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.

The function of calcium entry or release channels is often modulated by the cytosolic free calcium concentration. When such channels are studied in isolation, calcium buffer solutions are usually used to control the free calcium at the cytosolic face of the channel. Such solutions are generally formulated on the basis of equilibrium considerations. We calculate the gradient of [Ca2+] in the vicinity of a channel pore, in the presence of such buffers. We find that the effective degree of buffering near the pore is markedly affected by kinetic considerations. Commonly used EGTA solutions are completely ineffective in buffering [Ca2+] within macromolecular distances of the pore. In order to achieve useful buffering, the fastest buffers (e.g. BAPTA derivatives) must be used, in concentrations very much higher than those conventionally employed. Because of the diffusion limit on the maximum rate of binding of calcium to the buffer ligand, it is physically impossible to achieve good control of [Ca2+] at cytosolic levels at distances of less than a few nm from a pore conducting pico-ampere calcium current.

Local, rhythmic, subsarcolemmal Ca ²⁺ 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 ⁺ -Ca ²⁺ 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 β-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 ²⁺ cycling and beating rate is also present in vivo, as the regulation of beating rate by local β-adrenergic receptor stimulation of the sinoatrial node in intact dogs is markedly blunted when SR Ca ²⁺ cycling is disrupted by ryanodine. Thus, PKA-dependent phosphorylation of proteins that regulate cell Ca ²⁺ balance and spontaneous SR Ca ²⁺ cycling, ie, phospholamban and L-type Ca ²⁺ channels (and likely others not measured in this study), controls the phase and size of LCRs and the resultant Na ⁺ -Ca ²⁺ exchanger current and is crucial for both basal and reserve cardiac pacemaker function.

In cardiac muscle, release of activator calcium from the sarcoplasmic reticulum occurs by calcium- induced calcium release through ryanodine receptors (RyRs), which are clustered in a dense, regular, two-dimensional lattice array at the diad junction. We simulated numerically the stochastic dynamics of RyRs and L-type sarcolemmal calcium channels interacting via calcium nano-domains in the junctional cleft. Four putative RyR gating schemes based on single-channel measurements in lipid bilayers all failed to give stable excitation–contraction coupling, due either to insufficiently strong inactivation to terminate locally regenerative calcium-induced calcium release or insufficient cooperativity to discriminate against RyR activation by background calcium. If the ryanodine receptor was represented, instead, by a phenomenological four-state gating scheme, with channel opening resulting from simultaneous binding of two Ca²⁺ ions, and either calcium-dependent or activation-linked inactivation, the simulations gave a good semiquantitative accounting for the macroscopic features of excitation–contraction coupling. It was possible to restore stability to a model based on a bilayer-derived gating scheme, by introducing allosteric interactions between nearest-neighbor RyRs so as to stabilize the inactivated state and produce cooperativity among calcium binding sites on different RyRs. Such allosteric coupling between RyRs may be a function of the foot process and lattice array, explaining their conservation during evolution.