Singular perturbation analysis of cAMP signalling in Dictyostelium discoideum aggregates

Journal of Mathematical Biology

Volumn 52, Issue 5, 2006, Pages 682-718

  Liţcanu, Gabriela ^a   Velázquez, Juan J L ^b  

^a ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Diffusion systems; Reaction; Singular perturbation methods; Travelling waves

Indexed keywords

DICTYOSTELIUM DISCOIDEUM;

EID: 33645998097     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-005-0370-2     Document Type: Article

References (40)

1. Alcantara, F., Monk, M.: Signal propagation during aggregation in the slime mould Dictyostelium discoideum. J. Gen. Microbiol. 85, 321-334 (1974)
2. Ben-Jacob, E., Cohen, I.: Cooperative self-organization of microorganisms. Advances in Physics 49, 395-554 (2000)
3. Bonner, J.T.: The cellular slime molds. Princeton University Press, Princeton, New Jersey (1967)
4. Casten, R.G., Cohen, H., Lagerstrom, P.A.: Perturbation analysis of an approximation to the Hodgkin-Huxley theory. Quart. Appl. Math. 32, 365-402 (1975)
5. Courtemanche, M., Skaggs, W., Winfree, A.T.: Stable three-dimensional action potential circulation in the Fitzhugh-Nagumo model. Physica D 41, 173-182 (1990)
6. Cytrynbaum, E., Keener, J.P.: Stability conditions fo the travelling pulse: Modifying the restitution hypothesis. Chaos 12, 788-799 (2002)
7. Dallon, J.C., Othmer, H.G.: A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum. Phil. Trans. R. Soc. Lond. B 352, 391-417 (1997)
8. Durston, A.J.: Pacemaker activity during aggregation in Dictyostelium discoideum. Developmental Biology 37, 225-235 (1974)
9. Durston, A.J.: Pacemaker mutants of Dictyostelium discoideum. Developmental Biology 38, 308-319 (1974)
10. Dworkin, M., Keller, K.H.: Solubility and diffusion coefficient of adenosine 3′:5′monophosphate. J. Biol. Chem. 252, 864-865 (1977)
11. Falcke, M., Levine, H.: Pattern selection by gene expression in Dictyostelium discoideum. Phys. Rev. Lett. 80, 3875-3878 (1998)
12. Fife, P.: Mathematical Aspects of Reacting and Diffusing Systems. Sringer Verlag, Berlin 1979
13. Gerisch, G., Hülser, D., Malchow, D., Wick, U.: Cell communication by periodic cyclic-AMP pulses. Phil. Trans. R. Soc. Lond. B 272, 181-192 (1975)
14. Goldbeter, A., Segel, L.A.: Unified mechanism for relay and oscillation of cyclic AMP in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 74, 1543-1547 (1977)
15. Grindrod, P.: Patterns and Waves. The theory and applications of reaction-diffusion equations. Clarendon Press, Oxford 1991
16. Hagan, P.S., Cohen, M.S.: Diffusion-induced morphogenesis in the development of Dictyostelium. J. Theor. Biol. 93, 881-908 (1981)
17. Höfer, T., Sherratt, J.A., Maini, P.K.: Cellular pattern formation during Dictyostelium aggregation. Physica D 85, 425-444 (1995)
18. Jones, C.K.R.T.: Stability of the travelling wave solution of the FitzHugh-Nagumo system. Trans. Amer. Math. Soc. 286, 431-469 (1984)
19. Keener, J.P.: Waves in excitable media. SIAM J. Appl. Math. 39, 528-548 (1980)
20. Keener, J.P.: A geometrical theory for spiral waves in excitable media. SIAM J. Appl. Math. 46, 1039-1056 (1986)
21. Keener, J., Sneyd, J.: Mathematical Physiology. Springer-Verlag, New York 1998
22. Lee, K.J.: Wave pattern selection in a excitable system. Phys. Rev. Lett. 79, 2907-2910 (1997)
23. Lee, K.J., Cox, E.C., Goldstein, R.E.: Competing patterns of signalling activity in Dictyostelium discoideum. Phys. Rev. Lett. 76, 1174-1177 (1996)
24. Levine, H., Tsimring, L., Kessler, D.: Computational modeling of mound development in Dyctiostelium. Physica D 106, 375-388 (1997)
25. Martiel, J.L., Goldbeter, A.: A model based on receptor desensitization for cyclic AMP signalling in Dictyostelium cells. Biophys. J. 52, 807-828 (1987)
26. Monk, P.B., Othmer, H.G.: Cyclic AMP oscillations in suspension of Dictyostelium discoideum. Phil. Trans. R. Soc. Lond. 323, 185-224 (1989)
27. Murray, J.D.: Mathematical Biology, 3rd edn. Springer-Verlag, Berlin Heidelberg 2003
28. Müller, S.C., Mair, T., Steinbock, O.: Traveling waves in yeast extract and in cultures of Dictyostelium discoideum. Biophysical Chemistry 72, 37-47 (1998)
29. Nanjundiah, V.: Cyclic AMP oscillations in Dictyostelium discoideum: models and observation. Biophysical Chemistry 72, 1-8 (1998)
30. Othmer, H.G., Schaap, P.: Oscilatory cAMP signalling in the development of Dictyostelium discoideum. Comments on Theoretical Biology 5, 175-282 (1998)
31. Othmer, H.G., Tang, Y.: A G-protein-based model for cAMP dynamics in Dictyostelium discoideum. Math. Biosciences 120, 25-76 (1994)
32. Rinzel, J., Terman, D.: Propagation phenomena in a bistable reaction-diffusion system. SIAM J. Appl. Math. 42, 1111-1137 (1982)
33. Tang, Y., Othmer, H.G.: Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum. Phil. Trans. R. Soc. Lond. B 349, 179-195 (1995)
34. Tomchik, K.J., Devreotes, P.N.: Adenosine 3′,5′-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution-fluorography. Science 212, 443-446 (1981)
35. Tyson, J. J., Alexander, K.A., Manoranjan, V.S., Murray, J.D.: Spiral waves of cyclic AMP in a model of slime mold aggregation. Physica D 34, 193-207 (1989)
36. Tyson, J.J., Keener J.P.: Singular perturbation theory of traveling waves in excitable media (a review). Physica D 32, 327-361, (1988)
37. Tyson, J.J., Murray, J.D.: Cyclic-AMP waves during aggregation of Dictyostelium amoebae. Development 106, 421-426 (1989)
38. Volpert, A.I., Volpert, V.A., Volpert, V.A.: Traveling Wave solutions of Parabolic Systems. Translations of Mathematical Monographs, AMS, Providence, Rhode Island 1994
39. Winfree, A.T.: Spiral waves of chemical activity. Sci. Amer. 175, 634-636 (1972)
40. Winfree, A.T.: Wavefront geometry in excitable media. Physica D 12, 321-332 (1984)