Compartmental analysis of the Na+ flux ratio with application to data on frog skin epidermis

In this computer simulation study, the role of the topological factor on the Na+ influx/backflux (efflux) ratio in multicompartmental model membranes with active Na+ transport has been investigated. As in the classical "three compartment model", so also in multicompartment models with series order of compartments (series topology), the flux ratios are time-independent. By contrast, in models with series-parallel order of compartments (series-parallel topology), inclusive shunt pathways, the flux ratios are time-dependent. The values of the ratios can increase, or decrease with time, reaching steady state values, depending on the nature of the chosen topology. In a similar manner, the apparent value of the driving force, ENa, of the Na+-pumps, calculated from the Ussing-Teorell flux ratio equation and using global flux ratios, can vary in models with series-parallel topology. This is not the case in models with series topology. On the other hand, the true value of the driving forces of the Na+ pumps, calculated from local flux ratios, are higher, and time-independent. In the absence of Na+ pumps (simulated ouabain effect) the flux ratios have in all cases the values of 1.0. These theoretical results are in good agreement with the theoretical results recently published by Sten-Knudsen & Ussing (1981) whose analysis utilized principles differing from those used here. In the design of the multicompartment model and the choice of kinetic parameters, frog skin epidermis served as a guide, such that simulated outputs closely agreed with experimental data in the literature. This includes the realization of a "fast" paracellular, and a "slow" cellular pathway for transepidermal flow of Na+.