Flux ratio theorems for nonstationary membrane transport with temporary capture of tracer

It has been shown recently that the ratio of unidirectional tracer fluxes, passing in opposite directions through a membrane which has transport properties varying arbitrarily with the distance from a boundary, is independent of time from the very first appearance of the two outfluxes from the membrane. This surprising proposition has been proved for boundary conditions defining standard unidirectional fluxes, and then generalized to classes of time-dependent boundary conditions. The operational meaning of all the resulting theorems is that when any of them appear to be refuted experimentally, the presence of more than one parallel transport pathway (that is, of membrane heterogeneity transverse to the direction of transport) can be inferred and analyzed. Recent experimental data have been interpreted accordingly. However, the proofs of the theorems given so far have not taken into account the possibility of temporary capture of tracer at sites fixed in the membrane (including also entrances to microscopic culs-de-sac). The possible presence of such a process, which would not affect fluxes in the steady state, left a fundamental gap in the aforementioned inferences. It is shown here that all the theorems previously proved for the flux ratio under unsteady conditions remain valid when temporary capture of tracer is admitted, no matter how the rate of capture, and the probability distribution of residence times of tracer at capture sites, may depend on the distance from a membrane boundary. The validity of the aforementioned inferences from observed time-dependence of the flux ratio is thereby extended to a much wider class of membrane transport processes.