The diagram methods for the evaluation of exchange fluxes in membrane transport systems

In this paper theoretical methods for the evaluation of fluxes of ligand exchange processes in a transporter-mediated membrane transport system are studied. The exchange process of a transport system is defined as a set of reactions of the transporters in the membrane that do not result in a complete turnover and must include the following consecutive sequence of steps: the binding of ligands from bath 1 and a subsequent release of bound ligands to bath 2 followed immediately by a binding of ligands from bath 2 and a subsequent release of bound ligands to bath 1. Thus, unlike the ordinary one-way cycles, the completion of an exchange process does not result in a net transport of ligands across the membrane. However, since it exchanges the ligands between the two baths, the exchange process of a transport system is closely related to the operational tracer flux of labelled ligands in the system. In this paper, both the numerical and the analytical procedures for the evaluation of exchange fluxes in any given biochemical diagram are discussed. In particular, we show that the exchange fluxes of a given kinetic diagram, like one-way cycle fluxes, can be expressed analytically in terms of the rate constants of the diagram with the use of either the original diagram or an expanded diagram. The diagram methods presented in this paper should be very useful in analyzing the mechanisms of transporter-mediated transport systems when tracer flux data are available.