The Hodgkin-Huxley Na+ channel model versus the five-state Markovian model

In describing the Na+ channel-gating kinetics, it is generally believed the Hodgkin-Huxley model is inadequate and other types of Markovian models are more appropriate. In this paper, we perform detailed kinetic analyses to find out whether the Hodgkin-Huxley model is really unacceptable. Specifically, we consider two models for the analyses: A five-state Markovian model that allows inactivation to take place before opening and a Hodgkin-Huxley eight-state model. The criteria used to check the goodness of the two models are (a) Akaike's information criterion; (b) chi 2 tests on the waiting-time, open-time, and closed-time distributions, and the number of openings per record; and (c) comparison between all latency distributions and the probability of the open state predicted from the two models. In order to do this, we first develop a method of constructing probability density histograms of a specified event (e.g., waiting time, closed time, open time, number of openings per patch) from the multichannel patch-clamp recordings. The goodness of our method is checked by simulating multichannel patch recordings using a multinomial random number generator. Our kinetic analysis on the single Na+ channel recordings from the cardiac cells revealed that (a) on the basis of Akaike's information criterion, the Hodgkin-Huxley model is definitely a better model than the five-state model, but (b) on the basis of chi 2 tests on the probability density functions, the latter model is slightly better than the former. We find no evidence that the Hodgkin-Huxley model is inferior to the five-state model for this cell type.