Phase resetting in a model of sinoatrial nodal membrane: ionic and topological aspects

We describe the phase-resetting effect of injecting an isolated current pulse in an ionic model of a single cell of the sinoatrial node. Delivery of a depolarizing pulse early (late) in the cycle results in a prolongation (abbreviation) of the cycle length. With a hyperpolarizing pulse, the effect is reversed. We determine the topological type or degree of phase resetting in two ways: 1) by analyzing interbeat intervals extracted from the voltage waveform, and 2) by analyzing the waveform, not only of the voltage, but of all the activation and inactivation variables. The two methods give similar results. At low (high) pulse amplitudes, there is type 1 (0) phase resetting. When type 1 phase resetting occurs, the new phase is a monotonically increasing function of the old phase at sufficiently low stimulus amplitudes, whereas at higher stimulus amplitudes it is not. Leading roles in generating phase resetting are attributed to the slow inward current and to the leakage current. Comparison is made with experimental phase-resetting findings in the sinoatrial node and other cardiac oscillators. Implications for unidirectional and bidirectional synchronization are also sketched out.