Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study

Cardiac myocytes are excitable cells in which an external current stimulus depolarizes the membrane potential to elicit an action potential. This action potential then triggers calcium release from intracellular stores, which mediates contraction. Conversely, intracellular calcium also modulates membrane currents, affecting action potential morphology and action potential duration (APD). The interactions between action potential and calcium, termed excitation-contraction coupling, give rise to a rich spectrum of nonlinear dynamics, especially at rapid heart rates, which are important for cardiac contraction and the development of lethal arrhythmias. In this study, we developed a nonlinear iterated map model to investigate the dynamics of cardiac excitation-contraction coupling in a periodically stimulated cell. We first studied the nonlinear dynamics due to APD restitution, a functional relation between APD and its preceding diastolic interval. We then studied the nonlinear dynamics due to intracellular calcium cycling when total cell calcium is constant or varies at a beat-to-beat basis. Finally, we studied the nonlinear dynamics due to the bidirectional coupling of the two dynamical systems. Saddle-node bifurcations leading to bistability, period-doubling bifurcations leading to alternans, and period-doubling routes to chaos can independently occur in both action potential or intracellular calcium cycling subsystems as heart rate increases. A Hopf bifurcation leading to quasiperiodicity occurs when the two dynamical systems are coupled. Although these dynamics are predicted from low-dimensional iterated maps, the approach here provides valuable information which can be used as a basis to explore dynamical features of physiologically detailed ionic models, to illuminate experimental findings, and to design experimentally testable predictions for new biological experiments.