Can membrane transport parameters that vary with time be derived from electrochemical measurements in an external electrolyte?

Abstract

In this paper we examine whether the properties of a membrane transport system that varies with time can be determined via electrochemical measurements in an electrolyte that surrounds the membrane. Exact alternating-current (a.c.) solutions of the Nernst–Planck–Poisson equations show that time-varying currents through the membrane produce ‘waves’ of solute concentration within the external electrolyte that carry a small net charge that modifies the local electric field. The relationship between electric field and total current at any point in the electrolyte then depends upon the rate of change of the membrane currents. This raises obvious difficulties for the interpretation of time-varying measurements with the conventional vibrating probe. These variations in local activity and electric field also provide a coupling between the individual ionic currents that varies with position in the electrolyte. Consequently, the current of a species measured in the external electrolyte some distance away from the membrane can be quite different from its value in the membrane, and this raises uncertainties in the interpretation of measurements made with ion-selective probes. Calculations show that large errors in both the estimated magnitude and direction of membrane transport can occur under some conditions. For example, the coupling of currents might mean that a uniport at the membrane can progressively appear as a symport as measurements are made further away from the membrane in the external electrolyte.