A mathematical model of rat cortical collecting duct: determinants of the transtubular potassium gradient.

Abstract

In assessing disorders of potassium excretion, urine composition is used to calculate the transtubular gradient (TTKG), as an estimate of tubule fluid concentration, at a point when the fluid was last isotonic to plasma, namely, within the cortical collecting duct (CCD). A mathematical model of the CCD has been developed, consisting of principal cells and alpha- and beta-intercalated cells, and which includes Na(+), K(+), Cl(-), HCO, CO(2), H(2)CO(3), phosphate, ammonia, and urea. Parameters have been selected to achieve fluxes and permeabilities compatible with data obtained from perfusion studies of rat CCD under the influence of both antidiuretic hormone and mineralocorticoid. Both epithelial (flat sheet) and tubule models have been configured, and model calculations have focused on the determinants of the TTKG. Using the epithelial model, luminal K(+) concentrations can be computed at which K(+) secretion ceases (0-flux equilibrium), and this luminal concentration derives from the magnitude of principal cell peritubular uptake of K(+) via the Na-K-ATPase, relative to principal cell peritubular membrane K(+) permeability. When the model is configured as a tubule and examined in the context of conditions in vivo, osmotic equilibration of luminal fluid produces a doubling of the initial K(+) concentration, which, depending on delivered load, may be substantially greater than the zero-flux equilibrium value. Under such circumstances, the CCD will be a site for K(+) reabsorption, although the relatively low permeability ensures that this reabsorptive flux is likely to be small. Osmotic equilibration may also raise luminal NH(3) concentrations well above those in cortical blood. In this situation, diffusive reabsorption of NH(3) provides a mechanism for base reclamation without the metabolic cost of active proton secretion.