Ion transport and displacement currents with membrane-bound carriers

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Abstract
The standard carrier model for ion transport by a one-to-one mechanism is developed to predict the time-dependent currents for systems that are symmetrical at zero applied potential. The complete solution for ions and carriers bearing any charge is derived by assuming that the concentration of ions in the membrane is low and either that the applied potential is small or that the applied potential affects equally all of the association and dissociation reactions between the ions and the carriers. The response to an abruptly applied potential is then given by the sum of a constant and two declining exponential terms. The time constants of these relaxations are described by the equations derived for neutral carriers by Stark, Ketterer, Benz and Läuger in 1971 (Biophys. J. 11:981). The sum of the amplitudes of the exponentials for small applied potentials obeys a relation like that first derived by Markin and Liberman in 1973 (Biofizika 18:453). For small applied potentials expressions are also provided for the voltage transients in charge-pulse experiments and for the membrane admittance.