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

A problem often confronted in analyses of charge-carrying transport processes in vivo lies in identifying porter-specific 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 on dI-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 linking n (3 or more) discrete states of a carrier 'molecule.' State transitions include one membrane charge-transport step and one solute-binding step. Fundamental properties of dI-V relations are derived analytically for all n-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, illustrate dI-V curves under principle limiting conditions. Class I models generate a wide range of dI-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 of dI-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.(ABSTRACT TRUNCATED AT 400 WORDS)