Sinusoidal voltage clamp of the Hodgkin-Huxley model

A voltage clamp consisting of a sinusoidal voltage of amplitude V1 and frequency f, superimposed on a steady voltage level V0, is applied to the Hodgkin-Huxley model of the squid giant axon membrane. The steady-state response is a current composed of sinusoidal components of frequencies O, f, 2f, 3f,... The frequencies greater than f arise from the nonlinearity of the membrane. The total current is described by a power series in V1; each coefficient of this series is composed of current components for one or more frequencies. For different frequencies one can derive higher-order generalized admittances characterizing the nonlinear as well as the linear properties of the membrane. Formulas for the generalized admittances are derived from the Hodgkin-Huxley equations for frequencies up to 3f, using a perturbation technique. Some of the resulting theoretical curves are compared with experimental results, with good qualitative agreement.