Calcium oscillations and membrane transport: The importance of two time scales

Multiscale Modeling and Simulation

Volumn 3, Issue 2, 2005, Pages 245-264

  Tsaneva Atanasova, K ^a   Shuttleworth, Trevor J ^b   Yule, David I ^b   Thompson, Jill L ^b   Sneyd, J ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b UNIVERSITY OF ROCHESTER MEDICAL CENTER   (United States)

Author keywords

Bifurcation theory; Calcium oscillations; Homoclinic bifurcation; Hopf bifurcation; Mathematical model; Membrane fluxes; Two time scales

Indexed keywords

BIFURCATION (MATHEMATICS); BIOLOGICAL MEMBRANES; CALCIUM; CELLS; COMPUTER SIMULATION; INTEGRATION;

BIFURCATION THEORY; CALCIUM OSCILLATIONS; HOMOCLINIC BIFURCATION; HOPF BIFURCATION; MEMBRANE FLUXES; TWO TIME SCALE;

MATHEMATICAL MODELS;

EID: 21844447572     PISSN: 15403459     EISSN: None     Source Type: Journal    
DOI: 10.1137/030602472     Document Type: Article

References (37)

1. 2+ release, J. Gen. Physiol., 119 (2002), pp. 211-233.
2. A. Atri, J. Amundson, D. Clapham, and J. Sneyd, A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte, Biophys. J., 65 (1993), pp. 1727-1739.
3. M. J. Berridge, Inositol trisphosphate and calcium signalling, Nature (Lond.), 361 (1993), pp. 315-325.
4. M. J. Berridge and G. Dupont, Spatial and temporal signalling by calcium, Curr. Opin. Cell Biol., 6 (1994), pp. 267-274.
5. M. J. Berridge, Capacitative calcium entry, Biochem. J., 312 (1995), pp. 1-11.
6. 2+ signalling, EMBO J., 19 (2000), pp. 4926-4935.
7. P. Camello, J. Gardner, O. H. Petersen, and A. V. Tepikin, Calcium dependence of calcium extrusion and calcium uptake in mouse pancreatic acinar cells, J. Physiol., 490 (1996), pp. 585-593.
8. 2+ entry pathways upon cholinergic stimulation in mouse pancreatic acinar cells, J. Physiol., 516 (1999), pp. 399-408.
9. J.-F. Dufour, I. M. Arias, and T. J. Turner, Inositol 1,4,5- trisphosphate and calcium regulate the calcium channel function of the hepatic inositol 1,4,5- trisphosphate receptor, J. Biol. Chem., 272 (1997), pp. 2675-2681.
10. G. Dupont and A. Goldbeter, Oscillations and waves of cytosolic calcium: Insights from theoretical models, BioEssays, 14 (1992), pp. 485-493.
11. B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, Software Environ. Tools 14, SIAM, Philadelphia, 2002.
12. 2+ load of intracellular stores, J. Biol. Chem., 271 (1996), pp. 14925-14930.
13. S. Girard and D. Clapham, Acceleration of intracellular calcium waves in Xenopus oocytes by calcium influx, Science, 260 (1993), pp. 229-232.
14. M. Hoth and R. Penner, Depletion of intracellular calcium stores activates a calcium current in mast cells, Nature, 355 (1992), pp. 353-356.
15. J. P. Keener and J. Sneyd, Mathematical Physiology, Springer-Verlag, New York, 1998.
16. 2+ signalling, Cell Calcium, 14 (1993), pp. 698-710.
17. A. P. Lebeau, D. I. Yule, G. E. Groblewski, and J. Sneyd, Agonist-dependent phosphorylation of the inositol 1,4,5- trisphosphate receptor: A possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells, J. Gen. Physiol., 113 (1999), pp. 851-871.
18. J. Lechleiter and D. Clapham, Molecular mechanisms of intracellular calcium excitability in X. laevis oocytes, Cell, 69 (1992), pp. 283-294.
19. 2+] oscillations derived from a detailed kinetic model: A Hodgkin-Huxley-like formalism, J. Theoret. Biol., 166 (1994), pp. 461-473.
20. Y.-X. Li, S. S. Stojilković, J. Keizer, and J. Rinzel, Sensing and refilling calcium stores in an excitable cell, Biophys. J., 72 (1997), pp. 1080-1091.
21. 2+ store recycling, J. Membr. Biol., 181 (2001), pp. 185-193.
22. i oscillations in an exocrine cell, FEBS Lett., 352 (1994), pp. 32-36.
23. 2+ entry pathways, J. Biol. Chem., 276 (2001), pp. 35676-35683.
24. J. W. Putney, Jr., L. M. Broad, F. J. Braun, J. P. Lievremont, and G. S. Bird, Mechanisms of capacitative calcium entry, J. Cell Sci., 114 (2001), pp. 2223-2229.
25. J. Rinzel, Bursting oscillations in an excitable membrane model, in Ordinary and Partial Differential Equations, B. D. Sleeman and R. J. Jarvis, eds., Springer-Verlag, Berlin, 1985.
26. J. Rinzel, A formal classification of bursting mechanisms in excitable systems, in Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences, E. Teramoto and M. Yamaguti, eds., Lecture Notes in Biomath. 71, Springer-Verlag, Berlin, 1987.
27. T. A. Rooney, E. J. Sass, and A. P. Thomas, Characterization of cytosolic calcium oscillations induced by phenylephrine and vasopressin in single fura-2-loaded hepatocytes, J. Biol. Chem., 264 (1989), pp. 17131-17141.
28. A. S. Sherman, Y.-X. Li, and J. E. Keizer, Whole-cell models, in Computational Cell Biology, C. P. Fall, E. S. Marland, J. M. Wagner, and J. J. Tyson, eds., Springer-Verlag, New York, 2002, pp. 101-139.
29. 2+ release, Biochem. J., 313 (1996), pp. 815-819.
30. i oscillations? - Challenging the capacitative model, Cell Calcium, 25 (1999), pp. 237-246.
31. J. Sneyd and J. F. Dufour, A dynamic model of the type-2 inositol trisphosphate receptor, Proc. Natl. Acad. Sci. USA, 99 (2002), pp. 2398-2403.
32. J. Sneyd, K. Tsaneva-Atanasova, J. I. Bruce, S. V. Straub, D. R. Giovannucci, and D. I. Yule, A model of calcium waves in pancreatic and parotid acinar cells, Biophys. J., 85 (2003), pp. 1392-1405.
33. J. Sneyd, K. Tsaneva-atanasova, D. I. Yule, J. L. Thompson, and T. J. Shuttleworth, Control of calcium oscillations by membrane fluxes, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 1392-1396.
34. M. Wakui, B. V. L. Potter, and O. H. Petersen, Pulsatile intracellular calcium release does not depend on fluctuations in inositol trisphosphate concentration, Nature, 339 (1989), pp. 317-320.
35. D. I. Yule and D. V. Gallacher, Oscillations of cytosolic calcium in single pancreatic acinar cells stimulated by acetylcholine, FEBS Lett., 239 (1988), pp. 358-362.
36. D. I. Yule, A. M. Lawrie, and D. V. Gallacher, Acetylcholine and cholecystokinin induce different patterns of oscillating calcium signals in pancreatic acinar cells, Cell Calcium, 12 (1991), pp. 145-151.
37. 2+ pump during agonist stimulation of pancreatic acini, J. Biol. Chem., 267 (1992), pp. 15419-15425.