Nonequilibrium thermodynamic model of the rat proximal tubule epithelium

The rat proximal tubule epithelium is represented as well-stirred, compliant cellular and paracellular compartments bounded by mucosal and serosal bathing solutions. With a uniform pCO2 throughout the epithelium, the model variables include the concentrations of Na, K, Cl, HCO3, H2PO4, HPO4, and H, as well as hydrostatic pressure and electrical potential. Except for a metabolically driven Na-K exchanger at the basolateral cell membrane, all membrane transport within the epithelium is passive and is represented by the linear equations of nonequilibrium thermodynamics. In particular, this includes the cotransport of Na-Cl and Na-H2PO4 and countertransport of Na-H at the apical cell membrane. Experimental constraints on the choice of ionic conductivities are satisfied by allowing K-Cl cotransport at the basolateral membrane. The model equations include those for mass balance of the nonreacting species, as well as chemical equilibrium for the acidification reactions. Time-dependent terms are retained to permit the study of transient phenomena. In the steady state the energy dissipation is computed and verified equal to the sum of input from the Na-K exchanger plus the Gibbs free energy of mass addition to the system. The parameter dependence of coupled water transport is studied and shown to be consistent with the predictions of previous analytical models of the lateral intercellular space. Water transport in the presence of an end-proximal (HCO3-depleted) luminal solution is investigated. Here the lower permeability and higher reflection coefficient of HCO3 enhance net sodium and water transport. Due to enhanced flux across the tight junction, this process may permit proximal tubule Na transport to proceed with diminished energy dissipation.