Transfers between free and combined oxygen flows in determining facilitated transport with membranes on the transport path

The facilitated transport of a species brought about by a diffusible carrier is mediated by the sharing of the total flow between the flow of the free species (fd) and of the species-carrier compound (fc). The presence of membranes impermeable to the carrier on the transport path is accompanied by transfers between fd and fc in regions next to the membranes. These transfers are associated with differences between the current species-carrier concentration and the one that would exist at chemical equilibrium with the free species. These differences determine that the actual facilitated transport is smaller than the possible maximum. Analytic approximations to describe these differences are obtained; they are expressed in terms of physiochemical entities germane to the transport. This leads to a better conceptual understanding of the process. A relatively small system of algebraic equations for the numerical solution of the facilitated transport is formulated. A feature of this approach is that, instead of matching the values of functions at some points, the flows derived from integrals evaluated over some intervals are matched. The expressions for the physicochemical entities obtained contain the parameters explicitly; this permits analysis of the mechanisms involved in the dependence of the facilitated transport on the parameters of the system. It is shown, for instance, that the increase of the "on" chemical coefficient may result in either an increase or a decrease of the facilitated transport, depending on the current values of the parameters.