Effect of hyperpolarization-activated current I(f) on robustness of sinoatrial node pacemaking: theoretical study on influence of intracellular Na(+) concentration.

To elucidate the effects of hyperpolarization-activated current I(f) on robustness of sinoatrial node (SAN) pacemaking in connection with intracellular Na(+) concentration (Na(i)) changes, we theoretically investigated 1) the impacts of I(f) on dynamical properties of SAN model cells during inhibition of L-type Ca(2+) channel currents (I(CaL)) or hyperpolarizing loads and 2) I(f)-dependent changes in Na(i) and their effects on dynamical properties of model cells. Bifurcation analyses were performed for Na(i)-variable and Na(i)-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 I(f) conductance (g(f)) shrank I(CaL) conductance (g(CaL)) regions of unstable EPs and stable LCs (rhythmic firings) in the Na(i)-variable system but slightly broadened that of rhythmic firings at lower g(f) in the Na(i)-fixed system. In the Na(i)-variable system, increased g(f) yielded elevations in Na(i) at EPs and during spontaneous oscillations, which caused EP stabilization and shrinkage in the parameter regions of unstable EPs and rhythmic firings. As g(f) increased, parameter regions of unstable EPs and stable LCs determined for hyperpolarizing loads shrank in the Na(i)-variable system but were enlarged in the Na(i)-fixed system. These findings suggest that 1) I(f) does not enhance but rather attenuates robustness of rabbit SAN cells via facilitating EP stabilization and LC destabilization even in physiological g(f) ranges; and 2) the enhancing effect of I(f) on robustness of pacemaker activity, which could be observed at lower g(f) when Na(i) was fixed, is actually reversed by I(f)-dependent changes in Na(i).