A mathematical model of the inner medullary collecting duct of the rat: pathways for Na and K transport

Abstract

A mathematical model of the inner medullary collecting duct (IMCD) of the rat has been developed representing Na+, K+, Cl−,[Formula: see text] CO2, H2CO3, phosphate, ammonia, and urea. Novel model features include: finite rates of hydration of CO2, a kinetic representation of the H-K-ATPase within the luminal cell membrane, cellular osmolytes that are regulated in defense of cell volume, and the repeated coalescing of IMCD tubule segments to yield the ducts of Bellini. Model transport is such that when entering Na+ is 4% of filtered Na+, approximately 75% of this load is reabsorbed. This requirement renders the area-specific transport rate for Na+ comparable to that for proximal tubule. With respect to the luminal membrane, there is experimental evidence for both NaCl cotransport and an Na+ channel in parallel. The experimental constraints that transepithelial potential difference is small and that the fractional apical resistance is greater than 85% mandate that more than 75% of luminal Na+ entry be electrically silent. When Na+delivery is limited, an NaCl cotransporter can be effective at reducing luminal Na+ concentration to the observed low urinary values. Given the rate of transcellular Na+ reabsorption, there is necessarily a high rate of peritubular K+recycling; also, given the lower bound on luminal membrane Cl− reabsorption, substantial peritubular Cl− flux must be present. Thus, if realistic limits on cell membrane electrical resistance are observed, then this model predicts a requirement for peritubular electroneutral KCl exit.