Theoretical model for glomerular filtration of charged solutes

Abstract

Previous experimental studies have revealed that for a given molecular size, the glomerular capillary wall restricts the passage of polyanions more than that of neutral macromolecules, and restricts transport of the latter more than that of polycations. We have developed a theoretical model of this charge-selectivity based on the following principal assumptions: a) all ions (tracer macromolecule and univalent cations and anions) obey a modified Nernst-Planck flux expression, including terms for convection and size-selective retardation; b) the capillary wall has a homogeneous distribution of fixed negative charges; and c) Donnan equilibria exist at the surfaces of this "membrane." To allow specific application of the model we measured electrophoretic mobilities of narrow fractions of dextran sulfate (DS) and diethylaminoethyl dextran (DEAE), and used these to estimate effective molecular charge as a function of molecular size. Based on these measurements and fractional clearance data for DS and DEAE reported previously for the normal Munich-Wistar rat, the capillary wall has an apparent fixed charge concentration of 120--170 meq/liter. The effects of this membrane charge on the filtration of water and on the transcapillary electrical potential difference are also discussed.