A Mathematical Model of the Diluting Power of the Cortical Thick Ascending Limb of the Loop of Henle

Abstract

A mathematical model is presented that describes the ionic transport across the cortical thick ascending limb (cTAL) of the Henle's loop, taking into account its tubular geometry. A comprehensive description of the cTAL is given for the first time in terms of potential, ion concentrations and ion fluxes along the tubule. For given ion concentrations at the entrance of the tubule, the model simulates steady-state profiles and allows the fitting of existing experimentally measured values at its exit. Moreover, the model expands the potentialities of experiments in situ and enables testing the effect of different perturbations induced by drugs or mutation-altering transport activity. One of the main insights given by this model is the increase of the lumenal electrical potential from the entrance to the exit of the tubule with a profile determined by the transepithelial electrical potential difference and by the chemical gradients along the lumen, both reflecting transepithelial salt transport. Furthermore, model and experimental results are consistent, showing that when the TAL is perfused at high rates with a diluted NaCl solution in relation to the bath, the transepithelial electrical potential difference increases from 6.7 to 23.0 mV and the potential difference across the basolateral barrier changes very little. The model predicts that the same static head is obtained independently of the NaCl concentration at the entrance of the tubule. A final important insight concerns the lowest reported NaCl concentrations (20-30 mM) at the exit of the tubule, which is controlled by a very tight epithelium, where the back-leak is substantially reduced.