Reduced models for the pacemaker dynamics of cardiac cells

We introduce three- and two-dimensional biophysical models of cardiac excitability derived from a 14-dimensional model of the sinus venosus [Rasmusson, R., et al., 1990. Am. J. Physiol. 259, H352–369]. The reduced models capture normal pacemaking dynamics with a small complement of ionic currents. The two-dimensional model bears some similarities with the Morris–Lecar model [Morris, C., Lecar, H., 1981. Biophysical Journal, 35, 193–213]. Because they were reduced from a biophysical model, both models depend on parameters that were obtained from experimental data. Even though the correspondence with the original model is not exact, parameters may be adjusted to tune the reductions to fit experimental traces. As a consequence, unlike other generic low-dimensional models, the models introduced here provide a means to relate physiologically relevant characteristics of pacemaker potentials such as diastolic depolarization, plateau, and action potential frequency, to biophysical variables such as the relative abundance of membrane channels and channel kinetic rates. In particular, these models can lead to an explicit description of how the shape of cardiac action potentials depends on the relative contributions and states of inward and outward currents. By being physiologically derived and computationally efficient, the models presented in this article are useful tools for theoretical studies of excitability at the cellular and network levels.