Relations between chord and slope conductances and equivalent electromotive forces

Nonlinear current-voltage relations for ion movement across biological membranes have been observed and significantly complicate the interpretation of electrical measurements on these transport processes. To enable analysis of the electrical measurements two formalisms have evolved, chord and slope, by which equivalent conductances and electromotive forces (emfs) can be obtained. Because, in the presence of nonlinear relations between current and voltage, the chord conductances and emfs are generally not equal to their slope counterparts, it is imperative that they not be intermixed (8). However, when the functional relationship between the current and voltage is known, such as the Goldman-Hodgkin-Katz (GHK) flux equation, it becomes possible to compare the voltage dependencies of these parameters and examine interrelationships between them. In this communication analytical expressions are derived for the chord and slope conductances and emfs for transport of a single ionic species that obeys the GHK flux equation. Using these expressions, it is possible to convert electrical equivalent circuit parameters derived for one formalism to electrical equivalent parameters of the other formalism. Therefore data obtained using either formalism can be used to obtain values for intracellular activity and membrane permeability to the transported ion. Parallel analyses can be applied to other models of ion transport.