The consequences of cardiac excitation-contraction coupling by calcium-induced calcium release were studied theoretically, using a series of idealized models solved by analytic and numerical methods. "Common-pool" models, those in which the trigger calcium and released calcium pass through a common cytosolic pool, gave nearly all-or-none regenerative calcium releases (in disagreement with experiment), unless their loop gain was made sufficiently low that it provided little amplification of the calcium entering through the sarcolemma. In the linear (small trigger) limit, it was proven rigorously that no common-pool model can give graded high amplification unless it is operated on the verge of spontaneous oscillation. To circumvent this problem, we considered two types of "local-control" models. In the first type, the local calcium from a sarcolemmal L-type calcium channel directly stimulates a single, immediately opposed SR calcium release channel. This permits high amplification without regeneration, but requires high conductance of the SR channel. This problem is avoided in the second type of local control model, in which one L-type channel triggers a regenerative cluster of several SR channels. Statistical recruitment of clusters results in graded response with high amplification. In either type of local-control model, the voltage dependence of SR calcium release is not exactly the same as that of the macroscopic sarcolemmal calcium current, even though calcium is the only trigger for SR release. This results from the existence of correlations between the stochastic openings of individual sarcolemmal and SR channels. Propagation of regenerative calcium-release waves (under conditions of calcium overload) was analyzed using analytically soluble models in which SR calcium release was treated phenomenalogically. The range of wave velocities observed experimentally is easily explained; however, the observed degree of refractoriness to wave propagation requires either a strong dependence of SR calcium release on the rate of rise of cytosolic calcium or localization of SR release sites to one point in the sarcomere. We conclude that the macroscopic behavior of calcium-induced calcium release depends critically on the spatial relationships among sarcolemmal and SR calcium channels, as well as on their kinetics.

Abstract-Local, rhythmic, subsarcolemmal Ca 2ϩ releases (LCRs) from the sarcoplasmic reticulum (SR) during diastolic depolarization in sinoatrial nodal cells (SANC) occur even in the basal state and activate an inward Na ϩ -Ca 2ϩ exchanger current that affects spontaneous beating. Why SANC can generate spontaneous LCRs under basal conditions, whereas ventricular cells cannot, has not previously been explained. Here we show that a high basal cAMP level of isolated rabbit SANC and its attendant increase in protein kinase A (PKA)-dependent phosphorylation are obligatory for the occurrence of spontaneous, basal LCRs and for spontaneous beating. Gradations in basal PKA activity, indexed by gradations in phospholamban phosphorylation effected by a specific PKA inhibitory peptide were highly correlated with concomitant gradations in LCR spatiotemporal synchronization and phase, as well as beating rate. Higher levels of basal PKA inhibition abolish LCRs and spontaneous beating ceases. Stimulation of ␤-adrenergic receptors extends the range of PKA-dependent control of LCRs and beating rate beyond that in the basal state. The link between SR Ca 2ϩ cycling and beating rate is also present in vivo, as the regulation of beating rate by local ␤-adrenergic receptor stimulation of the sinoatrial node in intact dogs is markedly blunted when SR Ca 2ϩ cycling is disrupted by ryanodine. Thus, PKA-dependent phosphorylation of proteins that regulate cell Ca 2ϩ balance and spontaneous SR Ca 2ϩ cycling, ie, phospholamban and L-type Ca 2ϩ channels (and likely others not measured in this study), controls the phase and size of LCRs and the resultant Na ϩ -Ca 2ϩ exchanger current and is crucial for both basal and reserve cardiac pacemaker function. R ecent studies have demonstrated that in sinoatrial (SA) nodal cells (SANC) generate local, rhythmic, subsarcolemmal Ca 2ϩ releases (LCRs) under basal conditions, ie, even in the absence of experimental Ca 2ϩ loading or stimulation of ␤-adrenergic receptors (␤-ARs). [1][2][3] In rabbit SANC, spontaneous, rhythmic LCRs occur during the late diastolic depolarization and activate Na ϩ -Ca 2ϩ exchanger (NCX) to generate an inward current that accelerates the depolarization rate, and, thus, LCRs are involved in control of spontaneous beating rate of SANC. 1 The mechanisms that permit SANC, but not ventricular myocytes, to generate rhythmic LCRs under basal conditions, however, have not been delineated.Spontaneous SR Ca 2ϩ release is facilitated by factors that increase the rate at which the SR can pump Ca 2ϩ , foremost among which are elevated cell Ca 2ϩ or elevated cAMP and its attendant protein kinase A (PKA)-dependent protein phosphorylation that results from intense ␤-AR stimulation. Whereas the cytosolic Ca 2ϩ concentration does not appreciably differ in rabbit ventricular cells and SANC, 2,4 the cAMP level of the intact SA node is high, 5 and it has been suspected that the basal cAMP level within SANC is elevated. 6,7 The SA node, however, is highly innervated, and neither the basal cAMP le...

Determination of the calcium spark amplitude distribution is of critical importance for understanding the nature of elementary calcium release events in striated muscle. In the present study we show, on general theoretical grounds, that calcium sparks, as observed in confocal line scan images, should have a nonmodal, monotonic decreasing amplitude distribution, regardless of whether the underlying events are stereotyped. To test this prediction we developed, implemented, and verified an automated computer algorithm for objective detection and measurement of calcium sparks in raw image data. When the sensitivity and reliability of the algorithm were set appropriately, we observed highly left-skewed or monotonic decreasing amplitude distributions in skeletal muscle cells and cardiomyocytes, confirming the theoretical predictions. The previously reported modal or Gaussian distributions of sparks detected by eye must therefore be the result of subjective detection bias against small amplitude events. In addition, we discuss possible situations when a modal distribution might be observed.

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The elementary events of excitation-contraction coupling in heart muscle are Ca2+ sparks, which arise from one or more ryanodine receptors in the sarcoplasmic reticulum (SR). Here a simple numerical model is constructed to explore Ca2+ spark formation, detection, and interpretation in cardiac myocytes. This model includes Ca2+ release, cytosolic diffusion, resequestration by SR Ca2+-ATPases, and the association and dissociation of Ca2+ with endogenous Ca2+-binding sites and a diffusible indicator dye (fluo-3). Simulations in a homogeneous, isotropic cytosol reproduce the brightness and the time course of a typical cardiac Ca2+ spark, but underestimate its spatial size (approximately 1.1 micron vs. approximately 2.0 micron). Back-calculating [Ca2+]i by assuming equilibrium with indicator fails to provide a good estimate of the free Ca2+ concentration even when using blur-free fluorescence data. A parameter sensitivity study reveals that the mobility, kinetics, and concentration of the indicator are essential determinants of the shape of Ca2+ sparks, whereas the stationary buffers and pumps are less influential. Using a geometrically more complex version of the model, we show that the asymmetric shape of Ca2+ sparks is better explained by anisotropic diffusion of Ca2+ ions and indicator dye rather than by subsarcomeric inhomogeneities of the Ca2+ buffer and transport system. In addition, we examine the contribution of off-center confocal sampling to the variance of spark statistics.

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A technique that allows the continuous measurement of mitochondrial free Ca2+ ([Ca2+]m) in a single living cardiac myocyte is described. It involves the introduction of the fluorescent chelating agent indo-1 into the cell by exposure to the acetoxymethyl ester, followed by selective quenching of the fluorescence of indo-1 in the cytosol by Mn2+. The identity of the remaining fluorescence due to intramitochondrial indo-1 is established by its resistance to treatment of the cell with digitonin at concentrations that release cytosolic but not mitochondrial enzymes and by the finding that ruthenium red and carbonyl cyanide p-trifluoromethoxyphenylhydrazone prevent its response to elevated cytosolic free Ca2+ ([Ca2+]c). [Ca2+]m is found to be low (less than 100 nM) in unstimulated cells and to rise in procedures that chronically elevate [Ca2+]c, such as Na+ replacement. The gradient [Ca2+]m/[Ca2+]c is less than unity at values of [Ca2+]c of less than 500 nM but rapidly increases at higher values of [Ca2+]c. Although there is no detectable increase in [Ca2+]m during a single electrical stimulation, [Ca2+]m increases up to 600 nM as the pacing frequency is raised to 4 Hz in the presence of norepinephrine; this increase occurs over the course of many contractions. It is concluded that these findings are consistent with an increase in [Ca2+]m acting as a signal to increase dehydrogenase activity, and hence flux through oxidative phosphorylation, in response to increased work loads.

Abstract-Localized, subsarcolemmal Ca 2ϩ release (LCR) via ryanodine receptors (RyRs) during diastolic depolarization of sinoatrial nodal cells augments the terminal depolarization rate. We determined whether LCRs in rabbit sinoatrial nodal cells require the concurrent membrane depolarization, or are intrinsically rhythmic, and whether rhythmicity is linked to the spontaneous cycle length. Confocal linescan images revealed persistent LCRs both in saponin-permeabilized cells and in spontaneously beating cells acutely voltage-clamped at the maximum diastolic potential. During the initial stage of voltage clamp, the LCR spatiotemporal characteristics did not differ from those in spontaneously beating cells, or in permeabilized cells bathed in 150 nmol/L Ca 2ϩ . The period of persistent rhythmic LCRs during voltage clamp was slightly less than the spontaneous cycle length before voltage clamp. In spontaneously beating cells, in both transient and steady states, LCR period was highly correlated with the spontaneous cycle length; and regardless of the cycle length, LCRs occurred predominantly at a constant time, ie, 80% to 90% of the cycle length. Numerical model simulations incorporating LCRs reproduce the experimental results. We conclude that diastolic LCRs reflect rhythmic intracellular Ca 2ϩ cycling that does not require the concomitant membrane depolarization, and that LCR periodicity is closely linked to the spontaneous cycle length. Thus, the biological clock of sinoatrial nodal pacemaker cells, like that of many other rhythmic functions occurring throughout nature, involves an intracellular Ca 2ϩ rhythm.