Interpretation and use of electrical equivalent circuits in studies of epithelial tissues

Whereas transepithelial and intracellular voltages continue to be measured in renal and other epithelial tissues, the origins of these voltages, especially in renal epithelia, remain obscure. Because epithelial tissues have multiple transcellular and extracellular routes of ion transport, it is convenient to model them with electrical equivalent circuits and, in this way, attempt to understand the relative importance of and relationships between the parallel-series arrangements of the membranes and barriers involved. The interpretation of the equivalent electromotive forces and resistances can be complicated, however, by virtue of nonlinear current-voltage relationships of ionic channels. Thus, for ion transport pathways displaying nonlinear I-V relationships, it is important to distinguish between chord and slope formalisms in the use and interpretation of electrophysiological data. For ions like Na that are generally not at electrochemical equilibrium, the Thévenin electromotive force (emf) of the slope formalism is not synonymous with the Nernst equilibrium potential of the chord formalism nor are the slope and chord conductances equal or constant at all voltages. Thus, it is mandatory that the empirical data be calculated and interpreted in a way consistent with the formalism adopted. The existence of nonlinear behavior, characterized by either Goldman or other types of rectification, exacerbates determination of relative ionic permeabilities, fractional resistances, transference numbers, and other electrophysiological parameters for simple membranes and especially for epithelia. It is argued that the use and interpretation of electrical equivalent circuits of epithelia are not arbitrary but must take into account nonlinearities of the ionic current-voltage relationships and concentration and voltage dependencies of the emfs and conductances.