Non-linear dynamics and long-time phase correlations of beating cardiomyocytes

The observation of spontaneous calcium oscillations of ~ 1Hz in isolated, beating cardiac cells is typically explained by many coupled chemical reactions and parameters. We show that the separation of time scales of fast processes with slower calcium diffusion in the cell results in a single, non-linear dynamical equation that characterizes these oscillations with only a few physically relevant parameters, determined from independent experiments. The beating phase is related to the time-dependent deviation of the oscillations from their average frequency, due to noise and the resulting cellular response. Here, we demonstrate experimentally that in addition to the short-time (1-2 Hz), beat-to-beat variability there are long-time correlations (tens of minutes) in the beating phase dynamics of isolated cardiomyocytes. Our theoretical model relates these long-time correlations to cellular regulation that restores the frequency to its average, homeostatic value in response to stochastic perturbations. This defines a new mesoscaopic time scale in cardiac cell beating, which we call the regulation time.