Determination of K(+)-channel relaxation times in squid axon membrane by Hodgkin-Huxley and by direct linear analysis

Abstract

An assumption in the use of the Hodgkin-Huxley (HH) formulation (A.L. Hodgkin and A.F. Huxley, J. Physiol. 117 (1952) 500) to extract kinetic parameters from ion conductance responses to step voltage changes across biological membranes is that estimates obtained from such an analysis are equivalent to those obtained by direct, small-perturbation analysis. Comparison of the estimates of the K(+)-conductance relaxation time, tau n, derived from HH vs rapid, complex admittance determinations in the same squid giant axons shows significant differences for the same step changes over a 60 mV range from holding (-65 mV). The admittance determinations (2.5-5000 Hz) are shown to satisfy criteria of linear analysis (i.e., estimates are equivalent to a small-step analysis and are time invariant). The discrepancies between the two methods arise from the fact that the HH power-law description for a constant power does not yield a best fit of data over the voltage range examined and thus best estimates of tau n are power dependent. Furthermore, the large step changes in membrane voltage may excite nonlinear modes unrelated to conductance gating that contaminate the data to which the nonlinear formulation is applied to estimate linear kinetic parameters. Thus, the long-standing assumption that application of the HH methodology and empiricism is equivalent to a direct linear analysis is not substantiated. This result suggests that in comparisons between microscopic and macroscopic conduction data, microkinetic parameters derived from analysis of single ion-channel data should not be compared to macrokinetic parameters from a large population of the channel derived by HH analysis.