Flux Ratio and Driving Forces in a Model of Active Transport

In order to analyze the energetics of active transport, a hypothetical carrier model is considered in which the active transport process is reduced to a minimal number of elementary steps. The relation between the following three quantities is examined: The affinity of the reaction driving the active transport, the ratio of isotope fluxes between identical solutions (“short-circuit”), and the maximal chemical potential difference which the active transport system can maintain. The interdependence of isotopeinteraction and the degree of coupling between transport and chemical reaction is shown explicitly: when the transport and chemical reaction are completely coupled, there is marked isotope interaction. In general, the logarithm of the short-circuit flux ratio (multiplied by RT) and the maximal chemical potential are not equal. The two quantities are approximately equal, when coupling between metabolism and transport is very loose, or when the reaction step is much faster than the transfer of the adsorbed solute across the barrier. Without prior knowledge of the kinetic parameters of the carrier, the maximal potential and the dependence of the metabolic reaction on solute flow have to be measured in order to derive the affinity of the driving reaction. Measurement of the flux ratio in the same system will then yield independent information on the carrier mechanism.