Mathematical models of renal fluid and electrolyte transport: acknowledging our uncertainty

Abstract

Mathematical models of renal tubular function, with detail at the cellular level, have been developed for most nephron segments, and these have generally been successful at capturing the overall bookkeeping of solute and water transport. Nevertheless, considerable uncertainty remains about important transport events along the nephron. The examples presented include the role of proximal tubule tight junctions in water transport and in regulation of Na(+) transport, the mechanism by which axial flow in proximal tubule modulates solute reabsorption, the effect of formate on proximal Cl(-) transport, the assessment of potassium transport along collecting duct segments inaccessible to micropuncture, the assignment of pathways for peritubular Cl(-) exit in outer medullary collecting duct, and the interaction of carbonic anhydrase-sensitive and -insensitive pathways for base exit from inner medullary collecting duct. Some of these uncertainties have had intense experimental interest well before they were cast as modeling problems. Indeed, many of the renal tubular models have been developed based on data acquired over two or three decades. Nevertheless, some uncertainties have been delineated as the result of model exploration and represent communications from the modelers back to the experimental community that certain issues should not be considered closed. With respect to model refinement, incorporating more biophysical detail about individual transporters will certainly enhance model reliability, but ultimate confidence in tubular models will still be contingent on experimental development of critical information at the tubular level.

Quantitative estimation of transmembrane ion transport in rat renal collecting duct principal cells

“…A significant contribution to the development of epithelial cell models in the context of renal physiology was made by Weinstein (Weinstein 1997(Weinstein , 1999(Weinstein , 2000(Weinstein , 2001(Weinstein , 2003, who focused on the simulation of in vivo conditions and on modeling of cells as a part of the epithelial layer to answer the questions raised by the results of microperfusion experiments on renal tubules (Weinstein, 2003). He developed a mathematical model of the OMCD consisting only of α-intercalated cells (Weinstein 2000) and then updated it (Weinstein 2010) to include a population of principal cells that were identical to those of CCD.…”

“…A biophysical model could be useful as an instrument for interpretation of the data and extrapolation of the tubule function from experimental conditions to those in vivo. Existing models of principal collecting duct cells made by Weinstein (Weinstein 1997(Weinstein , 1999(Weinstein , 2000(Weinstein , 2001(Weinstein , 2003 were used to simulate the function of the renal epithelium in vivo. Due to their complexity it is impossible to use them as a practical tool to analyze experimental recordings obtained from individual cells.…”

Activation of the apical Na+/H+exchanger NHE3 by formate: a basis of enhanced fluid and electrolyte reabsorption by formate in the kidney

“…Two studies in microperfused kidney proximal tubule have not been consistent in detecting stimulation of apical Cl Ϫ /base exchange by formate (7,20). These results have raised serious questions in regard to the role of apical Cl Ϫ /formate exchange as the mediator of enhanced Na ϩ and Cl Ϫ reabsorption in the proximal tubule by formate (45).…”

A computational model for emergent dynamics in the kidney

“…Chang & Fujita's (2001) model also models water and solute reabsorption, and potassium secretion. These models are able to reproduce a wide range of experimental data, but there still remains considerable uncertainty about transporters along the nephron tubule (Weinstein 2003).…”