Steady-state rate equations for unidirectional (isotope-exchange) rates can become so complex, even for rather simple (reversible) enzyme or membrane transport models, that they are useless for detailed data analysis. In this paper a procedure is described for simultaneous simulation of net (chemical) and isotope-exchange rates. The method employs an expanded version of the basic model to monitor explicitly the fate of the label in an experiment. The procedure is quite general, and can be used for steady-state as well as transient kinetic situations, or it can be used in conjunction with existing interactive computer programs for steady-state model analysis. Three numerical examples are presented. First, it is shown, using the conventional (Post-Albers) model for Na+/K(+)-ATPase, that the change in concentration of a labelled intermediate after a change in experimental conditions does not in general reflect the change in the total concentration of that intermediate, and thus labelled intermediate concentrations may be misleading. Second, using a standard co-transport model and a prototype active-transport model (equivalent to a ligand-ATPase), it is shown that the ratio of tracer transport fluxes at steady state yields transport stoichiometries which depend on the experimental conditions, are different from the net apparent stoichiometries, and whose changes with conditions are also different from that of the net stoichiometries. It follows that conclusions drawn on the basis of experimentally determined tracer fluxes should be viewed with some caution. Specifically, a measured influx stoichiometry ligand/ATP (in the ATPase case) of higher than 1:1 does not necessarily imply the existence of more than one site for either ligand on the enzyme.
Use of experimental isotope-exchange fluxes in reversible enzyme and membrane transport models, assessed by simultaneous computer simulation of unidirectional and net chemical rates