Geodesic
The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
H. G. Othmer1 ; K. Painter2 ; D. Umulis3 ; C. Xue4
1 School of Mathematics and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455 USA
2 Department of Mathematics, Department of Mathematics and Maxwell, Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
3 Agricultural & Biological Engineering, Purdue University, West Lafayette, IN USA 47907 USA
4 Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210 USA
Mathematical modelling of natural phenomena, Tome 4 (2009) no. 4, pp. 3-82.

Voir la notice de l'article provenant de la source EDP Sciences

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding of how these processes produce the observed patterns, and illustrate how theoretical and experimental approaches can interact to lead to a better understanding of development. As John Bonner said long ago
`We have arrived at the stage where models are useful to suggest experiments, and the facts of the experiments in turn lead to new and improved models that suggest new experiments. By this rocking back and forth between the reality of experimental facts and the dream world of hypotheses, we can move slowly toward a satisfactory solution of the major problems of developmental biology.'
DOI : 10.1051/mmnp/20094401

H. G. Othmer 1 ; K. Painter 2 ; D. Umulis 3 ; C. Xue 4

1 School of Mathematics and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455 USA
2 Department of Mathematics, Department of Mathematics and Maxwell, Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
3 Agricultural & Biological Engineering, Purdue University, West Lafayette, IN USA 47907 USA
4 Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210 USA 
@article{MMNP_2009_4_4_a1,
     author = {H. G. Othmer and K. Painter and D. Umulis and C. Xue},
     title = {The {Intersection} of {Theory} and {Application} in {Elucidating} {Pattern} {Formation} in {Developmental} {Biology}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {3--82},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2009},
     doi = {10.1051/mmnp/20094401},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094401/}
}
TY  - JOUR
AU  - H. G. Othmer
AU  - K. Painter
AU  - D. Umulis
AU  - C. Xue
TI  - The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
JO  - Mathematical modelling of natural phenomena
PY  - 2009
SP  - 3
EP  - 82
VL  - 4
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094401/
DO  - 10.1051/mmnp/20094401
LA  - en
ID  - MMNP_2009_4_4_a1
ER  - 
%0 Journal Article
%A H. G. Othmer
%A K. Painter
%A D. Umulis
%A C. Xue
%T The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
%J Mathematical modelling of natural phenomena
%D 2009
%P 3-82
%V 4
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094401/
%R 10.1051/mmnp/20094401
%G en
%F MMNP_2009_4_4_a1
H. G. Othmer; K. Painter; D. Umulis; C. Xue. The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 4, pp. 3-82. doi : 10.1051/mmnp/20094401. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094401/

[1] J. Adler Science 1966 708 716

[2] G. Allen, R. Steene, M. Allen. A guide to angelfishes and butterflyfishes. Odyssey, 1998.

[3] K. Amonlirdviman, N. A. Khare, D. R. Tree, W. S. Chen, J. D. Axelrod, C. J. Tomlin. Mathematical modeling of planar cell polarity to understand domineering nonautonomy. Science, 307 (2005), No. 5708, 423–6.

[4] R. P. Araujo, D. L. S. Mcelwain Bull. Math. Biol. 2004 1039 1091

[5] P. Arcuri, J. Murray J. Math. Biol. 1986 141 165

[6] R. Asai, E. Taguchi, Y. Kume, M. Saito, S. Kondo Mech Dev 1999 87 92

[7] M. Ashkenazi, H. G. Othmer Jour. Math. Biol. 1978 305 350

[8] S. Atkinson, C. Y. Chang, R. E. Sockett, M. Camara, P. Williams J Bacteriol 2006 1451 61

[9] J. Bagnara, M. Hadley. Chromatophores and color change. Prentice-Hall, Eaglewood Cliffs, New Jersey. 1973.

[10] R. E. Baker, E. A. Gaffney, P. K. Maini Nonlinearity 2008 251 290

[11] R. E. Baker, P. K. Maini J Math Biol 2007 597 622

[12] J. Bard J. Zool. 1977 527 539

[13] J. Bard J. Theor. Biol. 1981 363 385

[14] J. Bard, V. French J. Embryol. Exp. Morph. 1984 255 274

[15] R. Barrio, C. Varea, J. Aragn, P. Maini Bull. Math. Biol. 1999 483 505

[16] B. L. Bassler Curr Opin Microbiol 1999 582 587

[17] E. Ben-Jacob, I. Cohen, A. Czirok, T. Vicsek, D. L. Gutnick. Chemomodulation of cellular movement, collective formation of vortices by swarming bacteria, and colonial development. 238 (1997), No. 1, 181–.

[18] E. Ben-Jacob, I. Cohen, H. Levine Advances in Physics 2000 395 554

[19] E. Ben-Jacob, I. Cohen, O. Shochet, I. Aranson, H. Levine. Complex bacterial patterns. 373 (1995), No. 6515, 566–557.

[20] E. Ben-Jacob, O. Schochet, A. Tenenbaum, I. Cohen, A. Czirok. Generic modelling of cooperative growth patterns in bacterial colonies. 368 (1994), No. 6466, 46–49.

[21] D. Ben-Zvi, B. Shilo, A. Fainsod, N. Barkai Nature 2008 1205 1211

[22] H. Berg. Random walks in biology 1983.

[23] H. C. Berg Physics Today 2000 24 29

[24] H. C. Berg. http://webmac.rowland.org/labs/bacteria/movies/others/. (2008).

[25] M. D. Betterton, M. P. Brenner Physical Review E 2001 061904

[26] K. Bisset, C. Douglas J. Med. Microbiol. 1976 229 31

[27] V. Bolos, J. Grego-Bessa, J. L. De La Pompa Endocr Rev 2007 339 63

[28] J. T. Bonner. The development of Dictyostelium , Chapter Comparative Biology of Cellular Slime Molds. Academic Press 1982, 1–33.

[29] R. B. Bourret, K. A. Borkovich, M. I. Simon. Signal transduction pathways involving protein phosphorylation in prokaryotes. 60 (1991), 401–441.

[30] P. Brakefield, V. French Dev. Biol. 1995 98 111

[31] M. P. Brenner, L. S. Levitov, E. O. Budrene. Physical mechanisms for chemotactic pattern formation by bacteria. 74 (1998), No. 4, 1677–1693.

[32] C. Brunetti, J. Selegue, A. Monteiro, V. French, P. Brakefield, S. Carroll Curr. Biol. 2001 1578 1585

[33] E. O. Budrene. Personal communication 2005.

[34] E. O. Budrene, H. C. Berg Nature 1991 630 633

[35] E. O. Budrene, H. C. Berg. Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature, 376 (1995), No. 6535, 49–53.

[36] C. Caicedo-Carvajal, T. Shinbrot Dev. Biol. 2008 397 403

[37] S. Carroll, J. Gates, D. Keys, S. Paddock, G. Panganiban, J. Selegue, J. Williams Science 1994 109 114

[38] J. Casanova, G. Struhl Nature 1993 152 155

[39] V. Castets, E. Dulos, P. D. Kepper. Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. 64 (1990), No. 24, 2953–2956.

[40] C. M. Child. Patterns and problems of development. University of Chicago Press 1941.

[41] S. Childress, J. K. Percus. Nonlinear aspects of chemotaxis. 56 (1981) 217–237.

[42] J. H. Claxton J. Theor. Biol. 1964 302 317

[43] J. H. Claxton. Developmental origin of even spacing between the microchaetes of Drosophila melanogaster. Aust J Biol Sci, 29 (1976) 131–135.

[44] P. Cluzel, M. Surette, S. Leibler Science 2000 1652 1655

[45] E. Conway, D. Hoff, J. Smoller. Large time behavior of solutions of systems of nonlinear reaction-diffusion equations. SIAM J. Appl. Math., (1977).

[46] M. Coppey, A. Berezhkovskii, Y. Kim, A. Boettiger, S. Shvartsman Dev. Biol. 2007 623 630

[47] M. Coppey, A. Boettiger, A. Berezhkovskii, S. Shvartsman Curr. Biol. 2008 915 919

[48] E. Crampin, W. Hackborn, P. Maini Bull. Math. Biol. 2002 747 769

[49] E. J. Crampin, E. A. Gaffney, P. K. Maini Bulletin of Mathematical Biology 1999 1093 1120

[50] O. Crauk, N. Dostatni. Bicoid determines sharp and precise target gene expression in the Drosophila embryo. Curr Biol, 15 (2005), No. 21, 1888–1898, comparative Study.

[51] F. H. Crick Nature 1970 420 422

[52] M. C. Cross, P. C. Hohenberg. Pattern formation out of equilibrium. 65 (1993), No. 3, 851–1112.

[53] R. Daniels, J. Vanderleyden, J. Michiels FEMS Microbiol Rev. 2004 261 89

[54] P. de Kepper, V. Castets, E. Dulos, J. Boissonade. Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction. D 49 (1991) 161–169.

[55] R. Dilão, J. Sainhas Proc. Biol. Sci. 2004 1565 1569

[56] R. Dillon, P. K. Maini, H. G. Othmer Journal of Mathematical Biology 1994 345 393

[57] R. Dillon, H. G. Othmer J. Theor. Biol. 1999 295 330

[58] W. Driever, C. Nüsslein-Volhard Cell 1988 83 93

[59] W. Driever, C. Nusslein-Volhard Cell 1988 95 104

[60] S. Eglen Mathematical Medicine and Biology 2006 79 99

[61] A. Eldar, R. Dorfman, D. Weiss, H. Ashe, B. Z. Shilo, N. Barkai Nature 2002 304 308

[62] R. Erban. From individual to collective behavior in biological systems. Ph.D. thesis, University of Minnesota 2005.

[63] R. Erban, H. Othmer. From signal transduction to spatial pattern formation in E. coli: A paradigm for multiscale modeling in biology. 3 (2005), No. 2, 362–394.

[64] R. Erban, H. G. Othmer SIAM J. Appl. Math. 2004 361 391

[65] R. Erban, H. G. Othmer J Math Biol 2007 847 885

[66] B. Ermentrout Proc. Roy. Soc. Lond. A. 1991 413 417

[67] T. Evans, J. Marcus. A simulation study of the genetic regulatory hierarchy for butterfly eyespot focus determination. Evol. Dev., 8 (2006) 273–283.

[68] A. Filloux, I. Vallet Med Sci (Paris) 2003 77 83

[69] P. R. Fisher, R. Merkl, G. Gerisch J. Cell. Biol. 1989 973 984

[70] R. M. Ford, D. A. Lauffenburger. Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients. 53 (1991), No. 5, 721–749.

[71] R. M. Ford, D. A. Lauffenburger Biotechnol. Bioeng. 1991 661 672

[72] R. M. Ford, B. R. Phillips, J. A. Quinn, D. A. Lauffenburger. Measurement of bacterial random motility and chemotaxis coefficients: I. stopped–flow diffusion chamber assay. Biotechnol. Bioeng., 37 (1991) 647–660.

[73] C. Fowlkes, C. Hendriks, S. Kernen, G. Weber, O. Rbel, M. Huang, S. Chatoor, A. Depace, L. Simirenko, C. Henriquez, A. Beaton, R. Weiszmann, S. Celniker, B. Hamann, D. Knowles, M. Biggin, M. Eisen, J. Malik Cell 2008 364 374

[74] H. Fricke Marine Ecology 1980 133 141

[75] A. Gierer, H. Meinhardt. A theory of biological pattern formation. 12 (1972), No. 1, 30–39.

[76] L. Glass Science 1973 1061 1063

[77] L. A. Goentoro, G. T. Reeves, C. P. Kowal, L. Martinelli, T. Schpbach, S. Y. Shvartsman Dev. Cell 2006 263 272

[78] A. B. Goryachev, D. J. Toh, T. Lee Biosystems 2006 178 87

[79] C. Graván, R. Lahoz-Beltra Int. J. Appl. Math. Comput. Sci. 2004 351 361

[80] E. P. Greenberg Nature 2003 134

[81] T. Gregor, W. Bialek, R. R. De Ruyter Van Proc Natl Acad Sci U S A 2005 18403 7

[82] T. Gregor, D. W. Tank, E. F. Wieschaus, W. Bialek Cell 2007 153 164

[83] T. Gregor, E. F. Wieschaus, A. P. Mcgregor, W. Bialek, D. W. Tank Cell 2007 141 152

[84] D. Grunwald, J. Eisen Nat. Rev. Genet. 2002 717 724

[85] P. Haffter, J. Odenthal, M. C. Mullins, S. Lin, M. J. Farrell, L. Vogelsang Dev. Genes. Evol. 1996 260 276

[86] H. Berg, D. Brown Nature 1972 502 507

[87] D. Headon, K. J. Painter. Stippling the skin: Generation of anatomical periodicity by reaction-diffusion mechanisms. Submitted to MMNP, (2008).

[88] M. Herrero, J. Velázquez J. Math. Biol. 1996 177 194

[89] T. Hillen, H. G. Othmer Siam J. Appl. Math. 2000 751 775

[90] T. Hillen, K. Painter J. Math. Biol. 2008 183 217

[91] M. Hirata, K.-i. Nakamura, T. Kanemaru, Y. Shibata, S. Kondo. Pigment cell organization in the hypodermis of zebrafish. Dev Dyn, 227 (2003) 497–503.

[92] D. Horstmann Jahresbericht der DMV 2003 103 165

[93] D. Horstmann. A constructive approach to traveling waves in chemotaxis. Journal of Nonlinear Science, 14 (2004), 1–25(25).

[94] B. Houchmandzadeh, E. Wieschaus, S. Leibler Nature 2002 798 802

[95] L. Hufnagel, A. A. Teleman, H. Rouault, S. M. Cohen, B. I. Shraiman. On the mechanism of wing size determination in fly development. Proc Natl Acad Sci U S A, 104 (2007), No. 10, 3835–40, epub 2007 Feb 28.

[96] J. Jaeger, J. Reinitz Bioessays 2006 1102 11

[97] J. Jaeger, S. Surkova, M. Blagov, H. Janssens, D. Kosman, K. Kozlov Nature 2004 368 71

[98] W. Jäger, S. Luckhaus. On explosions of solutions to a system of partial differential equations modelling chemotaxis. 329 (1992), No. 2, 819–824.

[99] S. L. Johnson, D. Africa, C. Walker, J. A. Weston Dev Biol 1995 27 33

[100] H. S. Jung, P. H. Francis-West, R. B. Widelitz, T. X. Jiang, S. Ting-Berreth, C. Tickle, L. Wolpert, C. M. Chuong. Local inhibitory action of BMPs and their relationships with activators in feather formation: implications for periodic patterning. Dev Biol, 196 (1998), No. 1, 11–23.

[101] D. Kaiser Nat. Rev. Microbiol. 2003 45 54

[102] D. Kaiser Annual Review of Genetics 2008 109 130

[103] E. F. Keller, G. M. Odell Mathematical Biosciences 1975 309 317

[104] E. F. Keller, L. A. Segel J. Theor. Biol. 1970 399 415

[105] E. F. Keller, L. A. Segel J. Theor. Biol. 1971 225 234

[106] E. F. Keller, L. A. Segel J. Theor. Biol. 1971 235 248

[107] R. N. Kelsh, M. Brand, Y. J. Jiang, C. P. Heisenberg, S. Lin, P. Haffter, J. Odenthal, M. C. Mullins, F. J. Van Eeden Development 1996 369 389

[108] S.V. Keranen, C.C. Fowlkes, C.L. Luengo Hendriks, D. Sudar, D.W. Knowles, J. Malik, M.D. Biggin. Three-dimensional morphology and gene expression in the Drosophila blastoderm at cellular resolution II: dynamics. Genome Biol. 7 (1006), R124

[109] M. Kerszberg, L. Wolpert J. Theor. Biol. 1998 103 114

[110] A. Kicheva, P. Pantazis, T. Bollenbach, Y. Kalaidzidis, T. Bittig, F. Julicher, M. Gonzalez-Gaitan Science 2007 521 525

[111] P. Koch, D. Keys, T. Rocheleau, K. Aronstein, M. Blackburn, S. Carroll Development 1998 2303 2313

[112] R. Kolter, E. P. Greenberg Nature 2006 300 302

[113] S. Kondo, R. Asai Nature 1995 675 768

[114] P. Kulesa, G. Cruywagen, S. Lubkin, P. Maini, J. Sneyd, M. Ferguson, J. Murray J. Theor. Biol. 1996 287 296

[115] A. D. Lander Cell 2007 245 256

[116] A. D. Lander, Q. Nie, F. Y. M. Wan. Do morphogen gradients arise by diffusion? Dev. Cell, 2 (2002), No. 6, 785–96.

[117] I. R. Lapidus, R. Schiller. A model for traveling bands of chemotactic bacteria. Biophys J., 22 (1978), No. 1, 1–13.

[118] D. Lauffenburger, C. R. Kennedy, R. Aris. Traveling bands of chemotactic bacteria in the context of population growth. Bulletin of Mathematical Biology, 46 (1984), No. 1, 19–40.

[119] N. Le Douarin, C. Kalcheim. The neural crest. CUP, Cambridge, 2nd edition 1999.

[120] I. Lengyel, I. R. Epstein. Modelling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system. Science, 251 (1991) 650–652.

[121] S. Liaw, C. Yang, R. Liu, J. Hong Phys Rev E Stat Nonlin Soft Matter Phys 2001 041909

[122] R. Liu, S. Liaw, P. Maini Phys Rev E Stat Nonlin Soft Matter Phys 2006 011914

[123] R. Lux, W. Shi Crit. Rev. Oral. Biol. Med. 2004 207 20

[124] M. Lyons, L. Harrison. Stripe selection: An intrinsic property of some pattern-forming models with nonlinear dynamics. Dev. Dyn., 195 (1992) 201–215.

[125] F. Maderspacher, C. Nüsslein-Volhard Development 2003 3447 3457

[126] A. Madzvamuse, P. Maini, A. Wathen, T. Sekimura Hiroshima Math. J. 2002 325 336

[127] P. K. Maini, K. J. Painter, H. P. C. Nguyen J Chem Soc Faraday Trans 1997 3601 10

[128] N. V. Mantzaris, S. Webb, H. G. Othmer. Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol., 49 (2004), No. 2, 111–87.

[129] J. Marcus, T. Evans BioSystems 2008 250 255

[130] M. McClure. Development and evolution of melanophore patterns in fishes of the genus Danio (Teleostei: Cyprinidae). J. Morphol., 241 (1999) 83–105.

[131] H. Meinhardt. Models of biological pattern formation. Academic Press, New York 1980.

[132] H. Meinhardt. Models for positional signalling with application to the dorsoventral patterning of insects and segregation into different cell types. Development, supplement (1989), 169–180.

[133] H. Meinhardt, P. Prusinkiewicz, D. Fowler. The algorithmic beauty of sea shells. Springer 2003.

[134] B. A. Mello, Y. Tu Proc. Nat. Acad. Sci. (USA) 2003 8223 8228

[135] D. Míguez, A. Muñuzuri Biophys. Chem. 2006 161 167

[136] N. Milos, A. D. Dingle J Exp Zool 1978 205 216

[137] N. Mittal, E. O. Budrene, M. P. Brenner, A. Oudenaarden Proc. Natl. Acad. Sci. (USA) 2003 13259 63

[138] C. M. Mizutani, Q. Nie, F. Y. Wan, Y. T. Zhang, P. Vilmos, R. Sousa-Neves, E. Bier, J. L. Marsh, A. D. Lander Dev. Cell 2005 915 24

[139] A. Monteiro, V. French, G. Smit, P. Brakefield, J. Metz Acta Biotheor. 2001 77 88

[140] J. R. Mooney, B. N. Nagorcka J. Theor. Biol. 1985 299 317

[141] J. Moreira, A. Deutsch. Pigment pattern formation in zebrafish during late larval stages: a model based on local interactions. Dev. Dyn., 232 (2005).

[142] C. Mou, B. Jackson, P. Schneider, P. A. Overbeek, D. J. Headon Proc. Natl. Acad. Sci. U.S.A. 2006 9075 9080

[143] J. D. Murray. A pattern formation mechanism and its application to mammalian coat markings. volume 39 of Lecture Notes in Biomathematics, Springer, Berlin, Heidelberg, New York. 1979, (360–399).

[144] J. D. Murray Phil. Trans. Roy. Soc. Lond. B 1981 473 496

[145] J. D. Murray J. Theor. Biol. 1981 161 199

[146] J. D. Murray. Mathematical biology ii: Spatial models and biomedical applications. Springer, New York, 3rd edition 2003.

[147] J. D. Murray, D. Deeming, M. Ferguson Proc. Roy. Soc. Lond. B 1990 279 293

[148] J. D. Murray, M. Myerscough J. Theor. Biol. 1991 339 360

[149] J. D. Murray. Mathematical biology, volume 19 of Biomathematics 1989.

[150] B. N. Nagorcka, J. R. Mooney. The role of a reaction–diffusion system in the formation of hair fibres. J. Theor. Biol., 98 (1982) 575–607.

[151] B. N. Nagorcka, J. R. Mooney J. Theor. Biol. 1985 243 272

[152] T. Naitoh, A. Morioka, Y. Omura Zool. Sci. 1985 59

[153] J. Nelson. Fishes of the world. John Wiley and Sons, New York, 3rd edition 1993.

[154] F. S. Neuman-Silberberg, T. Schupbach Cell 1993 165 74

[155] H. Nijhout J. Exp. Zool. 1978 119 136

[156] H. Nijhout Proc. Roy. Soc. Lond. B 1990 81 113

[157] H. Nijhout, P. K. Maini, A. Madzvamuse, A. Wathen, T. Sekimura C. R. Biol. 2003 717 727

[158] M. B. O'Connor, D. M. Umulis, H. G. Othmer, S. S. Blair Development 2006 183 93

[159] J. Odenthal, K. Rossnagel, P. Haffter, R. N. Kelsh, E. Vogelsang, M. Brand, F. J. Van Eeden Development 1996 391 398

[160] J. Otaki J. Insect Physiol. 2008 1099 1112

[161] H. G. Othmer. Interactions of reaction and diffusion in open systems. Ph.D. thesis, University of Minnesota, Minneapolis 1969.

[162] H. G. Othmer. Current problems in pattern formation. In Some mathematical questions in biology, volume VIII, Amer. Math. Soc., Providence, R.I. 1977, (57–85).

[163] H. G. Othmer. Synchronized and differentiated modes of cellular dynamics. In H. Haken, editor, Dynamics of Synergetic Systems, Springer-Verlag.

[164] H. G. Othmer, J. A. Aldridge J. Math. Biol. 1978 169 200

[165] H. G. Othmer, S. R. Dunbar, W. Alt. Models of dispersal in biological systems. J. Math. Biol., 26 (1988), No. 3, 263–298.

[166] H. G. Othmer, T. Hillen SIAM JAM 2002 1222 1260

[167] H. G. Othmer, E. F. Pate Proc Natl Acad Sci U S A 1980 4180 4184

[168] H. G. Othmer, P. Schaap Comments on Theoretical Biology 1998 175 282

[169] H. G. Othmer, L. E. Scriven J. Theor. Biol. 1971 507 537

[170] H. G. Othmer, A. Stevens SIAM J. Appl. Math. 1997 1044 1081

[171] Q. Ouyang, H. L. Swinney Nature 1991 610 612

[172] K. Painter. Mathematical models for biological pattern formation, chapter Modelling of pigment patterns in fish. Number 121 in IMA Volumes in Mathematics and its Applications, Springer-Verlag, Berlin 2000, (59–82).

[173] K. J. Painter, P. K. Maini, H. G. Othmer Proc. Nat. Acad. Sci. 1999 5549 5554

[174] K. J. Painter, P. K. Maini, H. G. Othmer J. Math. Biol. 2000 285 314

[175] D. Parichy J. Exp. Zool. B Mol. Dev. Evol. 2007 578 590

[176] D. M. Parichy, D. G. Ransom, B. Paw, L. I. Zon, S. L. Johnson Development 2000 3031 3044

[177] D. M. Parichy, J. M. Turner Development 2003 817 833

[178] D. M. Parichy, J. M. Turner Dev Biol 2003 242 257

[179] D. M. Parichy, J. M. Turner, N. B. Parker Dev Biol 2003 221 241

[180] E. Pate, H. G. Othmer J. Theor. Biol. 1986 301 319

[181] C. S. Patlak Bull. of Math. Biophys. 1953 311 338

[182] J. E. Pearson, W. Horsthemke Journal of Chemical Physics 1989 1588 1599

[183] F. Peri. The role of EGF and TGF-b signaling in specifying the polarity of the Drosophila egg and embryo. Doctoral, University of Cologne 2001.

[184] T. J. Perkins, J. Jaeger, J. Reinitz, L. Glass PLoS Comput Biol 2006 0417 28

[185] A. A. Polezhaev, R. A. Pashkov, A. I. Lobanov, I. B. Petrov Int J Dev Biol 2006 309 14

[186] R. Prum, R. Torres J. Exp. Biol. 2004 2157 2172

[187] R. Prum, S. Williamson Proc. Biol. Sci. 2002 781 792

[188] C. V. Rao, J. R. Kirby, A. P. Arkin. Design and diversity in bacterial chemotaxis: A comparative study in Escherichia coli and Bacillus subtilis. PLoS Biol, 2 (2004), No. 2, E49.

[189] O. Rauprich, M. Matsushita, C. J. Weijer, F. Siegert, S. E. Esipov, J. A. Shapiro J Bacteriol 1996 6525 38

[190] G. Reeves, R. Kalifa, D. Klein, M. Lemmon, S. Shvartsman Dev. Biol. 2005 523 535

[191] G. T. Reeves, C. B. Muratov, T. Schupbach, S. Y. Shvartsman Dev Cell 2006 289 300

[192] T. Roose, S. J. Chapman, P. K. Maini SIAM Review 2007 179 208

[193] G. Ruxton Mammal. Rev. 2002 237 244

[194] M. J. Saxton Biophysical Journal 2007 1178

[195] H. Scher, M. Lax Phys. Rev. B 1973 4491 502

[196] B. Schwanwitsch. On the groundplan of the wing pattern in nymphalids and certain other families of rhopalocara. Proc. Zool. Sci. Lond., 34 (1924) 509–528.

[197] J. E. Segall, S. M. Block, H. C. Berg Proc. Nat. Acad. Sci. USA 1986 8987 8991

[198] L. A. Segel SIAM Journal on Applied Mathematics 1977 653 665

[199] T. Sekimura, A. Madzvamuse, A. Wathen, P. K. Maini Proc. Biol. Sci. 2000 851 859

[200] M. Serpe, D. Umulis, A. Ralston, J. Chen, D. Olson, A. Avanesov, H. Othmer, M. O'Connor, S. Blair. The BMP-binding protein Crossveinless 2 is a short-range, concentration-dependent, biphasic modulator of BMP signaling in Drosophila. Dev. Cell, 14 (2008) 940–953.

[201] J. A. Shapiro Ann Rev Microbiol 1998 81 104

[202] T. S. Shimizu, S. V. Aksenov, D. Bray J. Mol. Biol. 2003 291 309

[203] O. Shimmi, D. Umulis, H. G. Othmer, M. B. O'Connor Cell 2005 873 86

[204] H. Shoji, Y. Iwasa, A. Mochizuki, S. Kondo J. Theor. Biol. 2002 549 561

[205] H. Shoji, A. Mochizuki, Y. Iwasa, M. Hirata, T. Watanabe, S. Hioki, S. Kondo Dev. Dyn. 2003 627 633

[206] S. Y. Shvartsman, C. B. Muratov, D. A. Lauffenburger Development 2002 2577 2589

[207] S. Sick, S. Reinker, J. Timmer, T. Schlake Science 2006 1447 50

[208] D. Silver, L. Hou, W. Pavan Adv. Exp. Med. Biol. 2006 155 169

[209] R. Singh, D. Paul, R. K. Jain J. Math. Biol. 2006 389 97

[210] P. A. Spiro, J. S. Parkinson, H. G. Othmer PNAS. 1997 7263 7268

[211] A. Spirov, K. Fahmy, M. Schneider, E. Frei, M. Noll, S. Baumgartner Development. 2009 605 614

[212] M. Steinberg Curr. Opin. Genet. Dev. 2007 281 286

[213] F. Süffert Z. Morph. Ökol. Tiere 1929 338 359

[214] M. Sugimoto Comp. Biochem. Physiol. 1993 513

[215] M. Sugimoto. Morphological color changes in fish: regulation of pigment cell density and morphology. Microsc. Res. Tech., 58 (2002) 496–503.

[216] K. Tosney Dev. Dyn. 2004 99 108

[217] P. Trainor Semin. Cell Dev. Biol. 2005 683 693

[218] L. Tsimring, H. Levine, I. Aranson, E. Ben-Jacob, I. Cohen, O. Shochet, W. N. Reynolds Phys. Rev. Letts 1995 1859 1862

[219] A. M. Turing Phil. Trans. R. Soc. London 1952 37 72

[220] R. Tyson, S. Lubkin, J. Murray J Math Biol 1999 359 375

[221] R. Tyson, S. R. Lubkin, J. D. Murray Proc. R. Soc. Lond. B 1999 299 304

[222] R. Tyson, L. Stern, R. Leveque J. Math. Biol. 2000 455 75

[223] D. Umulis, M. O'Connor, H. Othmer. Robustness of embryonic spatial patterning in Drosophila melanogaster. Curr. Top. Dev. Biol., 81 (2008) 65–111.

[224] D. M. Umulis, M. Serpe, M. B. O'Connor, H. G. Othmer Proc Natl Acad Sci U S A 2006 11613 8

[225] C. Varea, J. L. Aragon, R. A. Barrio Phys. Rev. E. 1997 1250 1253

[226] B. J. Varnum-Finney, E. Voss, D. R. Soll. Frequency and orientation of pseudopod formation of Dictyostelium discoideum amebae chemotaxing in a spatial gradient: Further evidence for a temporal mechanism. 8 (1987), No. 1, 18–26.

[227] G. Von Dassow, E. Meir, E. M. Munro, G. M. Odell Nature 2000 188 92

[228] G. H. Wadhams, J. P. Armitage Nat. Rev. Mol. Cell Biol. 2004 1024 37

[229] M. Walters, V. Sperandio. Quorum sensing in Escherichia coli and Salmonella. Int J Med Microbiol., 296 (2006), No. 2-3, 125–31.

[230] X. Wang, R. Harris, L. Bayston, H. Ashe Nature 2008 72 77

[231] Y. C. Wang, E. L. Ferguson Nature 2005 229 34

[232] M. P. Weir, C. W. Lo. Gap-junctional communication. compartments in the Drosophila wing imaginal disc. Developmental Biology, 102 (1984) 130–146.

[233] L. Werdelin, L. Olsson. How the leopard got its spots: a phylogenetic view of the evolution of felid coat patterns. Biol. J. Linn. Soc., 62 (1997) 383–400.

[234] N. A. Whitehead, A. M. Barnard, H. Slater, N. J. Simpson, G. P. Salmond. Quorum-sensing in gram-negative bacteria. FEMS Microbiol Rev., 25 (2001), No. 4, 365–404.

[235] L. Wolpert J. Theor. Biol. 1969 1 67

[236] L. Wolpert Curr. Topics in Dev. Biol. 1971 183 224

[237] D. E. Woodward, R. Tyson, M. R. Myerscough, J. D. Murray, E. O. Budrene, H. C. Berg Biophys. J. 1995 2181 2189

[238] C. Xue. Mathematical models of taxis-driven bacterial pattern formation. Ph.D. thesis, University of Minnesota 2008.

[239] C. Xue, H. G. Othmer. Radial and spiral streams formation in bacterium Proteus mirabilis colonies 2009, preprint.

[240] C. Xue, H. G. Othmer. Multiscale models of taxis-driven patterning in bacterial populations. SIAM J. Appl. Math., to appear (2009).

[241] N. Yakoby, C. A. Bristow, I. Gouzman, M. P. Rossi, Y. Gogotsi, T. Schpbach, S. Y. Shvartsman Syst Biol (Stevenage) 2005 276 284

[242] M. Yamaguchi, E. Yoshimoto, S. Kondo Proc. Natl. Acad. Sci. U.S.A. 2007 4790 4793

[243] D. Young Math. Biosci. 1984 51 58

[244] Y. Zhang, A. Lander, Q. Nie J. Theor. Biol. 2007 579 589

Cité par Sources :