Use of a Fixed Charge Model to Determine the pK of the Negative Sites on the External Membrane Surface

Dear Sir: Hille (1968) has measured the effect of the external pH on the sodium conductance of a frog node. He fit the data for the magnitude of the sodium conductance vs. pH very well with the dissociation curve of a weak acid for a pKa of 5.2. His data for the voltage shift of the sodium conductance vs. pH were simply fit empirically We have recently presented a surface charge model to explain voltage shifts of potassium conductance when the external divalent cation concentration is varied in a squid axon (Gilbert and Ehrenstein, 1969 a) and we have now applied this model to Hille's voltage shift data (Gilbert and Ehrenstein, 1969 b). In essence, the surface charge model explains the shift of the conductance-voltage curve along the voltage axis as the result of an additional component of electric field inside the membrane. This electric field is produced by the double layer consisting of the fixed negative surface charge and neutralizing cations in solution. The concentration of divalent cations (or hydrogen ions) and the binding constant of the surface charge groups determine how much of the surface charge is neutralized. This, in turn, determines the magnitude of the field caused by the double layer and the resulting shift of conductance along the voltage axis. If the concentration of the binding cation does not appreciably affect the ionic strength, then the surface charge model can be used to determine the average separation between fixed charges as a function of three parameters: the valence of the binding cation, the ionic strength of the solution, and the maximum slope of the graph of voltage shift vs. logarithm of binding cation concentration. Fig. 1 shows this relationship for solutions in which there is a uni-univalent electrolyte solution to which small amounts of the binding cation are added. Hille's data give a maximum slope of about 10 mv/e-fold change in hydrogen ion concentration for conditions corresponding to case I of Fig. 1. This corresponds to an average spacing between fixed charges of about 15 A. The average spacing will also be determined below in the process of determining the binding constant. The following equation was used to determine the equilibrium constant for the binding process, and is the same as equation (11) of Gilbert and Ehrenstein (1969 a),