A mathematical model of the rat proximal tubule

Abstract

The equations of mass conservation and electroneutrality are used to extend a nonequilibrium thermodynamic model of the rat proximal tubule epithelium to a representation of a 0.5-cm segment of tubule. The output of the tubule model includes the luminal profiles and absolute proximal reabsorption of Na, K, Cl, HCO3, HPO4, H2PO4, glucose, and urea, generated by the epithelial model. Transport rates and permeabilities, chosen in agreement with those of the rat, result in luminal glucose and bicarbonate depletion and a transition from an electronegative to positive lumen. Despite the development of significant transepithelial osmotic driving forces (a transepithelial glucose gradient and Cl-HCO3 asymmetry), intraepithelial solute-solvent coupling remains an important force for water reabsorption along the proximal tubule length. In particular, this means that when osmotic gradients that appear under free-flow conditions are used in the calculation of the epithelial water permeability, a substantial overestimate of this permeability will be obtained. A single first-order differential equation has been derived in conjunction with an approximate nonelectrolyte model of the proximal tubule that represents both coupled and gradient-driven water reabsorption. In the present work, this equation is shown to yield an accurate description of water transport by the comprehensive tubule model.