Incorporation of membrane potential into theoretical analysis of electrogenic ion pumps.

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Abstract
The transport rate of an electrogenic ion pump, and therefore also the current generated by the pump, depends on the potential difference (.DELTA..PSI.) between the two sides of the membrane. This dependence arises from at least three sources: (i) charges carried across the membrane by the transported ions; (ii) protein charges in the ion binding sites that alternate between exposure to (and therefore electrical contact with) the two sides of the membrane; (iii) protein charges or dipoles that move within the domain of the membrane as a result of conformational changes linked to the transport cycle. Quantitative prediction of these separate effects requires presently unavailable molecular information, so that there is great freedom in assigning voltage dependence to individual steps of a transport cycle when one attempts to make theoretical calculations of physiological behavior for an ion pump for which biochemical data (mechanism, rate constants, etc.) are already established. The need to make kinetic behavior consistent with thermodynamic laws, however, limits this freedom, and in most cases two points on a curve of rate versus .DELTA..PSI. will be fixed points independent of how voltage dependence is assigned. Theoretical discussion of these principles is illustrated by reference to ATP-driven Na, K pumps. Physiological data for this system suggest that all three of the possible mechanisms for generating voltage dependence do in fact make significant contributions.