A Thermodynamic Analysis of Fluxes and Flux-Ratios in Biological Membranes

Flux and flux-ratio equations are derived on the basis of the phenomenological equations of irreversible thermodynamics. Deviations of flux-ratios from that given by the often quoted Ussing (1949) relation are predicted, even in the absence of active transport, by considering the dependence of coupled fluxes on the membrane potential. The treatment is extended to include the interpretation of fluxes measured with tracers. Estimation of the numerical values of the resistance coefficients show that the voltage dependence of the entrainment terms can adequately account for the departures from the Ussing relation and the discrepancies between isotopically and electrically measured membrane conductances