Analysis and modeling of na current in cardiac muscles

The (Na)^+ channel plays essential roles in initiation and conduction of action potential in a variety of excitable tissues including nerves, hearts and muscles. Na channels undergo activation and inactivation depending on the membrane voltage and time. Hodgkin & Huxley (H-H), early in 1950s, proposed a mathematical model to describe Na channel properties of the squid axonal membrane, based on voltage-clamp (V-C) study. For the next 3 decades since then, direct recording of the Na current by V-C method and hence the study of Na channel property have been hampered in cardiac tissues largely by the complicated geometry of the tissue. Recent electrophysiological studies using V-C method with patch-pipettes on dispersed single heart cells have demonstrated that the gating-kinetics of Na channels is much more complicated than predicted from the H-H model. To establish a new model which enables describing Na channel events in heart, we conducted V-C study in embryonic chick heart cells. In this preparation, we found pronounced differences in the inactivation and re-inactivation mechanisms from those in the axon, suggesting a presence of one conductive and two inactivated states among which voltage-dependent transitions were permitted (a cyclic reaction model). According to the model, we experimentally determined rate-constants of the reaction. We also found a delay in onset of inactivation as well as activation in voltage-clamped heart cells, and derived empirical equations for such delays in onset. Taken above together, we could faithfully reproduce the Na channel currents observed in heart cells under V-C conditions.