Self-similar action potential cycle-to-cycle variability of Ca2+ and current oscillators in cardiac pacemaker cells
Ca2+ and Vm transitions occurring throughout AP cycles in sinoatrial nodal (SAN) cells are cues that: (1) not only regulate activation states of molecules operating within criticality (Ca2+ domain) and limit-cycle (Vm domain) mechanisms of a coupled-clock system that underlies SAN cell automaticity; (2) but are also regulated by the activation states of the clock molecules they regulate. In other terms, these cues are both causes and effects of clock molecular activation (recursion). Recently, we demonstrated that Ca2+ and Vm transitions during AP cycles in single SAN cells isolated from mice, guinea pigs, rabbits and humans are self-similar (obey a power law) and are also self-similar to trans-species AP firing intervals of these cells in vitro, to heart rate in vivo, and to body mass. Neurotransmitter stimulation of {beta} adrenergic receptor or cholinergic receptor initiated signaling in SAN cells modulates their AP firing rate and rhythm by impacting on the degree to which SAN clocks couple to each other, creating the broad physiologic range of SAN cell mean AP firing intervals and firing interval variabilities. Here we show that Ca2+ and Vm domain kinetic transitions (time to AP ignition in diastole and 90% AP recovery) occurring within given AP, the mean AP firing intervals, and AP firing interval variabilities within time-series of APs in 230 individual SAN cells are self-similar (obey power laws). In other terms, these long-range correlations inform on self-similar distributions of order among SAN cells across the entire broad physiologic range of SAN AP firing intervals, regardless of whether autonomic receptors of these cells are stimulated or not, and regardless of the type (adrenergic or cholinergic) of autonomic receptor stimulation. These long-range correlations among distributions of Ca2+ and Vm kinetic functions that regulate SAN cell clock coupling during each AP cycle in different individual, isolated SAN cells not in contact with each other. Our numerical model simulations further extended our perspectives to the molecular scale and demonstrated that many ion currents also behave self-similar across autonomic states. Thus, to ensure rapid flexibility of AP firing rates in response to different types and degrees of autonomic input, nature "did not reinvent molecular wheels within the coupled-clock system of pacemaker cells", but differentially engaged or scaled the kinetics of gears that regulate the rate and rhythm at which the "wheels spin" in a given autonomic input context.