Interpretation of current-voltage relationships for “active” ion transport systems: II. Nonsteady-state reaction kinetic analysis of class-I mechanisms with one slow time-constant

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Abstract
The temporal behavior of current through a biological membrane can display more than one time constant. This study represents the reaction kinetic analysis of the nonsteady-state behavior of a class of membrane transporters with one voltage-sensitive reaction step, one dominant (large) time constant, but arbitrary reaction scheme of the voltage-insensitive part of transporter. This class of transporters which shows uniform behavior under steady-state conditions splits into two fundamentally different subclasses, when nonsteady-state behavior is examined: Subclass (Model) A: the slow reaction controls the redistribution of states within the reaction cycle upon an (electrical) perturbation; model B: this redistribution is fast but the transporting cycle can slowly equilibrate with an inactive, “lazy” state. The electrical appearance of model A in a membrane requires specific features of the transporter in the membrane: high densities (10−8 mol m−2), low turnover rates (103 sec−1) and high stoichiometry (z>1) of transported charges per cycle. The kinetics of both models can formally be described by an equivalent circuit with a steady-state slope conductance (G 0) shunted by a (transporter specific) capacitance (G t ) and a conductance (C t ) in series. The voltage dependence ofC t and ofG t can be used to identify model A or model B. In the range of maximumG 0 in the steady-state current-voltage curve,C t in model A displays a maximum (which may characteristically split into two maxima) and vanishes for larger voltage displacements.C t can be used for the determination of transporter densities in the membrane. In contrast to model A, the appearance of model B in the nonsteady-state behavior of a membrane does not depend on high densities, low turnover rates and high stoichiometry; it can, therefore, be found also in membranes with sparsely distributed, rapidly transporting channels of any stoichiometry. Particular to model B is a change in the signs ofC t andG t at the reversal potential of the steady-state current-voltage relationship. This implies switching from capacitive to inductive behavior (under vanishing amplitudes). Also in model B, the nonsteady-state effects disappear for large voltage displacements from the reversal potential. Model B is expected to occur preferably in transporters subject to metabolic control.