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The Hodgkin–Huxley Na + channel model versus the five‐state Markovian model
Author(s) -
Chay Teresa Ree
Publication year - 1991
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360311306
Subject(s) - akaike information criterion , goodness of fit , hodgkin–huxley model , statistical physics , mathematics , multinomial distribution , statistics , markov process , physics , neuroscience , biology
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) χ 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 χ 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.