On the ionic displacement current in lipid bilayer membranes

Abstract

It is shown that the constant field approximation must be amended to make it apply to time-dependent signals. The necessary additional term corresponds to the ionic displacement current. In the absence of adsorption, this ionic displacement current is found to have a characteristic time of the order of a fraction of a microsecond. We confirm its mathematical form as given by Cole (1965). When the membrane-soluble ions are strongly adsorbed, an additional, purely exponential transient of much larger time constant is calculated, with a time dependence identical to that of the translocation of adsorbed ions. Our results support the pseudostationary approximation used by Andersen and Fuchs (1975) in the description of such exponential transients. Explicit expressions are given for the current after a voltage step as for the admittance, both in the absence and presence of adsorption, for a membrane with a rectangular potential energy profile.