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. 1996 Jan;70(1):246–263. doi: 10.1016/S0006-3495(96)79567-X

Simplification and analysis of models of calcium dynamics based on IP3-sensitive calcium channel kinetics.

Y Tang 1, J L Stephenson 1, H G Othmer 1
PMCID: PMC1224924  PMID: 8770202

Abstract

We study the models for calcium (Ca) dynamics developed in earlier studies, in each of which the key component is the kinetics of intracellular inositol-1,4,5-trisphosphate-sensitive Ca channels. After rapidly equilibrating steps are eliminated, the channel kinetics in these models are represented by a single differential equation that is linear in the state of the channel. In the reduced kinetic model, the graph of the steady-state fraction of conducting channels as a function of log10(Ca) is a bell-shaped curve. Dynamically, a step increase in inositol-1,4,5-trisphosphate induces an incremental increase in the fraction of conducting channels, whereas a step increase in Ca can either potentiate or inhibit channel activation, depending on the Ca level before and after the increase. The relationships among these models are discussed, and experimental tests to distinguish between them are given. Under certain conditions the models for intracellular calcium dynamics are reduced to the singular perturbed form epsilon dx/d tau = f(x, y, p), dy/d tau = g(x, y, p). Phase-plane analysis is applied to a generic form of these simplified models to show how different types of Ca response, such as excitability, oscillations, and a sustained elevation of Ca, can arise. The generic model can also be used to study frequency encoding of hormonal stimuli, to determine the conditions for stable traveling Ca waves, and to understand the effect of channel properties on the wave speed.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  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. 1993 Oct;65(4):1727–1739. doi: 10.1016/S0006-3495(93)81191-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Bezprozvanny I., Ehrlich B. E. Inositol (1,4,5)-trisphosphate (InsP3)-gated Ca channels from cerebellum: conduction properties for divalent cations and regulation by intraluminal calcium. J Gen Physiol. 1994 Nov;104(5):821–856. doi: 10.1085/jgp.104.5.821. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Bezprozvanny I. Theoretical analysis of calcium wave propagation based on inositol (1,4,5)-trisphosphate (InsP3) receptor functional properties. Cell Calcium. 1994 Sep;16(3):151–166. doi: 10.1016/0143-4160(94)90019-1. [DOI] [PubMed] [Google Scholar]
  4. 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. 1991 Jun 27;351(6329):751–754. doi: 10.1038/351751a0. [DOI] [PubMed] [Google Scholar]
  5. Boitano S., Dirksen E. R., Sanderson M. J. Intercellular propagation of calcium waves mediated by inositol trisphosphate. Science. 1992 Oct 9;258(5080):292–295. doi: 10.1126/science.1411526. [DOI] [PubMed] [Google Scholar]
  6. De Young G. W., Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A. 1992 Oct 15;89(20):9895–9899. doi: 10.1073/pnas.89.20.9895. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Fay F. S., Gilbert S. H., Brundage R. A. Calcium signalling during chemotaxis. Ciba Found Symp. 1995;188:121–140. doi: 10.1002/9780470514696.ch8. [DOI] [PubMed] [Google Scholar]
  8. Finch E. A., Turner T. J., Goldin S. M. Calcium as a coagonist of inositol 1,4,5-trisphosphate-induced calcium release. Science. 1991 Apr 19;252(5004):443–446. doi: 10.1126/science.2017683. [DOI] [PubMed] [Google Scholar]
  9. Gmaj P., Murer H. Calcium transport mechanisms in epithelial cell membranes. Miner Electrolyte Metab. 1988;14(1):22–30. [PubMed] [Google Scholar]
  10. 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 U S A. 1990 Feb;87(4):1461–1465. doi: 10.1073/pnas.87.4.1461. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Gorelova N. A., Bures J. Spiral waves of spreading depression in the isolated chicken retina. J Neurobiol. 1983 Sep;14(5):353–363. doi: 10.1002/neu.480140503. [DOI] [PubMed] [Google Scholar]
  12. Györke S., Fill M. Ryanodine receptor adaptation: control mechanism of Ca(2+)-induced Ca2+ release in heart. Science. 1993 May 7;260(5109):807–809. doi: 10.1126/science.8387229. [DOI] [PubMed] [Google Scholar]
  13. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Hirose K., Iino M. Heterogeneity of channel density in inositol-1,4,5-trisphosphate-sensitive Ca2+ stores. Nature. 1994 Dec 22;372(6508):791–794. doi: 10.1038/372791a0. [DOI] [PubMed] [Google Scholar]
  15. Iino M., Endo M. Calcium-dependent immediate feedback control of inositol 1,4,5-triphosphate-induced Ca2+ release. Nature. 1992 Nov 5;360(6399):76–78. doi: 10.1038/360076a0. [DOI] [PubMed] [Google Scholar]
  16. Irvine R. F. 'Quantal' Ca2+ release and the control of Ca2+ entry by inositol phosphates--a possible mechanism. FEBS Lett. 1990 Apr 9;263(1):5–9. doi: 10.1016/0014-5793(90)80692-c. [DOI] [PubMed] [Google Scholar]
  17. Jacob R., Merritt J. E., Hallam T. J., Rink T. J. Repetitive spikes in cytoplasmic calcium evoked by histamine in human endothelial cells. Nature. 1988 Sep 1;335(6185):40–45. doi: 10.1038/335040a0. [DOI] [PubMed] [Google Scholar]
  18. Keizer J., De Young G. Effect of voltage-gated plasma membrane Ca2+ fluxes on IP3-linked Ca2+ oscillations. Cell Calcium. 1993 May;14(5):397–410. doi: 10.1016/0143-4160(93)90044-7. [DOI] [PubMed] [Google Scholar]
  19. Kijima H., Kijima S. 'Steady/equilibrium approximation' in relaxation and fluctuation. II. Mathematical theory of approximations in first-order reaction. Biophys Chem. 1983 Jun;17(4):261–283. doi: 10.1016/0301-4622(83)80012-x. [DOI] [PubMed] [Google Scholar]
  20. Koster H. P., van Os C. H., Bindels R. J. Ca2+ oscillations in the rabbit renal cortical collecting system induced by Na+ free solutions. Kidney Int. 1993 Apr;43(4):828–836. doi: 10.1038/ki.1993.117. [DOI] [PubMed] [Google Scholar]
  21. Lechleiter J. D., Clapham D. E. Molecular mechanisms of intracellular calcium excitability in X. laevis oocytes. Cell. 1992 Apr 17;69(2):283–294. doi: 10.1016/0092-8674(92)90409-6. [DOI] [PubMed] [Google Scholar]
  22. Lechleiter J., Girard S., Peralta E., Clapham D. Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science. 1991 Apr 5;252(5002):123–126. doi: 10.1126/science.2011747. [DOI] [PubMed] [Google Scholar]
  23. Li Y. X., Rinzel J. Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol. 1994 Feb 21;166(4):461–473. doi: 10.1006/jtbi.1994.1041. [DOI] [PubMed] [Google Scholar]
  24. Lo T. M., Thayer S. A. Refilling the inositol 1,4,5-trisphosphate-sensitive Ca2+ store in neuroblastoma x glioma hybrid NG108-15 cells. Am J Physiol. 1993 Mar;264(3 Pt 1):C641–C653. doi: 10.1152/ajpcell.1993.264.3.C641. [DOI] [PubMed] [Google Scholar]
  25. Lupu-Meiri M., Shapira H., Oron Y. Hemispheric asymmetry of rapid chloride responses to inositol trisphosphate and calcium in Xenopus oocytes. FEBS Lett. 1988 Nov 21;240(1-2):83–87. doi: 10.1016/0014-5793(88)80344-2. [DOI] [PubMed] [Google Scholar]
  26. 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. 1990 Feb 25;265(6):3005–3008. [PubMed] [Google Scholar]
  27. Meyer T. Cell signaling by second messenger waves. Cell. 1991 Feb 22;64(4):675–678. doi: 10.1016/0092-8674(91)90496-l. [DOI] [PubMed] [Google Scholar]
  28. Meyer T., Stryer L. Calcium spiking. Annu Rev Biophys Biophys Chem. 1991;20:153–174. doi: 10.1146/annurev.bb.20.060191.001101. [DOI] [PubMed] [Google Scholar]
  29. Meyer T., Stryer L. Molecular model for receptor-stimulated calcium spiking. Proc Natl Acad Sci U S A. 1988 Jul;85(14):5051–5055. doi: 10.1073/pnas.85.14.5051. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Meyer T., Stryer L. Transient calcium release induced by successive increments of inositol 1,4,5-trisphosphate. Proc Natl Acad Sci U S A. 1990 May;87(10):3841–3845. doi: 10.1073/pnas.87.10.3841. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Nathanson M. H., Padfield P. J., O'Sullivan A. J., Burgstahler A. D., Jamieson J. D. Mechanism of Ca2+ wave propagation in pancreatic acinar cells. J Biol Chem. 1992 Sep 5;267(25):18118–18121. [PubMed] [Google Scholar]
  32. Nedergaard M. Direct signaling from astrocytes to neurons in cultures of mammalian brain cells. Science. 1994 Mar 25;263(5154):1768–1771. doi: 10.1126/science.8134839. [DOI] [PubMed] [Google Scholar]
  33. Nuccitelli R. How do sperm activate eggs? Curr Top Dev Biol. 1991;25:1–16. doi: 10.1016/s0070-2153(08)60409-3. [DOI] [PubMed] [Google Scholar]
  34. Oldershaw K. A., Nunn D. L., Taylor C. W. Quantal Ca2+ mobilization stimulated by inositol 1,4,5-trisphosphate in permeabilized hepatocytes. Biochem J. 1991 Sep 15;278(Pt 3):705–708. doi: 10.1042/bj2780705. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. 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 U S A. 1990 Jan;87(1):260–264. doi: 10.1073/pnas.87.1.260. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Rooney T. A., Renard D. C., Sass E. J., Thomas A. P. Oscillatory cytosolic calcium waves independent of stimulated inositol 1,4,5-trisphosphate formation in hepatocytes. J Biol Chem. 1991 Jul 5;266(19):12272–12282. [PubMed] [Google Scholar]
  37. Shuttleworth T. J. Ca2+ release from inositol trisphosphate-sensitive stores is not modulated by intraluminal [Ca2+]. J Biol Chem. 1992 Feb 25;267(6):3573–3576. [PubMed] [Google Scholar]
  38. Sneyd J., Charles A. C., Sanderson M. J. A model for the propagation of intercellular calcium waves. Am J Physiol. 1994 Jan;266(1 Pt 1):C293–C302. doi: 10.1152/ajpcell.1994.266.1.C293. [DOI] [PubMed] [Google Scholar]
  39. Tang Y., Othmer H. G. A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine-sensitive calcium channels. Biophys J. 1994 Dec;67(6):2223–2235. doi: 10.1016/S0006-3495(94)80707-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Tang Y., Othmer H. G. Frequency encoding in excitable systems with applications to calcium oscillations. Proc Natl Acad Sci U S A. 1995 Aug 15;92(17):7869–7873. doi: 10.1073/pnas.92.17.7869. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Taylor A., Windhager E. E. Possible role of cytosolic calcium and Na-Ca exchange in regulation of transepithelial sodium transport. Am J Physiol. 1979 Jun;236(6):F505–F512. doi: 10.1152/ajprenal.1979.236.6.F505. [DOI] [PubMed] [Google Scholar]
  42. Taylor C. W., Potter B. V. The size of inositol 1,4,5-trisphosphate-sensitive Ca2+ stores depends on inositol 1,4,5-trisphosphate concentration. Biochem J. 1990 Feb 15;266(1):189–194. doi: 10.1042/bj2660189. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Thastrup O., Cullen P. J., Drøbak B. K., Hanley M. R., Dawson A. P. Thapsigargin, a tumor promoter, discharges intracellular Ca2+ stores by specific inhibition of the endoplasmic reticulum Ca2(+)-ATPase. Proc Natl Acad Sci U S A. 1990 Apr;87(7):2466–2470. doi: 10.1073/pnas.87.7.2466. [DOI] [PMC free article] [PubMed] [Google Scholar]
  44. Thomas A. P., Renard D. C., Rooney T. A. Spatial and temporal organization of calcium signalling in hepatocytes. Cell Calcium. 1991 Feb-Mar;12(2-3):111–126. doi: 10.1016/0143-4160(91)90013-5. [DOI] [PubMed] [Google Scholar]
  45. Wakui M., Osipchuk Y. V., Petersen O. H. Receptor-activated cytoplasmic Ca2+ spiking mediated by inositol trisphosphate is due to Ca2(+)-induced Ca2+ release. Cell. 1990 Nov 30;63(5):1025–1032. doi: 10.1016/0092-8674(90)90505-9. [DOI] [PubMed] [Google Scholar]
  46. Wakui M., Petersen O. H. Cytoplasmic Ca2+ oscillations evoked by acetylcholine or intracellular infusion of inositol trisphosphate or Ca2+ can be inhibited by internal Ca2+. FEBS Lett. 1990 Apr 24;263(2):206–208. doi: 10.1016/0014-5793(90)81374-w. [DOI] [PubMed] [Google Scholar]
  47. Wakui M., Potter B. V., Petersen O. H. Pulsatile intracellular calcium release does not depend on fluctuations in inositol trisphosphate concentration. Nature. 1989 May 25;339(6222):317–320. doi: 10.1038/339317a0. [DOI] [PubMed] [Google Scholar]
  48. Wang W. H., Geibel J., Giebisch G. Mechanism of apical K+ channel modulation in principal renal tubule cells. Effect of inhibition of basolateral Na(+)-K(+)-ATPase. J Gen Physiol. 1993 May;101(5):673–694. doi: 10.1085/jgp.101.5.673. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Watras J., Bezprozvanny I., Ehrlich B. E. Inositol 1,4,5-trisphosphate-gated channels in cerebellum: presence of multiple conductance states. J Neurosci. 1991 Oct;11(10):3239–3245. doi: 10.1523/JNEUROSCI.11-10-03239.1991. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Wong S. M., Chase H. S., Jr Role of intracellular calcium in cellular volume regulation. Am J Physiol. 1986 Jun;250(6 Pt 1):C841–C852. doi: 10.1152/ajpcell.1986.250.6.C841. [DOI] [PubMed] [Google Scholar]
  51. Woods N. M., Cuthbertson K. S., Cobbold P. H. Repetitive transient rises in cytoplasmic free calcium in hormone-stimulated hepatocytes. Nature. 1986 Feb 13;319(6054):600–602. doi: 10.1038/319600a0. [DOI] [PubMed] [Google Scholar]
  52. Wootton J. F., Corrie J. E., Capiod T., Feeney J., Trentham D. R., Ogden D. C. Kinetics of cytosolic Ca2+ concentration after photolytic release of 1-D-myo-inositol 1,4-bisphosphate 5-phosphorothioate from a caged derivative in guinea pig hepatocytes. Biophys J. 1995 Jun;68(6):2601–2607. doi: 10.1016/S0006-3495(95)80444-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Zhao H., Loessberg P. A., Sachs G., Muallem S. Regulation of intracellular Ca2+ oscillation in AR42J cells. J Biol Chem. 1990 Dec 5;265(34):20856–20862. [PubMed] [Google Scholar]

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