Synchronization in chains of pacemaker cells by phase resetting action potential effects

Abstract

Interactions between pacemaker cells in a chain were calculated according to a “phase-reset” model. It is based on effects of action potentials in the cells on the cycle lengths of neighbouring cells. These effects were defined for each cell by a latency-phase curve (LPC), giving the latency time (L) until the onset of the next action potential in that cell, as a function of the phase (ø) at which a neighbour cell fired an action potential. Neighbour cells with simultaneous action potentials did not influence each others cycle length. We investigated how stable synchronization depends on the shape of the LPC's of the pacemaker cells and on chain length. Three types of interactive behaviour were distinguished. First, anti-phase synchrony, in which neighbouring cells fired with large phase differences with respect to the synchronized periodP _s .Second, asynchrony, in which the periods of the cells did not become equal and constant. Third, in-phase synchrony, in which the phase differences between the neighbouring cells were zero or much smaller than the synchronized periodP _s ,depending on the differences between the intrinsic periods. Asynchrony and antiphase synchrony may be seen as cardiophysiological arrhythmias, while in-phase synchrony represents the physiological type of synchrony in the heart. In-phase synchrony appeared to be strongly favoured by LPC's, which have a no-effect (refractory) part at early phases, a lengthened latency (or phase delay) part at intermediate phases and a shortened latency (or phase advance) part at late phases in the cycle. Such LPC-shapes are commonly found in preparations of cardiac pacemaker cells. When the pacemaker cells were identical, the synchronized periodP _s during in-phase synchrony was equal to their intrinsic periodP ⁱ_* . For different intrinsic periods,P _s was equal to the intrinsic period of the fastest cell if the LPC's contained a sufficiently long initial no-effect period at early phases and a shorteried latency part at late phases. When, on the other hand, such cell chains had a linear gradient in their intrinsic periods, “action potentials” started from the fast end and traveled along the chain. The propagation of an action potential wave slowed down as it reached the slower cells. When the gradient in the intrinsic periods was too steep, only the intrinsically fast end of the chain developed synchrony. Surprisingly, by making the intrinsic gradient some-what irregular such a chain of cells could be made to exhibit areas of cells that were locally synchronized at different frequencies. These model results show that the concept of phase resetting provides a useful framework to understand interactions between pacemaker cells by action potential effects.