Bulletin of Mathematical Biology

, Volume 56, Issue 3, pp 459–490 | Cite as

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

  • Thomas A. Krahn
  • Peter S. Aronson
  • Alan M. Weinstein


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.


Formic Acid Proximal Tubule Weak Acid Brush Border H2CO 
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Copyright information

© Elsevier Science Ltd 1994

Authors and Affiliations

  • Thomas A. Krahn
    • 1
  • Peter S. Aronson
    • 1
  • Alan M. Weinstein
    • 2
  1. 1.Yale University School of MedicineNew HavenU.S.A.
  2. 2.Cornell University Medical CollegeNew YorkU.S.A.

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