Internally perfused protease-treated squid giant axons were prepared for gating current measurements. Gating current records obtained under large amplitude sinusoidal voltage clamp allowing for settling times into dynamic steady-states were analyzed as functions of the mean membrane potential of the test sinusoid for which the amplitude and frequency were held constant. Non-linear analysis measured the harmonic content (amplitudes and phases) of the distorted periodic current records. The most pronounced feature is a dominant second harmonic. This second harmonic is centered at Emean = +10 mV. A number of other characteristic harmonic behaviors were also observed. The harmonics tend to die away for very negative (less than -60 mV) and very positive (greater than +72 mV) values of Emean. This harmonic behavior is basically different from that seen in gating current simulations of standard models, including the Hodgkin-Huxley model. The axonal data suggest two moving molecular components with independent degrees of freedom. On this basis, a new kinetic model of sodium activation gating was derived which differs from previous models in being over-determined by the data. The kinetics that simulate the experimental data contain two independently constrained molecular processes. The model predicts 1) sizable gating currents in response to hyperpolarizing voltage steps from rest, 2) a substantial increase in the initial peak of the gating current following voltage steps from prehyperpolarized potentials, 3) a small delay in the onset of sodium ion current following voltage steps from prehyperpolarized potentials, and 4) flickering during the open state in single channel current records. The present model reproduces the phenomenological development of Na conductance during the initiation and development of action potentials. A model gate based on this kinetic scheme and the primary amino acid structure of the sodium channel has been constructed.
