Advertisement

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
Article

Abstract

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.

Keywords

Formic Acid Proximal Tubule Weak Acid Brush Border H2CO 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Aronson, P. S. 1984. Electrochemical driving forces for secondary active transport: energetics and kinetics of Na+−H+ exchange and Na+-glucose cotransport.In:Electrogenic Transport: Fundamental Principles and Physiological Implications, M. P. Blaustein and L. Lieberman (Eds), pp. 49–70. New York: Raven Press.Google Scholar
  2. Barry, P. and J. Diamond. 1984. Effects of unstirred layers on membrane phenomena.Physiol. Rev. 64, 763–872.Google Scholar
  3. Carpi-Medina, P., E. Gonzalez and G. Whittembury. 1983. Cell osmotic water permeability of isolated rabbit proximal convoluted tubules.Am. J. Physiol. 244, F554-F563.Google Scholar
  4. Cassola, A. C., M. Mollenhauer and E. Frömter. 1983. The intracellular chloride activity of rat kidney proximal tubular cells.Pflügers Arch. ges. Physiol. 399, 259–265.CrossRefGoogle Scholar
  5. Dobyan, D. C. and R. E. Bulger. 1982. Renal carbonic anhydrase.Am. J. Physiol. 243, F311-F324.Google Scholar
  6. DuBose, T. D., L. R. Pucacco, D. W. Seldin and N. W. Carter. 1978. Direct determination of pCO2 in the rat renal cortex.J. Clin. Invest. 62, 338–348.Google Scholar
  7. Edelman, A., S. Curci, I. Samarzija and E. Frömter. 1978. Determination of intracellular K+ activity in rat kidney proximal tubular cells.Pflügers Arch. ges. Physiol. 378, 37–45.CrossRefGoogle Scholar
  8. Guth, D. and W. von Engelhardt. 1989. Is gastro-intestinal mucus an ion-selective barrier?Symp. Soc. Exp. Biol. 43, 117–121.Google Scholar
  9. Gutknecht, J. and D. C. Tosteson. 1973. Diffusion of weak acids across lipid bilayer membranes: effects of chemical reactions in the unstirred layers.Science 182, 1258–1261.Google Scholar
  10. Irving, M., J. Maylie, N. L. Sizto and W. K. Chandler. 1990. Intracellular diffusion in the presence of mobile buffers: application to proton movement inmuscle.Biophys. J. 57, 717–721.CrossRefGoogle Scholar
  11. Junge, W. and S. McLaughlin. 1987. The role of fixed and mobile buffers in the kinetics of proton movement.Biochim. Biophys. Acta 890, 1–5.CrossRefGoogle Scholar
  12. Karniski, L. and P. Aronson. 1985. Chloride/formate exchange with formic acid recycling: a mechanism of active chloride transport across epithelial membranes.Proc. natn. Acad. Sci. U.S.A. 82, 6362–6365.CrossRefGoogle Scholar
  13. Kurtz, I., R. Star, R. S. Balaban, J. L. Garvin and M. A. Knepper. 1986. Spontaneous luminal disequilibrium pH in S3 proximal tubules. Role in ammonia and bicarbonate transport.J. Clin. Invest. 78, 989–996.Google Scholar
  14. Lonnerholm, G. and Y. Ridderstrale. 1980. Intracellular distribution of carbonic anhydrase in the rat kidney.Kidney. Int. 17, 162–174.Google Scholar
  15. Maunsbach, A. B. 1973. Ultrastructure of the proximal tubule. In:Handbook of Physiology. Renal Physiology, J. Orloff, R. W. Berliner and S. R. Geiger (Eds), Sec. 8, Chap. 2, pp. 31–79. Washington, DC: American Physiological Society.Google Scholar
  16. Maunsbach, A. B., G. H. Giebisch and B. A. Stanton. 1987. Effects of flow rate on proximal tubule ultrastructure.Am. J. Physiol. 253, F582-F587.Google Scholar
  17. Passow, H. 1967. Steady-state diffusion of non-electrolytes through epithelial brush borders.J. theor. Biol. 17, 383–398.CrossRefGoogle Scholar
  18. Preisig, P. and R. Alpern. 1989. Contributions of cellular leak pathways to net NaHCO3 and NaCl absorption.J. clin. Invest. 83, 1859–1867.Google Scholar
  19. Richardson, I. W. 1977. Membrane structure and passive flows.Adv. biol. Med. Phys. 16, 195–205.Google Scholar
  20. Richardson, I. W., V. Licko and E. Bartoli. 1973. The nature of passive flows through tightly folded membranes. The influence of microstructure.J. Membrane Biol. 11, 293–308.CrossRefGoogle Scholar
  21. Schild, L., G. Giebisch, L. Karniski and P. Aronson. 1987. Effect of formate on volume reabsorption in the rabbit proximal tubule.J. clin. Invest. 79, 32–38.CrossRefGoogle Scholar
  22. Stephenson, J. L. 1978. Analysis of the transient behavior of kidney models.Bull. math. Biol. 40, 211–221.MathSciNetGoogle Scholar
  23. Walter, A., D. Hastings and J. Gutknecht. 1982. Weak acid permeability through lipid bilayer membranes: role of chemical reactions in the unstirred layer.J. gen. Physiol. 79, 917–933.CrossRefGoogle Scholar
  24. Wang, T., G. Giebisch and P. S. Aronson. 1992. Effects of formate and oxalate on volume absorption in rat proximal tubule.Am. J. Physiol. 263, F37-F42.Google Scholar
  25. Weinstein, A. M. 1990. A mathematical model of the proximal nephron.Math. Comput. Modelling 14, 522–528.MATHCrossRefGoogle Scholar
  26. Weinstein, A. M. 1992. Chloride transport in a mathematical model of the rat proximal tubule.Am. J. Physiol. 263, F784-F798.Google Scholar
  27. Welling, L. W. and D. J. Welling. 1975. Surface areas of brush border and lateral cell walls in the rabbit proximal nephron.Kidney Int. 8, 343–348.Google Scholar
  28. Welling, L. W., D. J. Welling and T. J. Ochs. 1983. Video measurement of basolateral membrane hydraulic conductivity in the proximal tubule.Am. J. Physiol. 245, F123-F129.Google Scholar
  29. Winne, D. 1978. The permeability coefficient of the wall of a villous membrane.J. math. Biol. 6, 95–108.MATHGoogle Scholar
  30. Yoshitomi, K. and E. Frömter. 1985. How big is the electrochemical potential difference of Na+ across rat renal proximal tubular cell membranesin vivo?Pflügers Arch. gen. Physiol. 405, S121-S126.CrossRefGoogle Scholar

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.

Personalised recommendations