A model of the phase-sensitivity of the pacemaking cell in the bullfrog heart

In this study, mathematical models of the bullfrog sinus venosus (SV) pacemaker cell (Rasmusson et al., 1990, Am. J. Physiol. 259, H352-H369) and the ACh-sensitive K+ channel (Shumaker et al., 1990, Biophys. J. 57, 567-576) are combined to simulate the response of the SV myocyte to brief hyperpolarizing currents or acetylcholine (ACh) pulses. These simulations provide an ionic basis for the interpretation of the response of this pacemaker cell to either single perturbation or periodic stimuli. The model predicts that the effects of ACh stimulation on the pacemaker cycle length are dependent both on the phase and temporal characteristics of the [ACh] waveform. For example, the simulations show that (1) although ACh normally has an inhibitory effect on the pacemaker model, for cases where the rise time and duration of the [ACh] waveform are sufficiently brief, ACh can paradoxically accelerate the beat in which a single stimulus is given; (2) the SV pacemaker normally exhibits type 1 (odd) phase-resetting in response to ACh delivery, however type 0 (even) phase-resetting behavior may be exhibited when the [ACh] waveform is large enough and has a very fast rise time; and (3) the SV pacemaker may become phase-locked to a repetitive ACh stimulus applied with either a constant period or coupling interval. In the latter case, this entrainment phenomenon has implications for the control of the cardiac pacemaker by a neural oscillator (e.g. located in the medullary cardiovascular control center) which provides input to the pacemaker cell via the vagus nerve. In these regions of capture, repetitive ACh stimulation produces a well-known paradoxical accelerative effect on the SV pacemaker cell, similar to that seen in a variety of other species.