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.

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

The chapter 'Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model' has now been made available open access under a CC BY 4.0 license.

Analysis of the sodium recirculation theory of solute-coupled water transport in small intestine.

Our previous mathematical model of solute-coupled water transport through the intestinal epithelium is extended for dealing with electrolytes rather than electroneutral solutes. A 3Na+-2K+ pump in the lateral membranes provides the energy-requiring step for driving transjunctional and translateral flows of water across the epithelium with recirculation of the diffusible ions maintained by a 1Na+-1K+-2Cl- cotransporter in the plasma membrane facing the serosal compartment. With intracellular non-diffusible anions and compliant plasma membranes, the model describes the dependence on membrane permeabilities and pump constants of fluxes of water and electrolytes, volumes and ion concentrations of cell and lateral intercellular space (lis), and membrane potentials and conductances. Simulating physiological bioelectrical features together with cellular and paracellular fluxes of the sodium ion, computations predict that the concentration differences between lis and bathing solutions are small for all three ions. Nevertheless, the diffusion fluxes of the ions out of lis significantly exceed their mass transports. It is concluded that isotonic transport requires recirculation of all three ions. The computed sodium recirculation flux that is required for isotonic transport corresponds to that estimated in experiments on toad small intestine. This result is shown to be robust and independent of whether the apical entrance mechanism for the sodium ion is a channel, a SGLT1 transporter driving inward uphill water flux, or an electroneutral Na+-K+-2Cl- cotransporter.