.
101. C. N. D. Coelho and R. A. Kosher, Dev. Biol., 1991, 148, 529.
102. J. D. Murray, J. Theor. Biol., 1981, 88, 161.
103. J. D. Murray, Sci. Am., 1988, 258, 80.
104. S. Kondo and R. Asai, Nature (London), 1995, 376, 765.
105. T. Höfer and P. K. Maini, Nature (London), 1996, 380, 678.
106. K. Painter, P. K. Maini and H. G. Othmer, in preparation.
107. S. Kondo and R. Asai, Nature (London), 1996, 380, 678.
108. B. Westergaard and M. W. J. Ferguson, J. Zool. London, 1986, 210, 575.
109. B. Westergaard and M. W. J. Ferguson, J. Zool. London, 1987, 212, 191.
110. B. Westergaard and M. W. J. Ferguson, Am. J. Anatomy, 1990, 187, 393.
111. P. M. Kulesa, G. C. Cruywagen, S. R. Lubkin, P. K. Maini, J. Sneyd, M. W. J. Ferguson and J. D. Murray, J. Theor. Biol., 1996, 180, 287.
112. B. Ermentrout, Proc. R. Soc. London, Ser. A, 1991, 434, 413.
113. B. N. Nagorcka and J. R. Mooney, IMA J. Math. Appl. Med. Biol., 1992, 9, 249.
114. M. J. Lyons and L. G. Harrison, Dev. Dyn., 1992, 195, 201.