A rapid method for determining voltage-concentration relations across membranes

Abstract

A rapid method is described for obtaining curves relating the potential difference (p.d.) across a membrane to solute concentration gradients. The experiment consists of measuring the p.d. as a function of time while the concentration at the membrane is continuously increasing from 0 to Co (or decreasing from Co to 0) owing to diffusion through an unstirred layer. The voltage trace is then analysed with a piece of transparent paper, on which lines corresponding to solutions of the diffusion equation convert the time axis of the voltage trace into a concentration axis. Superposition of this paper on an experimental voltage trace permits one to read off the p.d. corresponding to any concentration between 0 and Co . The relation between diffusion potentials and NaCl concentration, and between streaming potentials and concentrations of impermeant nonelectrolytes, has been reconstructed by this procedure in rabbit gall-bladder. The method yields non-linear voltage-concentration curves in good agreement with those obtained by conventional methods, but requires much less time and experimental manipulation. The conditions that must exist for the method to be valid are discussed. The thicknesses of the unstirred layers in rabbit gall-bladder are measured, and are shown to have a negligible effect upon steady-state streaming potentials and NaCl diffusion potentials. The changes of permeability with osmolarity described in rabbit gall-bladder must be complete within a fraction of a second, in agreement with the interpretation that they represent swelling and shrinking of the cell membrane itself.