Theoretical computation of phase locking in embryonic atrial heart cell aggregates

The effects of periodic stimulation of spontaneously beating aggregates of chick atrial heart cells are considered. Provided the effects of a single stimulus do not change the properties of the oscillation, and that the oscillation is re-established rapidly following a stimulus, this system can be modeled by one-dimensional finite difference equations. These equations employ experimentally generated phase resetting data that describe the effects of a single isolated stimulus at different phases of the oscillation. A complete analysis of the predicted dynamics is given over a broad range of stimulation frequencies and amplitudes. Prominent features of the dynamics include phase locking, bistability, chaos, and disappearance of Arnold tongues at large stimulation amplitudes. The fine details of the bifurcations are sensitive to properties of the phase resetting curves, and consequently, the observed bifurcations are not expected to be "universal" for larger stimulation amplitudes. Experimental traces show many correspondences with theoretical computations.