Synchronization of stochastic Ca²(+) release units creates a rhythmic Ca²(+) clock in cardiac pacemaker cells

In sinoatrial node cells of the heart, beating rate is controlled, in part, by local Ca²(+) releases (LCRs) from the sarcoplasmic reticulum, which couple to the action potential via electrogenic Na(+)/Ca²(+) exchange. We observed persisting, roughly periodic LCRs in depolarized rabbit sinoatrial node cells (SANCs). The features of these LCRs were reproduced by a numerical model consisting of a two-dimensional array of stochastic, diffusively coupled Ca²(+) release units (CRUs) with fixed refractory period. Because previous experimental studies showed that β-adrenergic receptor stimulation increases the rate of Ca²(+) release through each CRU (dubbed I(spark)), we explored the link between LCRs and I(spark) in our model. Increasing the CRU release current I(spark) facilitated Ca²(+)-induced-Ca²(+) release and local recruitment of neighboring CRUs to fire more synchronously. This resulted in a progression in simulated LCR size (from sparks to wavelets to global waves), LCR rhythmicity, and decrease of LCR period that parallels the changes observed experimentally with β-adrenergic receptor stimulation. The transition in LCR characteristics was steeply nonlinear over a narrow range of I(spark), resembling a phase transition. We conclude that the (partial) periodicity and rate regulation of the "Calcium clock" in SANCs are emergent properties of the diffusive coupling of an ensemble of interacting stochastic CRUs. The variation in LCR period and size with I(spark) is sufficient to account for β-adrenergic regulation of SANC beating rate.