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. 2001 Jan;80(1):103–120. doi: 10.1016/S0006-3495(01)75998-X

Evolution of cardiac calcium waves from stochastic calcium sparks.

L T Izu 1, W G Wier 1, C W Balke 1
PMCID: PMC1301217  PMID: 11159386

Abstract

We present a model that provides a unified framework for studying Ca2+ sparks and Ca2+ waves in cardiac cells. The model is novel in combining 1) use of large currents (approximately 20 pA) through the Ca2+ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca2+ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudinal (separation distance of 2 microm) and transverse (separated by 0.4-0.8 microm) directions of the cell; and 4) anisotropic diffusion of Ca2+ and fluorescent indicator to study the evolution of Ca2+ waves from Ca2+ sparks. The model mimics the important features of Ca2+ sparks and Ca2+ waves in terms of the spontaneous spark rate, the Ca2+ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca2+ sensitivity (approximately 15 microM). Stochastic control of CRU firing is important because it imposes constraints on the Ca2+ sensitivity of the CRU. Even with moderate (approximately 5 microM) Ca2+ sensitivity the very high spontaneous spark rate triggers numerous Ca2+ waves. In contrast, a single Ca2+ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca2+ sensitivity is sufficiently high. The combination of low CRU Ca2+ sensitivity (approximately 15 microM), high cytosolic Ca2+ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca2+ release. This allows Ca2+ waves to form and propagate given a sufficiently large initiation region, but prevents a single spark or a small group of sparks from triggering a wave.

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Selected References

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  1. Backx P. H., de Tombe P. P., Van Deen J. H., Mulder B. J., ter Keurs H. E. A model of propagating calcium-induced calcium release mediated by calcium diffusion. J Gen Physiol. 1989 May;93(5):963–977. doi: 10.1085/jgp.93.5.963. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Balke C. W., Egan T. M., Wier W. G. Processes that remove calcium from the cytoplasm during excitation-contraction coupling in intact rat heart cells. J Physiol. 1994 Feb 1;474(3):447–462. doi: 10.1113/jphysiol.1994.sp020036. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Blatter L. A., Hüser J., Ríos E. Sarcoplasmic reticulum Ca2+ release flux underlying Ca2+ sparks in cardiac muscle. Proc Natl Acad Sci U S A. 1997 Apr 15;94(8):4176–4181. doi: 10.1073/pnas.94.8.4176. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Bugrim A. E., Zhabotinsky A. M., Epstein I. R. Calcium waves in a model with a random spatially discrete distribution of Ca2+ release sites. Biophys J. 1997 Dec;73(6):2897–2906. doi: 10.1016/S0006-3495(97)78318-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Carl S. L., Felix K., Caswell A. H., Brandt N. R., Ball W. J., Jr, Vaghy P. L., Meissner G., Ferguson D. G. Immunolocalization of sarcolemmal dihydropyridine receptor and sarcoplasmic reticular triadin and ryanodine receptor in rabbit ventricle and atrium. J Cell Biol. 1995 May;129(3):673–682. doi: 10.1083/jcb.129.3.673. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Cheng H., Lederer M. R., Lederer W. J., Cannell M. B. Calcium sparks and [Ca2+]i waves in cardiac myocytes. Am J Physiol. 1996 Jan;270(1 Pt 1):C148–C159. doi: 10.1152/ajpcell.1996.270.1.C148. [DOI] [PubMed] [Google Scholar]
  7. Cheng H., Lederer W. J., Cannell M. B. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. Science. 1993 Oct 29;262(5134):740–744. doi: 10.1126/science.8235594. [DOI] [PubMed] [Google Scholar]
  8. Cornell-Bell A. H., Finkbeiner S. M. Ca2+ waves in astrocytes. Cell Calcium. 1991 Feb-Mar;12(2-3):185–204. doi: 10.1016/0143-4160(91)90020-f. [DOI] [PubMed] [Google Scholar]
  9. Endo M., Tanaka M., Ogawa Y. Calcium induced release of calcium from the sarcoplasmic reticulum of skinned skeletal muscle fibres. Nature. 1970 Oct 3;228(5266):34–36. doi: 10.1038/228034a0. [DOI] [PubMed] [Google Scholar]
  10. Engel J., Fechner M., Sowerby A. J., Finch S. A., Stier A. Anisotropic propagation of Ca2+ waves in isolated cardiomyocytes. Biophys J. 1994 Jun;66(6):1756–1762. doi: 10.1016/S0006-3495(94)80997-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Fabiato A., Fabiato F. Excitation-contraction coupling of isolated cardiac fibers with disrupted or closed sarcolemmas. Calcium-dependent cyclic and tonic contractions. Circ Res. 1972 Sep;31(3):293–307. doi: 10.1161/01.res.31.3.293. [DOI] [PubMed] [Google Scholar]
  12. Ford L. E., Podolsky R. J. Regenerative calcium release within muscle cells. Science. 1970 Jan 2;167(3914):58–59. doi: 10.1126/science.167.3914.58. [DOI] [PubMed] [Google Scholar]
  13. Girard S., Lückhoff A., Lechleiter J., Sneyd J., Clapham D. Two-dimensional model of calcium waves reproduces the patterns observed in Xenopus oocytes. Biophys J. 1992 Feb;61(2):509–517. doi: 10.1016/S0006-3495(92)81855-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Györke I., Györke S. Regulation of the cardiac ryanodine receptor channel by luminal Ca2+ involves luminal Ca2+ sensing sites. Biophys J. 1998 Dec;75(6):2801–2810. doi: 10.1016/S0006-3495(98)77723-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Györke S., Lukyanenko V., Györke I. Dual effects of tetracaine on spontaneous calcium release in rat ventricular myocytes. J Physiol. 1997 Apr 15;500(Pt 2):297–309. doi: 10.1113/jphysiol.1997.sp022021. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Harkins A. B., Kurebayashi N., Baylor S. M. Resting myoplasmic free calcium in frog skeletal muscle fibers estimated with fluo-3. Biophys J. 1993 Aug;65(2):865–881. doi: 10.1016/S0006-3495(93)81112-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Hüser J., Lipsius S. L., Blatter L. A. Calcium gradients during excitation-contraction coupling in cat atrial myocytes. J Physiol. 1996 Aug 1;494(Pt 3):641–651. doi: 10.1113/jphysiol.1996.sp021521. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Ishida H., Genka C., Hirota Y., Nakazawa H., Barry W. H. Formation of planar and spiral Ca2+ waves in isolated cardiac myocytes. Biophys J. 1999 Oct;77(4):2114–2122. doi: 10.1016/S0006-3495(99)77052-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Izu L. T., Mauban J. R., Balke C. W., Wier W. G. Large currents generate cardiac Ca2+ sparks. Biophys J. 2001 Jan;80(1):88–102. doi: 10.1016/S0006-3495(01)75997-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Jiang Y. H., Klein M. G., Schneider M. F. Numerical simulation of Ca2+ "sparks" in skeletal muscle. Biophys J. 1999 Nov;77(5):2333–2357. doi: 10.1016/s0006-3495(99)77072-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Kargacin G., Fay F. S. Ca2+ movement in smooth muscle cells studied with one- and two-dimensional diffusion models. Biophys J. 1991 Nov;60(5):1088–1100. doi: 10.1016/S0006-3495(91)82145-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Keizer J., Smith G. D., Ponce-Dawson S., Pearson J. E. Saltatory propagation of Ca2+ waves by Ca2+ sparks. Biophys J. 1998 Aug;75(2):595–600. doi: 10.1016/S0006-3495(98)77550-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Keizer J., Smith G. D. Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes. Biophys Chem. 1998 May 5;72(1-2):87–100. doi: 10.1016/s0301-4622(98)00125-2. [DOI] [PubMed] [Google Scholar]
  24. Lakatta E. G., Guarnieri T. Spontaneous myocardial calcium oscillations: are they linked to ventricular fibrillation? J Cardiovasc Electrophysiol. 1993 Aug;4(4):473–489. doi: 10.1111/j.1540-8167.1993.tb01285.x. [DOI] [PubMed] [Google Scholar]
  25. Lukyanenko V., Gyorke S. Ca2+ sparks and Ca2+ waves in saponin-permeabilized rat ventricular myocytes. J Physiol. 1999 Dec 15;521(Pt 3):575–585. doi: 10.1111/j.1469-7793.1999.00575.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Lukyanenko V., Subramanian S., Gyorke I., Wiesner T. F., Gyorke S. The role of luminal Ca2+ in the generation of Ca2+ waves in rat ventricular myocytes. J Physiol. 1999 Jul 1;518(Pt 1):173–186. doi: 10.1111/j.1469-7793.1999.0173r.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Lukyanenko V., Wiesner T. F., Gyorke S. Termination of Ca2+ release during Ca2+ sparks in rat ventricular myocytes. J Physiol. 1998 Mar 15;507(Pt 3):667–677. doi: 10.1111/j.1469-7793.1998.667bs.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Miura M., Boyden P. A., ter Keurs H. E. Ca2+ waves during triggered propagated contractions in intact trabeculae. Determinants of the velocity of propagation. Circ Res. 1999 Jun 25;84(12):1459–1468. doi: 10.1161/01.res.84.12.1459. [DOI] [PubMed] [Google Scholar]
  29. Parker I., Zang W. J., Wier W. G. Ca2+ sparks involving multiple Ca2+ release sites along Z-lines in rat heart cells. J Physiol. 1996 Nov 15;497(Pt 1):31–38. doi: 10.1113/jphysiol.1996.sp021747. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Ridgway E. B., Gilkey J. C., Jaffe L. F. Free calcium increases explosively in activating medaka eggs. Proc Natl Acad Sci U S A. 1977 Feb;74(2):623–627. doi: 10.1073/pnas.74.2.623. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Rousseau E., Meissner G. Single cardiac sarcoplasmic reticulum Ca2+-release channel: activation by caffeine. Am J Physiol. 1989 Feb;256(2 Pt 2):H328–H333. doi: 10.1152/ajpheart.1989.256.2.H328. [DOI] [PubMed] [Google Scholar]
  32. Ríos E., Stern M. D., González A., Pizarro G., Shirokova N. Calcium release flux underlying Ca2+ sparks of frog skeletal muscle. J Gen Physiol. 1999 Jul;114(1):31–48. doi: 10.1085/jgp.114.1.31. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Satoh H., Blatter L. A., Bers D. M. Effects of [Ca2+]i, SR Ca2+ load, and rest on Ca2+ spark frequency in ventricular myocytes. Am J Physiol. 1997 Feb;272(2 Pt 2):H657–H668. doi: 10.1152/ajpheart.1997.272.2.H657. [DOI] [PubMed] [Google Scholar]
  34. Shacklock P. S., Wier W. G., Balke C. W. Local Ca2+ transients (Ca2+ sparks) originate at transverse tubules in rat heart cells. J Physiol. 1995 Sep 15;487(Pt 3):601–608. doi: 10.1113/jphysiol.1995.sp020903. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Smith G. D., Keizer J. E., Stern M. D., Lederer W. J., Cheng H. A simple numerical model of calcium spark formation and detection in cardiac myocytes. Biophys J. 1998 Jul;75(1):15–32. doi: 10.1016/S0006-3495(98)77491-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Stern M. D. Theory of excitation-contraction coupling in cardiac muscle. Biophys J. 1992 Aug;63(2):497–517. doi: 10.1016/S0006-3495(92)81615-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Wussling M. H., Scheufler K., Schmerling S., Drygalla V. Velocity-curvature relationship of colliding spherical calcium waves in rat cardiac myocytes. Biophys J. 1997 Sep;73(3):1232–1242. doi: 10.1016/S0006-3495(97)78156-6. [DOI] [PMC free article] [PubMed] [Google Scholar]

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