OF WORK The 2D phenomenalogical model has been exercised extensively to generate statistics showing how periodicity of the calcium clock emerges as the RyR calcium release current is increased, allowing the clock to entrain with membrane currents to regulate the heart rate. The results of those simulations have been published in Biophysical Journal. The full Monte-Carlo couplon model with a single cytosolic compartment has been updated to include the effects of local depletion of calcium at individual calcium release terminals of the junctional SR. Simulations of the parallelized model run on Biowulf confirm that local depletion makes a critical contribution to calcium spark termination and that it suffices as the only termination mechanism. However, in that case, there is a critical relationship between the intra-lumenal diffusion rate of SR calcium and the gating kinetics of the RyR that must be satisfied to prevent instability of sparks with delayed termination. This phenomenon, now renamed "spark metastability" has been extensively studied by Monte Carlo simulation, and by analytical computations on a simplified continuum model of the couplon. The results have been published in Journal of General Physiology Under calcium overload, the single-cytosol couplon model does not oscillate. A new 3D algorithm, combining the full couplon model with a spatially resolved cytosolic space using an operator splitting method, has now been completed. It demonstrated that the propagation of local calcium releases seen experimentally in sino-atrial node cells (SANC) can only occur if there are close, bridging clusters of RyRs to conduct the activation. Examination of 3D confocal sections of immunofluorescent labeled SANC reveals that such a network is present on the surface of these cells, unlike ventricular cells. By simulating the network, the 3D model reproduced propagating local calcium release that couple to membrane currents and drive the beating rate, as posited in the "coupled clock" theory developed in this Laboratory. The model reproduces the regulation of rate by modulating the function of the various proteins in the calcium cycling system, as would occur due to phosphorylation in response to autonomic activation. The sodium-calcium exchanger (NCX) was found to have a paradoxical effect, in that it provides the coupling to drive the membrane voltage, but, itself, inhibits the propagation of local calcium waves. The effect of NCX expression therefore has a biphasic effect on rate, clarifying experimental results of NCX knock-down experiments by others. A paper is in preparation for Journal of General Physiology to be submitted in about a month,

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Stern, Michael D; Maltseva, Larissa A; Juhaszova, Magdalena et al. (2014) Hierarchical clustering of ryanodine receptors enables emergence of a calcium clock in sinoatrial node cells. J Gen Physiol 143:577-604
Maltsev, Victor A; Yaniv, Yael; Maltsev, Anna V et al. (2014) Modern perspectives on numerical modeling of cardiac pacemaker cell. J Pharmacol Sci 125:6-38
Stern, Michael D; Rios, Eduardo; Maltsev, Victor A (2013) Life and death of a cardiac calcium spark. J Gen Physiol 142:257-74
Rios, Eduardo; Zhou, Jingsong; Brum, Gustavo et al. (2008) Calcium-dependent inactivation terminates calcium release in skeletal muscle of amphibians. J Gen Physiol 131:335-48