A mathematical model of the brush border of the proximal tubule (T. A. Krahn, P. S. Aronson, and A. M. Weinstein. Bull. Math. Biol, 56: 459-490, 1994) has been extended by the inclusion of CO2 and H2CO3 as diffusible species and by the inclusion of finite rate constants for the hydration of CO2. This permits the simulation of carbonic anhydrase (CA) activity and its inhibition. We confirm the result of our previous study, which is that, in the presence of CA, the unstirred layer has only a modest effect on the observed formic acid permeability. CA inhibition results in disequilibrium pH gradients, and the effect of these gradients on formic acid permeability depends on the presence of other membrane transport proteins. We also examined the impact of CA activity on the flux of total CO2 through the brush border. Under physiological conditions, CA inhibition depressed NaHCO3 reabsorption through the brush border by interfering with the HCO3(-)-facilitated diffusion of CO2. However, the determination of brush-border CO2 permeability, using an imposed CO2 gradient, was relatively uninfluenced by CA activity. Finally, we inserted a kinetic representation of the Na+/H+ exchanger into the brush-border model. Even when luminal and cytosolic diffusion coefficients were increased 1,000-fold, there was no effect on brush-border Na+ flux. This suggests that variations in the unstirred layer cannot be responsible for the flow dependence of Na+ reabsorption.
Determination of unidirectional uptake rates for lipids across the intestinal brush border
