Roles of sarcoplasmic reticulum Ca2+ cycling and Na+/Ca2+ exchanger in sinoatrial node pacemaking: insights from bifurcation analysis of mathematical models

To elucidate the roles of sarcoplasmic reticulum (SR) Ca(2+) cycling and Na(+)/Ca(2+) exchanger (NCX) in sinoatrial node (SAN) pacemaking, we have applied stability and bifurcation analyses to a coupled-clock system model developed by Maltsev and Lakatta (Am J Physiol Heart Circ Physiol 296: H594-H615, 2009). Equilibrium point (EP) at which the system is stationary (i.e., the oscillatory system fails to function), periodic orbit (limit cycle), and their stability were determined as functions of model parameters. The stability analysis to detect bifurcation points confirmed crucial importance of SR Ca(2+) pumping rate constant (P(up)), NCX density (k(NCX)), and L-type Ca(2+) channel conductance for the system function reported in previous parameter-dependent numerical simulations. We showed, however, that the model cell does not exhibit self-sustained automaticity of SR Ca(2+) release at any clamped voltage and therefore needs further tuning to reproduce oscillatory local Ca(2+) release and net membrane current reported experimentally at -10 mV. Our further extended bifurcation analyses revealed important novel features of the pacemaker system that go beyond prior numerical simulations in relation to the roles of SR Ca(2+) cycling and NCX in SAN pacemaking. Specifically, we found that 1) NCX contributes to EP instability and enhancement of robustness in the full system during normal spontaneous action potential firings, while stabilizing EPs to prevent sustained Ca(2+) oscillations under voltage clamping; 2) SR requires relatively large k(NCX) and subsarcolemmal Ca(2+) diffusion barrier (i.e., subspace) to contribute to EP destabilization and enhancement of robustness; and 3) decrementing P(up) or k(NCX) decreased the full system robustness against hyperpolarizing loads because EP stabilization and cessation of pacemaking were observed at the lower critical amplitude of hyperpolarizing bias currents, suggesting that SR Ca(2+) cycling contributes to enhancement of the full system robustness by modulating NCX currents and promoting EP destabilization.