To elucidate the effects of hyperpolarization-activated current If on robustness of sinoatrial node (SAN) pacemaking in connection with intracellular Na+ concentration ( Nai) changes, we theoretically investigated 1) the impacts of If on dynamical properties of SAN model cells during inhibition of L-type Ca2+ channel currents ( ICaL) or hyperpolarizing loads and 2) If-dependent changes in Nai and their effects on dynamical properties of model cells. Bifurcation analyses were performed for Nai-variable and Nai-fixed versions of mathematical models for rabbit SAN cells; equilibrium points (EPs), limit cycles (LCs), and their stability were determined as functions of model parameters. Increasing If conductance ( gf) shrank ICaL conductance ( gCaL) regions of unstable EPs and stable LCs (rhythmic firings) in the Nai-variable system but slightly broadened that of rhythmic firings at lower gf in the Nai-fixed system. In the Nai-variable system, increased gf yielded elevations in Nai at EPs and during spontaneous oscillations, which caused EP stabilization and shrinkage in the parameter regions of unstable EPs and rhythmic firings. As gf increased, parameter regions of unstable EPs and stable LCs determined for hyperpolarizing loads shrank in the Nai-variable system but were enlarged in the Nai-fixed system. These findings suggest that 1) If does not enhance but rather attenuates robustness of rabbit SAN cells via facilitating EP stabilization and LC destabilization even in physiological gf ranges; and 2) the enhancing effect of If on robustness of pacemaker activity, which could be observed at lower gf when Nai was fixed, is actually reversed by If-dependent changes in Nai.
Effect of defects on the line shape of electron paramagnetic resonance signals from the single-molecule magnet Mn12: A theoretical study