Weak acid permeability of a villous membrane: Formic acid transport across rat proximal tubule

Chloride/formate exchange, in parallel with Na⁺/H⁺ exchange and nonionic diffusion of H₂CO₂, has been proposed as a mechanism of electroneutral transcellular Cl⁻ reabsorption by the proximal tubule. However, the measured brush border H₂CO₂ permeability of the rat proximal tubule is at least an order of magnitude too low to support sufficient H₂CO₂ recycling. To investigate the possibility that an unstirred layer within the brush border might depress the measured H₂CO₂ permeability, we constructed a mathematical model of a villous membrane. Axial fluxes along villous and intervillous spaces were specified by Nernst-Planck diffusion equations. Model parameters were set to achieve agreement with ion and water fluxes measured in the rat proximal tubule. The equations were solved numerically to generate steady-state concentration profiles in the villous and intervillous spaces. An apparent brush border H₂CO₂ permeability was determined by perturbing luminal [H₂CO₂] and calculating the change in H₂CO₂ flux. Overall, the ratio of apparent brush border H₂CO₂ permeability to cell membrane H₂CO₂ permeability was greater than 90%. Contributing to the small decrease in apparent permeability are finite diffusion coefficients, folding of the membrane, and acidification of the luminal solution. An approximate analysis of this system shows the critical parameters of brush border formate transport to be the actual membrane H₂CO₂ permeability, and the diffusion coefficients of HCO ₃ ⁻ and HCO ₃ ⁻ . Nevertheless, decreasing the diffusion coefficients by one order of magnitude failed to depress apparent brush border H₂CO₂ permeability by more than an additional 25%. We conclude that although permeability is systematically underestimated across a villous membrane, unstirred layer effects in the brush border are still too small to resolve the discrepancy between the measured value of H₂CO₂ permeability and the value needed to allow recycling.