Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking: insights from stability and bifurcation analyses of a mathematical model

Abstract

To elucidate the dynamical mechanisms of the sinoatrial (SA) node pacemaker activity, we investigated the roles of L-type Ca2+ (ICa,L) and delayed-rectifier K+ (IKr) currents in pacemaking by stability and bifurcation analyses of our rabbit SA node model (Kurata Y, Hisatome I, Imanishi S, and Shibamoto T. Am J Physiol Heart Circ Physiol 283: H2074-H2101, 2002). Equilibrium points (EPs), periodic orbits, stability of EPs, and Hopf bifurcation points were calculated as functions of conductance or gating time constants of the currents for constructing bifurcation diagrams. Structural stability (robustness) of the system was also evaluated by computing stability and dynamics during applications of constant bias currents (Ibias). Blocking ICa,L or IKr caused stabilization of an EP and cessation of pacemaking via a Hopf bifurcation. The unstable zero-current potential region determined with Ibias applications, where spontaneous oscillations appear, shrunk and finally disappeared as ICa,L diminished, but shrunk little when IKr was eliminated. The reduced system, including no time-dependent current except ICa,L, exhibited pacemaker activity. These results suggest that ICa,L is responsible for EP instability and pacemaker generation, whereas IKr is not necessarily required for constructing a pacemaker cell system. We further explored the effects of various K+ currents with different kinetics on stability and dynamics of the model cell. The original IKr of delayed activation and inward rectification appeared to be most favorable for generating large-amplitude oscillations with stable frequency, suggesting that IKr acts as an oscillation amplifier and frequency stabilizer. IKr may also play an important role in preventing bifurcation to quiescence of the system.