We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models.

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.

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Membrane potential was changed uniformly in segments, 0.7-1.0 mm long, of guinea pig papillary muscles excised from the right ventricle by using extracellular polarizing current pulses applied across two electrically insulated cf preparations superfused with Tyrode's solution at maximum diastolic membrane potentials ranging from-35.2+/-7.5 (threshold) to +4.0+/-9.2 mV. The average maximum dV/dt of RAD ranged from 17.1 to 18.0 V/sec within a membrane potential range of -40 to +20 mV. Raising extracellular Ca2+ concentration [Ca2+]0 from 1.8 to 6.8 mM, or application of isoproterenol (10(-6)g/ml) enhanced the rate of RAD, but lowering [Ca2+]0 to 0.4 mM or exposure to MnCl2 (6 mM) abolished RAD. RAD were enhanced by lowering extracellular K+ concentration [K+]0 from 5.4 to 1.5 mM. RAD were suppressed in 40% of fibers by raising [K+]0 to 15.4 mM, and in all fibers by raising [K+]0 to 40.4 mM. This suppression was due to increased [K+]0 and not to K-induced depolarization because it persisted when membrane potential was held by means of a conditioning hyperpolarizing puled gradually after maximum repolarization. These observations suggest that the development of RAD in depolarized myocardium is associated with a time-dependent decrease in outward current (probably K current) and with increase in the background inward current, presumably flowing through the slow cha-nel carrying Ca or Na ions, or both.