Regulation of K transport in a mathematical model of the cortical collecting tubule.

The effect of luminal flow rate and peritubular pH on Na and K transport is investigated in a mathematical model of the rabbit cortical collecting tubule. The model is used to simulate a 0.4-cm segment of tubule comprised of principal cell, alpha- and beta-intercalated cells, and lateral interspace. Calculations produce luminal profiles of Na, K, Cl, HCO3, and phosphate, as well as of electrical potential and pH. Parameter sets are developed that permit representation of both unstimulated and deoxycorticosterone acetate-stimulated tubules. A series of simulations is performed in which initial luminal flow rate is varied over the range of values between 0.1 and 30 nl/min. A marked flow-dependent enhancement of Na reabsorption and K secretion is seen, especially at lower flows, while Cl and HCO3 transport remain relatively constant. In experimental studies, it has been observed that metabolic alkalosis stimulates and metabolic acidosis inhibits K secretion, while leaving Na transport relatively unaffected [B. A. Stanton and G. Giebisch. Am. J. Physiol. 242 (Renal Fluid Electrolyte Physiol. 11): F544-F551, 1982; K. Tabei, S. Muto, Y. Ando, Y. Sakairi, and Y. Asano. J. Am. Soc. Nephrol. 1: 693, 1990; and K. Tabei, S. Muto, H. Furuya, and Y. Asano. J. Am. Soc. Nephrol. 2: 752, 1991]. Model calculations indicate that, when ion permeabilities are fixed and not dependent on pH, the impact of peritubular HCO3 on K secretion cannot be simulated. When junctional Cl permeability decreases with increasing interspace pH (E. M. Wright and J. M. Diamond. Biochim. Biophys. Acta 163: 57-74, 1968) in the model, there is a marked stimulation of K secretion with alkalosis and inhibition with acidosis. Furthermore, inclusion of a pH-dependent apical Na permeability [L. G. Palmer and G. Frindt. Am. J. Physiol. 253 (Renal Fluid Electrolyte Physiol. 22): F333-F339, 1987] that increases with increasing principal cell pH significantly reduces the change in Na+ reabsorption seen with the pH-dependent junctional Cl permeability alone. In these calculations, a pH-dependent apical K permeability [W. Wang, A. Schwab, and G. Giebisch. Am. J. Physiol. 259 (Renal Fluid Electrolyte Physiol. 28): F494-F502, 1990] that increases with increasing principal cell pH shows relatively little impact on K secretion.