Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model.

Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171-186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces intracellular solute concentrations, ion and water fluxes, and electrophysiology of proximal convoluted tubule. The following were shown: 1. Water flux is given by active Na⁺ flux into lateral spaces, while osmolarity of absorbed fluid depends on osmotic permeability of apical membranes. 2. Following aquaporin "knock-out," water uptake is not reduced but redirected to the paracellular pathway. 3. Reported decrease in epithelial water uptake in aquaporin-1 knock-out mouse is caused by downregulation of active Na⁺ absorption. 4. Luminal glucose stimulates Na⁺ uptake by instantaneous depolarization-induced pump activity ("cross-talk") and delayed stimulation because of slow rise in intracellular [Na⁺]. 5. Rate of fluid absorption and flux of active K⁺ absorption would have to be attuned at epithelial cell level for the [K⁺] of the absorbate being in the physiological range of interstitial [K⁺]. 6. Following unilateral osmotic perturbation, time course of water fluxes between intraepithelial compartments provides physical explanation for the transepithelial osmotic permeability being orders of magnitude smaller than cell membranes' osmotic permeability. 7. Fluid absorption is always hyperosmotic to bath. 8. Deviation from isosmotic absorption is increased in presence of glucose contrasting experimental studies showing isosmotic transport being independent of glucose uptake. 9. For achieving isosmotic transport, the cost of Na⁺ recirculation is predicted to be but a few percent of the energy consumption of Na⁺/K⁺ pumps.