## Abstract

Evidence is given for a high density of negative surface charge near the sodium channel of myelinated nerve fibres. The voltage dependence of peak sodium permeability is measured in a voltage clamp. The object is to measure voltage shifts in sodium activation as the following external variables are varied: divalent cation concentration and type, monovalent concentration, and pH. With equimolar substitution of divalent ions the order of effectiveness for giving a positive shift is: Ba = Sr < Mg < Ca < Co <latex>$\approx$</latex> Mn < Ni < Zn. A tenfold increase of concentration of any of these ions gives a shift of +20 to +25 mV. At low pH, the shift with a tenfold increase in Ca<latex>$^{2+}$</latex> is much less than at normal pH, and conversely for high pH. Solutions with no added divalent ions give a shift of -18 mV relative to 2 mM Ca<latex>$^{2+}$</latex>. Removal of <latex>$\frac{7}{8}$</latex> of the cations from the calcium-free solution gives a further shift of -35 mV. All shifts are explained quantitatively by assuming that changes in an external surface potential set up by fixed charges near the sodium channel produce the shifts. The model involves a diffuse double layer of counterions at the nerve surface and some binding of H<latex>$^+$</latex> ions and divalent ions to the fixed charges. Three types of surface groups are postulated: (1) an acid pK<latex>$_a$</latex> = 2.88, charge density -0.9 nm<latex>$^{-2}$</latex>; (2) an acid pK<latex>$_a$</latex> = 4.58, charge density -0.58 nm<latex>$^{-2}$</latex>; (3) a base pK<latex>$_a$</latex> = 6.28, charge density +0.33 nm<latex>$^{-2}$</latex>. The two acid groups also bind Ca<latex>$^{2+}$</latex> ions with a dissociation constant K = 28 M. Reasonable agreement can also be obtained with a lower net surface charge density and stronger binding of divalent ions and H<latex>$^+$</latex> ions.