Velocity and stability of solitary planar travelling wave solutions of intracellular [Ca]2+

Normal cardiac muscle contraction occurs in response to a rapid rise followed by a slower decay in intracellular calcium concentration. When cardiac muscle cells are loaded with calcium, an intracellular store releases calcium into the cytosol by the process of calcium-induced calcium release (CICR). This release contributes to the rise in intracellular calcium which in turn triggers contraction. We use two qualitative piecewise linear reaction-diffusion models of this behaviour to investigate the speed, stability and waveform of plane waves using singular perturbation techniques.

[1]  D. Noble,et al.  Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms , 1987, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[2]  Donald M. Bers,et al.  Excitation-Contraction Coupling and Cardiac Contractile Force , 2001, Developments in Cardiovascular Medicine.

[3]  J. Sneyd,et al.  Calcium wave propagation by calcium-induced calcium release: an unusual excitable system. , 1993, Bulletin of mathematical biology.

[4]  James Sneyd,et al.  Curvature dependence of a model for calcium wave propagation , 1993 .

[5]  M. Stern,et al.  Theory of excitation-contraction coupling in cardiac muscle. , 1992, Biophysical journal.

[6]  A. Goldbeter,et al.  Biochemical Oscillations And Cellular Rhythms: Contents , 1996 .

[7]  J Rinzel,et al.  Traveling wave solutions of a nerve conduction equation. , 1973, Biophysical journal.

[8]  K Kuba,et al.  Simulation of intracellular Ca2+ oscillation in a sympathetic neurone. , 1981, Journal of theoretical biology.

[9]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[10]  C. Luo,et al.  A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. , 1991, Circulation research.

[11]  M. C. Viola,et al.  Distinct patterns of calcium transients during early and delayed afterdepolarizations induced by isoproterenol in ventricular myocytes. , 1995, Circulation.

[12]  E. Lakatta,et al.  Excitation-contraction coupling in heart: new insights from Ca2+ sparks. , 1996, Cell calcium.

[13]  A. Y. Wong,et al.  A model of excitation-contraction coupling of mammalian cardiac muscle. , 1981, Journal of theoretical biology.

[14]  P. Lipp,et al.  To quark or to spark, that is the question , 1997, The Journal of physiology.

[15]  W. Wier.  Cytoplasmic [Ca2+] in mammalian ventricle: dynamic control by cellular processes. , 1990, Annual review of physiology.

[16]  D DiFrancesco,et al.  A model of cardiac electrical activity incorporating ionic pumps and concentration changes. , 1985, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[17]  E Niggli,et al.  Microscopic spiral waves reveal positive feedback in subcellular calcium signaling. , 1993, Biophysical journal.

[18]  C. H. Orchard,et al.  OSCILLATIONS AND WAVES OF INTRACELLULAR [CA2+] IN CARDIAC-MUSCLE-CELLS , 1995 .

[19]  L. Stryer,et al.  Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. , 1992, Science.

[20]  A. Fabiato,et al.  Contractions induced by a calcium‐triggered release of calcium from the sarcoplasmic reticulum of single skinned cardiac cells. , 1975, The Journal of physiology.

[21]  D. Noble,et al.  Improved guinea-pig ventricular cell model incorporating a diadic space, IKr and IKs, and length- and tension-dependent processes. , 1998, The Canadian journal of cardiology.

[22]  M. Boyett,et al.  Diastolic, systolic and sarcoplasmic reticulum [Ca2+] during inotropic interventions in isolated rat myocytes. , 1991, The Journal of physiology.

[23]  A Goldbeter,et al.  Properties of intracellular Ca2+ waves generated by a model based on Ca(2+)-induced Ca2+ release. , 1994, Biophysical journal.

[24]  D. Clapham,et al.  Spiral waves and intracellular calcium signalling , 1992, Journal of Physiology-Paris.

[25]  A. Y. Wong,et al.  Model of calcium-induced calcium release mechanism in cardiac cells , 1992, Bulletin of mathematical biology.

[26]  J. Keener,et al.  Singular perturbation theory of traveling waves in excitable media (a review) , 1988 .

[27]  R Y Tsien,et al.  Calcium channels, stores, and oscillations. , 1990, Annual review of cell biology.