Dynamical probing of the mechanisms underlying calcium oscillations

Journal of Nonlinear Science

Volumn 16, Issue 5, 2006, Pages 483-506

  Domijan, M ^a   Murray, R ^a   Sneyd, J ^b  

^a UNIVERSITY OF WAIKATO   (New Zealand)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Fast slow time scale analysis; inositol trisphosphate oscillations; mathematical modeling; physiology

Indexed keywords

EID: 84867977307     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-005-0744-z     Document Type: Article

References (56)

1. Atri, A., Amundson, J., Clapham, D., & Sneyd, J. A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte, Biophys J. 65: 1727-1739, 1993. (Pubitemid 23316993)
2. Berridge, M.J. Inositol trisphosphate and calcium signalling, Nature (Lond.) 361: 315-325, 1993. (Pubitemid 23041621)
3. Berridge, M.J., Cobbold, P.H., & Cuthbertson, K.S. Spatial and temporal aspects of cell signalling, Philos. Trans. Roy. Soc. Lond. B Biol. Sci. 320: 325-343, 1988.
4. Berridge, M.J., & Galione, A. Cytosolic calcium oscillators, FASEB Journal 2: 3074-3082, 1988.
5. Bezprozvanny, I., Watras, J., & Ehrlich, B.E. Bell-shaped calcium-response curves of Ins(1,4,5)P3-and calcium-gated channels from endoplasmic reticulum of cerebellum, Nature 351: 751-754, 1991. (Pubitemid 21896682)
6. Busa, W.B., Ferguson, J.E., Joseph, S.K., Williamson, J.R., & Nuccitelli, R. Activation of frog (Xenopus laevis) eggs by inositol trisphosphate. I. Characterization of Ca2+ release from intracellular stores, J. Cell. Biol. 101: 677-682, 1985. (Pubitemid 15239146)
7. Cuthbertson, K.S., & Cobbold, P.H. Phorbol ester and sperm activate mouse oocytes by inducing sustained oscillations in cell Ca2+, Nature 316: 541-542, 1985. (Pubitemid 16239362)
8. Cuthbertson, K.S.R., in Cell to Cell Signalling: From Experiments to Theoretical Models, ed. Goldbeter, A. (Academic Press, London), 1989.
9. De Young, G.W., & Keizer, J. A single pool IP3-receptor based model for agonist stimulated Ca2+ oscillations. Proc. Natl. Acad. Sci. USA 89: 9895-9899, 1992.
10. Doedel, E.J., Champneys, A.R., Fairgrieve, T.F., Kuznetsov, Y.A., Sandstede, B., Wang, X., Oldeman, B.E., & Paffenroth, R.C. AUTO2000: Continuation and bifurcation software for ordinary differential equations (with HomCont), http://indy.cs.concordia.ca/auto/main.html, 2002.
11. Dupont, G., & Erneux, C. Simulations of the effects of inositol 1,4,5-trisphosphate 3-kinase and 5-phosphatase activities on Ca2+ oscillations, Cell Calcium 22: 321-331, 1997. (Pubitemid 27523585)
12. Dupont, G., Koukoui, O., Clair, C., Erneux, C., Swillens, S., & Combettes, L. Ca2+ oscillations in hepatocytes do not require the modulation of InsP3 3-kinase activity by Ca2+, FEBS Lett. 534: 101-105, 2003. (Pubitemid 36084524)
13. Dupont, G., & Swillens, S. Quantal release, incremental detection, and long-period Ca2+ oscillations in a model based on regulatory Ca2+-binding sites along the permeation pathway, Biophys. J. 71: 1714-1722, 1996. (Pubitemid 26325954)
14. Eberhard, D.A.,&Holz, R.W. Intracellular Ca2+ activates phospholipase C, Trends Neurosci. 11: 517-520, 1988.
15. Endo, M., Tanaka, M., & Ogawa, Y. Calcium-induced release of calcium from the sarcoplasmic reticulum of skinned skeletal muscle fibres, Nature 228: 34-36, 1970.
16. Ermentrout, B. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students (SIAM), 2002.
17. Fabiato, A., & Fabiato, F. Contractions induced by a calcium-triggered release of calcium from the sarcoplasmic reticulum of single skinned cardiac cells, J. Physiology 249: 469-495, 1975.
18. Falcke, M. Reading the patterns in living cells-The physics of Ca2+ signaling, Advances in Physics 53: 255-440, 2004.
19. Finch, E.A., Turner, T.J., & Goldin, S.M. Calcium as a coagonist of inositol 1,4,5-trisphosphate-induced calcium release, Science 252: 443-446, 1991. (Pubitemid 21916983)
20. Glass, L., & Mackey, M.C. From Clocks to Chaos (Princeton University Press, Princeton), 1988.
21. Goldbeter, A., Dupont, G., & Berridge, M.J. Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation, Proc. Natl. Acad. Sci. USA 87: 1461-1465, 1990.
22. Harootunian, A.T., Kao, J.P., & Tsien, R.Y. Agonist-induced calcium oscillations in depolarized fibroblasts and their manipulation by photoreleased Ins(1,4,5)P3, Ca++, and Ca++ buffer, Cold Spring Harb. Symp. Quant. Biol. 53 Pt. 2: 935-943, 1988. (Pubitemid 20005426)
23. Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., & Iino, M. Spatiotemporal dynamics of inositol 1,4,5-trisphosphate that underlies complex Ca2+ mobilization patterns, Science 284: 1527-1530, 1999.
24. Houart, G., Dupont, G., & Goldbeter, A. Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5-trisphosphate signal in a model for intracellular Ca2+ oscillations, Bull. Math. Biol. 61: 507-530, 1999. (Pubitemid 29274618)
25. Iino, M. Biphasic Ca2+ dependence of inositol 1,4,5-trisphosphate-induced Ca2+ release in smooth muscle cells of the Guinea Pig Taenia Caeci, J. Gen. Physiol. 95: 1103-1122, 1990. (Pubitemid 20217305)
26. Iino, M., & Endo, M. Calcium-dependent immediate feedback control of inositol 1,4,5-trisphosphate-induced Ca2+ release, Nature 360: 76-78, 1992.
27. Jacob, R. Calcium oscillations in electrically non-excitable cells, Biochem. Biophys. Acta, 1052: 427-438, 1990. (Pubitemid 20168851)
28. Jacob, R., Merritt, J.E., Hallam, T.J., & Rink, T.J. Repetitive spikes in cytoplasmic calcium evoked by histamine in human endothelial cells, Nature 335: 40-45, 1988.
29. Keener, J.P., & Sneyd, J. Mathematical Physiology (Springer-Verlag, New York), 1998.
30. Keizer J., & De Young, G. Effect of voltage-gated plasma membrane Ca2+ fluxes on IP3-linked Ca2+ oscillations, Cell Calcium 14: 397-410, 1993. (Pubitemid 23162146)
31. Kuba, K., & Takeshita, S. Simulation of intracellular Ca2+ oscillation in a sympathetic neurone, J. Theor. Biol. 93: 1009-1031, 1981. (Pubitemid 12182013)
32. Li, Y.-X., Stojilkovíc, S.S., Keizer, J., & Rinzel, J. Sensing and refilling calcium stores in an excitable cell, Biophys. J. 72: 1080-1091, 1997. (Pubitemid 27113634)
33. Malgaroli, A., Fesce, R., & Meldolesi, J. Spontaneous [Ca2+]i fluctuations in rat chromaffin cells do not require inositol 1,4,5-trisphosphate elevations but are generated by a caffeine-and ryanodine-sensitive intracellular Ca2+ store, J. Biol. Chem. 265: 3005-3008, 1990.
34. Malgaroli, A., & Meldolesi, J. [Ca2+]i oscillations from internal stores sustain exocytic secretion from the chromaffin cells of the rat, FEBS Lett. 283: 169-172, 1991.
35. Meyer, T., & Stryer, L. Molecular model for receptor-stimulated calcium spiking, Proc. Natl. Acad. Sci. USA 85: 5051-5055, 1988.
36. Meyer, T., & Stryer, L. Calcium spiking, Ann. Rev. Biophys. Chem. 20: 153-174, 1991.
37. Nash, M.S.,Young,K.W., Challiss, R.A.,&Nahorski, S.R. Intracellular signalling: Receptorspecific messenger oscillations, Nature 413: 381-382, 2001. (Pubitemid 32928584)
38. Parker, I., & Ivorra, I. Inhibition by Ca2+ of inositol trisphosphate-mediated Ca2+ liberation: A possible mechanism for oscillatory release of Ca2+, Proc. Natl. Acad. Sci. USA 87: 260-264, 1990.
39. Parker, I., & Yao, Y. Regenerative release of calcium from functionally discrete subcellular stores by inositol trisphosphate, Proc. Roy. Soc. Lond. B 246: 269-274, 1991.
40. Parys, J.B., Sernett, S.W., DeLisle, S., Snyder, P.M., Welsh, M.J., & Campbell, K.P. Isolation, characterization, and localization of the inositol 1,4,5-trisphosphate receptor protein in Xenopus laevis oocytes, J. Biol. Chem. 267: 18776-18782, 1992.
41. Rinzel, J., in Ordinary and Partial Differential Equations, eds. Sleeman, B.D., and Jarvis, R.J. (Springer-Verlag, New York), 1985.
42. Rinzel, J., in Mathematical topics in population biology, morphogenesis, and neurosciences. Lecture Notes in Biomathematics, Vol. 71, eds. Teramoto, E., and Yamaguti, M. (Springer-Verlag, Berlin), 1987.
43. Schuster, S., Marhl, M., & Ḧofer, T. Modelling of simple and complex calcium oscillations: From single-cell responses to intercellular signalling, Eur. J. Biochem. 269: 1333-1355, 2002. (Pubitemid 34227075)
44. Smith, G.D., Wagner, J., & Keizer, J. Validity of the rapid buffering approximation near a point source of calcium ions, Biophys. J. 70: 2527-2539, 1996. (Pubitemid 26000953)
45. Sneyd, J., Girard, S.,&Clapham, D. Calcium wave propagation by calcium-induced calcium release: An unusual excitable system, Bull. Math. Biol. 55: 315-344, 1993.
46. Sneyd, J., Tsaneva-Atanasova, K., Reznikov, V., Bai, Y., Sanderson, M.J., & Yule, D.I. A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations, Proc. Natl. Acad. Sci. USA, in press: 2006.
47. Sneyd, J., Tsaneva-Atanasova, K., Yule, D.I., Thompson, J.L., & Shuttleworth, T.J. Control of calcium oscillations by membrane fluxes, Proc. Natl. Acad. Sci. USA 101: 1392-1396, 2004. (Pubitemid 38182699)
48. Somogyi, R., & Stucki, J.W. Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model, J. Biol. Chem. 266: 11068-11077, 1991. (Pubitemid 21906913)
49. Swillens, S.,&Mercan, D. Computer simulation of a cytosolic calcium oscillator, Biochem. J. 271: 835-838, 1990. (Pubitemid 20384626)
50. Takazawa, K., Lemos, M., Delvaux, A., Lejeune, C., Dumont, J.E., & Erneux, C. Rat brain inositol 1,4,5-trisphosphate 3-kinase: Ca2+-sensitivity, purification and antibody production, Biochem. J. 268: 213-217, 1990. (Pubitemid 20166673)
51. Tang, Y., Stephenson, J.L., & Othmer, H.G. Simplification and analysis of models of calcium dynamics based on IP3-sensitive calcium channel kinetics, Biophys. J. 70: 246-263, 1996.
52. Tsaneva-Atanasova, K., Shuttleworth, T.J., Yule, D.I., Thompson, J.L., & Sneyd, J. Calcium oscillations and membrane transport: The importance of two time scales, SIAM J. Multiscale Modeling and Simulation 3: 245-264, 2004. (Pubitemid 40951971)
53. Tsien, R.W., & Tsien, R.Y. Calcium channels, stores, and oscillations, Ann. Rev. Cell Biol. 6: 715-760, 1990.
54. Tsunoda,Y. Oscillatory Ca2+ signaling and its cellular function, New Biologist 3: 3-17, 1991.
55. Wakui, J., Potter, B.V.L., & Petersen, O.H. Pulsatile intracellular calcium release does not depend on fluctuations in inositol trisphosphate concentration, Nature 339: 317-320, 1989.
56. Winfree, A.T. The Geometry of Biological Time (Springer-Verlag, Berlin), 1980.