Estimation of the steady-state characteristics of the Hodgkin-Huxley model from voltage-clamp data

In a companion paper in this issue we show that all the parameters and functions of the Hodgkin-Huxley (HH) model can be calculated in a unique and optimal manner from voltage-clamp peak current data when the steady-state activation (x infinite) and inactivation (z infinite) characteristics are known. Assuming that x infinite and z infinite can be adequately expressed by a Boltzmann equation with two parameters, the present paper describes an optimization procedure to estimate these parameters from peak current data without any constraint on the time constants of activation and inactivation. The required voltage-clamp data are the peak ionic current value (Ip) and its time of occurrence (tp), as provided by two complementary voltage-clamp protocols involving, in each case, a single fixed value of clamp potential. The performance of the procedure was very good with simulated medium- or high-resolution data as it was then possible to determine with confidence the degrees of the gating variables. The performance was also very good with low-resolution data, provided that the degrees of the gating variables were chosen correctly. Good results were also obtained in the presence of Gaussian noise. On the other hand, estimates of x infinite and z infinite based on normalization of peak current measurements always give uncertain results that are likely to be incorrect in a number of circumstances. It is concluded that the HH model can be a useful tool for the interpretation of voltage-clamp peak current data when a reasonable database is available.