Influence of molecular variations of ionophore and lipid on the selective ion permeability of membranes: II. A theoretical model

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Abstract
The steady-state electrical properties induced by neutral carriers of ions in lipid bilayer membranes and the time dependence of the membrane current for low applied voltages are described theoretically in terms of a model which allows for a voltage dependence of the interfacial reactions, as well as for a trapezoidal shape of the internal free energy barrier for translocation of the complex. The basic features of the model are closely related to those of others presented previously (J.E. Hall, C.A. Mead & G. Szabo, 1973,J. Membrane Biol. 11:75; S.B. Hladky, 1974,Biochim. Biophys. Acta 352:71; S.B. Hladky, 1975,Biochim. Biophys. Acta 375:327; Eisenman, Krasne & Ciani, 1975,Ann. N.Y. Acad. Sci. 264:34), but the analysis of its consequences on the steady-state and nonsteady-state electrical characteristics is given here in greater detail and is extended to provide the expression for the zero-current potential in ionic gradients. It is shown that parameters, such as the width of the trapezoidal barrier, the plane of the reaction and the ratio of the rate constant of translocation across the membrane interior to the rate constant of dissociation of the complex, can be deduced from steady-state analysis, whereas the individual values of these constants and the distance between the equilibrium positions of the complexes are deducible from relaxation measurements.

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