Coupling of entry to exit by peritubular K+ permeability in a mathematical model of rat proximal tubule

In the proximal tubule in vivo, glomerulotubular balance requires that tubule epithelial cells accommodate a twofold variation in Na+ reabsorption through the Na+/H+ exchanger of the luminal membrane. In a mathematical model of proximal tubule, in which permeability coefficients are fixed, doubling flux through the Na+/H+ antiporter produces a substantial increase in cell volume and cytosolic HCO3-. In this model, it is possible to vary peritubular K+ permeability with changes in luminal Na+ entry, so that cell volume is constrained to be constant; In these calculations, the model predicts that peritubular hyperpolarization and nearly constant cytosolic HCO3- will accompany increases in luminal Na+ entry. Realistic models of variable peritubular K+ permeability might include a functional dependence on flux through the Na+-K+-adenosinetriphosphatase, cytosolic pH, or cell volume. When K+ permeability is represented as a function of any of these variables, homeostatic control of cell volume and pH can be obtained over a physiological variation of Na+/H+ flux. However, when luminal Na+ entry is via Na+-glucose cotransport, volume homeostasis is best when peritubular K+ permeability depends on the rate of active Na+ transport. For any modulator of K+ permeability, realistic constraints on the value of this parameter suggest that peritubular K+ permeability is, by itself, not sufficient to maintain cell volume within narrow limits. Parallel activation of another exit pathway, such as peritubular Na+-3 HCO3- cotransport, may be required to achieve the necessary homeostasis.