Development and applications of a model for cellular response to multiple chemotactic cues

Journal of Mathematical Biology

Volumn 41, Issue 4, 2000, Pages 285-314

  Painter, K J ^a,c   Maini, P K ^a   Othmer, H G ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b University of Minnesota ^*  (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Cell movement; Chemotaxis; Multiple signals; Pattern formation

Indexed keywords

CELL SURFACE RECEPTOR; CHEMOTACTIC FACTOR;

ANIMAL; ARTICLE; BACTERIAL PHENOMENA AND FUNCTIONS; BIOLOGICAL MODEL; CELL COUNT; CHEMOTAXIS; CYTOLOGY; MATHEMATICS; PHYSIOLOGY; SIGNAL TRANSDUCTION; SKIN; SKIN PIGMENTATION;

ANIMALS; BACTERIAL PHYSIOLOGY; CELL COUNT; CHEMOTACTIC FACTORS; CHEMOTAXIS; MATHEMATICS; MODELS, BIOLOGICAL; RECEPTORS, CELL SURFACE; SIGNAL TRANSDUCTION; SKIN; SKIN PIGMENTATION;

EID: 0034304765     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000035     Document Type: Article

References (40)

1. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D.: Molecular Biology of the Cell. Garland Publishing Inc., New York, London (1994)
2. Bard, J.B.L.: A model for generating aspects of zebra and other mammalian coat patterns. J. Theor. Biol. 93, 363-385 (1981)
3. Ben-Jacob, E., Cohen, I., Czirok, A., Vicsek, T., Gutnick., D.L.: Chemomodulation of cellular movement, collective formation of vortices by swarming bacteria, and colonial development. Physica A 238(1), 181-(1997)
4. Berg, H., Budrene., E.: Complex patterns formed by motile cells in E. coli. Nature 349, 630-633 (1991)
5. Block, S.M., Segall, J.E., Berg., H.C.: Impulse responses in bacterial chemotaxis. Cell 31, 215-226 November (1982)
6. Michael P. Brenner, Leonid S. Levitov, Elena O. Budrene: Physical mechanisms for chemotactic pattern formation by bacteria. Biophysical Journal 74 (4), 1677-1693 (1998)
7. Colamarino, S., Tessier-Lavigne, M.: The axonal chemoattractant netrin-1 is also a chemorepellent for trochlear motor axons. Cell 81, 621-629 (1995)
8. Davis, B.: Reinforced random walks. Prob. Thy. Rel. Fields pages 203-229 (1990)
9. Dillon, R., Maini, P.K., Othmer., H.G.: Pattern formation in generalised turing systems i. steady-state patterns in systems with mixed boundary conditions. J. Math. Biol. 32, 345-393 (1994)
10. Le Douarin, N.M.: Differentiation of Normal and Neoplastic Hematopoietic Cells., chapter Ontogeny of hematopoietic organs studied in avian interspecific chimeras., pages 5-31. Cold Spring Harbor Laboratory, New York (1978)
11. Dunford, N., Schwartz, J.T.: Linear Operators: Part I. Interscience Publishers, New York (1958)
12. Fan, J., Raper, J.A.: Localised collapsin cues can steer growth cones without inducing their further collapse. Neuron 14, 263-274 (1995)
13. Fife, P.C.: Mathematical Aspects of Reacting and Diffusing Systems, volume 28 of Lect. Notes in Biomath. Springer, Berlin, Heidelburg, New York (1979)
14. Fisher, P.R., Merkl, R., Gerisch, G.: Quantitative analysis of cell motility and chemotaxis in Dictyostelium discoideum by using an image processing system and a novel chemotaxis chamber providing stationary chemical gradients. J. Cell. Biol. 108, 973-984 (1989)
15. Foxman, E.F., Kunkel, E.J., Butcher., E.C.: Integrating conflicting chemotactic signals: The role of memory in leukocyte navigation. J. Cell Biology 147(3), 577-587 (1999)
16. Grindrod., P.: The Theory and Application of Reaction-Diffusion Equations. OUP, Oxford., 2nd edition edition (1996)
17. Horikawa, T., Norris, D.A., Yohn, J.J., Zekman, T., Travers, J.B., Morelli, J.G.: Melanocyte mitogens induce both melanocyte chemokinesis and chemotaxis. J. Invest. Derm. 104, 256-259 (1995)
18. Jotereau, F.V., Houssaint, E., Le Douarin, N.M.: Lymphoid stem cell homing to the early thymic primordium of the avian embryo. Eur. J. Immunol. 10, 620-627 (1980)
19. Koch, A.L., Carr, A., Ehrenfeld, D.W.: The problem of open-sea navigation: The migration of the green turtle to ascension island. J. Theor. Biol. 22, 163-179 (1969)
20. Lauffenburger, D.A., Linderman, J.J.: Receptors: Models for binding, trafficking and signaling. OUP (1993)
21. Le Douarin, N.M.: The Neural Crest. CUP, Cambridge. (1982)
22. Messersmith, E.K., Leonardo, E.D., Schatz, C., Tessier-Lavigne, M., Goodman, C.S., Kolodkin, A.L.: Semaphorin iii can function as a selective chemorepellent to pattern sensory projections in the spinal cord. Neuron 14, 949-959 (1995)
23. Murray, J.D.: volume 39 of Lecture Notes in Biomathematics, chapter A pattern formation mechanism and its application to mammalian coat markings, pages 360-399. Springer (1979)
24. Murray, J.D.: A pre-pattern formation mechanism for animal coat markings. J. Theor. Biol. 88, (1981)
25. Murray, J.D.: Mathematical Biology. Springer-Verlag, Berlin Heidelberg New York (1993)
26. Nagorcka, B.N., Manoranjan, V.S., Murray, J.D.: Complex spatial patterns from tissue interactions - an illustrative model. J. Theor. Biol., 128, 359-374 (1987)
27. Othmer, H. G., Aldridge, J.: The effects of cell density and metabolite flux on cellular dynamics. Journal of Mathematical Biology 5, 169-200 (1978)
28. Hans G. Othmer, Pauline Schaap: Oscillatory cAMP signaling in the development of Dictyostelium discoideum. Comments on Theor. Biol., 5, 175-282 (1998)
29. Hans G. Othmer, Angela Stevens: Aggregation, blowup and collapse: The ABC's of generalized taxis in reinforced random walks. SIAM J. Appled. Math. 57 (4), 1044-1081 (1997)
30. Painter, K.J., Maini, P.K., Othmer, H.G.: Stripe formation in juvenile pomacanthus explained by a generalized Turing mechanism with chemotaxis. Proc. Nat. Acad. Sci. (1999) To appear.
31. Parkinson, J.S.: Signal transduction schemes of bacteria. Cell 73, 857-871 (1993)
32. Purcell, E.M.: Life at low Reynolds number. American Journal of Physics 45, 3-11 (1977)
33. Serafini, T., Kennedy, T.E., Galko, M.J., Mirzayan, C., Jessel, T.M., Tessier-Lavigne, M.: The netrins define a family of axon outgrowth promoting proteins homologous to c. elegans unc-6. Cell 78, 409-424 (1994)
34. Shaw, L.J., Murray, J.D.: Analysis of a model for complex skin patterns. SIAM J. Appl. Math. 50, 628-648 (1990)
35. Song, H., Ming, G., Poo, M.: Camp-induced switching in turning direction of nerve growth cones. Nature 388, 275-279 (1997)
36. Peter A. Spiro, John S. Parkinson, Hans G. Othmer: A model of excitation and adaptation in bacterial chemotaxis. Proceedings of the National Academy of Sciences of the United States of America 94 (14), 7263-7268 (1997)
37. Stewart, R.C., Dahlquist, F.W.: Molecular components of bacterial chemotaxis. Chem. Rev. 87, 997-1025 (1987)
38. Lev Tsimring, Herbert Levine, Igor Aranson, Eshel Ben-Jacob, Inon Cohen, Ofer Shochet, Reynolds, William N.: Aggregation patterns in stressed bacteria. Physical Review Letters 75 (9), 1859-1862 (1995)
39. Turing, A.M.: The chemical basis for morphogenesis. Phil. Trans. Roy. Soc. Lond. B. 237, 37-72 (1952)
40. Young, D.A.: A local activator-inhibitor model of vertebrate skin patterns. Math. Biosci 72, 51-58 (1984)