A mathematical model of rat collecting duct. I. Flow effects on transport and urinary acidification.

A mathematical model of the rat collecting duct (CD) has been developed by concatenating previously published models of cortical (Weinstein AM. Am J Physiol Renal Physiol 280: F1072-F1092, 2001); outer medullary (Weinstein AM. Am J Physiol Renal Physiol 279: F24-F45, 2000); and inner medullary segments (Weinstein AM. Am J Physiol Renal Physiol 274: F841-F855, 1998). Starting with end-distal tubular flow rate and composition, plus interstitial solute profiles, the model predicts urinary solute flows, including the buffer concentrations required to assess net acid excretion. In the model CD, the interstitial corticomedullary osmotic gradient provides the basis for the flow effect on the transport of several solutes. For substances that have an interstitial accumulation and that can have diffusive secretion (e.g., urea and NH(4)(+)), enhanced luminal flow increases excretion by decreasing luminal accumulation. For substances that are reabsorbed (e.g., K+ and HCO(3)(-)), and for which luminal accumulation can enhance reabsorption, increasing luminal flow again increases excretion by decreasing luminal solute concentration. In model calculations, flow-dependent increases in HCO(3)(-) and NH(4)(+) approximately balance, so net acid excretion is little changed by flow, albeit at a higher urinary pH. The model identifies delivery flow rate to the CD as a potent determinant of urinary pH, with high flows blunting maximal acidification. At even modestly high flows (9 nl x min-1. tubule-1, with 6% of filtered Na+ entering the CD), the model cannot achieve a urinary pH <5.5 unless the delivered HCO(3)(-) concentration is extremely low (<2 mM). Nevertheless, simulation of Na2SO4 diuresis does yield both an increase in net acid excretion and a decrease in urinary HCO(3)(-) (i.e., a decrease in pH) despite the increase in urinary flow. This model should provide a tool for examining hypotheses regarding transport defects underlying distal renal tubular acidosis.