Closed channel-open channel equilibrium of the sodium channel of nerve. Simple models of macromolecular equilibria

Abstract

The consistency of an electrodiffusion kinetics to describe the time-dependent opening of sodium channels of nerve suggests that motions over relatively long distances (on the atomic scale) are involved in the equilibrium as well. As a result, it is expected that a relatively large fraction of possible macromolecular conformations are unreactive. An equilibrium constant between locally reactive forms and the unreactive conformations is introduced. The consequences of this formalism is investigated in a square well potential, a harmonic potential, and a system consisting of two harmonic potentials with different spatial extents. The limits of knowledge from Nernstian behavior are shown. As an alternative to the Nernstian analysis, the experimental data of the sodium channel's quasi-equilibrium - the probability of the channel's being open as a function of voltage - can be described as resulting from motion caused by an electric field on a charge which is confined by a harmonic potential. A force constant is found from this analysis. (Such Hookian force constants cannot be found from spectroscopic experiments in condensed systems where the large-displacement vibrations are overdamped and, hence, spectroscopically unobservable). From the force constant, an approximate value of the Young's modulus can be calculated. The modulus' value falls in the range for rubber. As for rubbers, the restoring force is, then, expected to be mostly entropic rather than enthalpic in origin. Using the appropriate theory for linear chains of rubber and the Young's modulus, the approximate length of the chain causing the rubber-like force is calculated. The result is found to be near the length suggested for the hydrophilic chains that connect transmembrane sections of the sodium channel.