Interpretation of steady-state current-voltage curves: Consequences and implications of current subtraction in transport studies

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Abstract
Summary A problem often confronted in analyses of chargecarrying transport processesin vivo lies in identifying porterspecific component currents and their dependence on membrane potential. Frequently, current-voltage (I–V)—or more precisely, difference-current-voltage (dI-V)—relations, both for primary and for secondary transport processes, have been extracted from the overall membrane current-voltage profiles by subtracting currents measured before and after experimental manipulations expected to alter the porter characteristics only. This paper examines the consequences of current subtraction within the context of a generalized kinetic carrier model for Class I transport mechanisms (U.-P. Hansen, D. Gradmann, D. Sanders and C.L. Slayman, 1981,J. Membrane Biol. 63:165–190). Attention is focused primarily ondI-V profiles associated with ion-driven secondary transport for which external solute concentrations usually serve as the experimental variable, but precisely analogous results and the same conclusions are indicated in relation to studies of primary electrogenesis. The model comprises a single transport loop linkingn (3 or more) discrete states of a carrier ‘molecule.’ State transitions include one membrane chargetransport step and one solute-binding step. Fundamental properties ofdI-V relations are derived analytically for alln-state formulations by analogy to common experimental designs. Additional features are revealed through analysis of a “reduced” 2-state empirical form, and numerical examples, computed using this and a “minimum” 4-state formulation, illustratedI-V curves under principle limiting conditions. Class I models generate a wide range ofdI-V profiles which can accommodate essentially all of the data now extant for primary and secondary transport systems, including difference current relations showing regions of negative slope conductance. The particular features exhibited by the curves depend on the relative magnitudes and orderings of reaction rate constants within the transport loop. Two distinct classes ofdI-V curves result which reflect the relative rates of membrane charge transit and carrier recycling steps. Also evident in difference current relations are contributions from ‘hidden’ carrier states not directly associated with charge translocation in circumstances which can give rise to observations of counterflow or exchange diffusion. Conductance-voltage relations provide a semi-quantitative means to obtaining pairs of empirical rate parameters. It is demonstrated thatdI-V relationscannot yield directly meaningful transport reversal potentials in most common experimental situations. Well-defined arramgements of reaction constants are shown to givedI-V curves which exhibit little or no voltage sensitivity and finite currents over many tens to hundreds of millivoltsincluding the true reversal potential. Furthermore, difference currents show apparent Michaelian kinetics with solute concentration atall membrane potentials. These findings bring into question several previous reports of reversal potentials, stoichiometries and apparent current-source behavior based primarily on difference current analysis. They also provide a coherent explanation for anomolous and shallow conductances and paradoxical situations in which charge stoichiometry varies with membrane potential.