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A model of NaCl and water flow through paracellular pathways of renal proximal tubules

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Summary

To explain how hydrostatic pressure differences between tubule lumen and interstitium modulate isotonic reabsorption rates, we developed a model of NaCl and water flow through paracellular pathways of the proximal tubule. Structural elements of the model are a tight junction membrane, an intercellular channel whose walls transport NaCl actively at a constant rate, and a basement membrane. Equations of change were derived for the channel, boundary conditions were formulated from irreversible thermodynamics, and a pressure-area relationship typical of thin-walled tubing was assumed. The boundary value problem was solved numerically. The principal conclusions are: 1) channel NaCl concentration must remain within a few mOsm of isotonic values for reabsorption rates to be modulated by transtubular pressure differences known to affect this system; 2) basement membrane and channel wall parameters determine reabsorbate tonicity; tight junction parameters affect the sensitivity of reabsorption to transmural pressure; 3) channel NaCl concentration varies inversely with transmural pressure difference; this concentration variation controls NaCl diffusion through the tight junction; 4) modulation of NaCl diffusion through the tight junction controls the rate of isotonic reabsorption; modulation of water flow can increase sensitivity to transmural pressure; 5) no pressure-induced change in permeability of the tight junction or basement membrane is needed for pressure to modulate reabsorption; and 6) system performance is indifferent to the distribution of active transport sites, to the numerical value of the compliance function, and to the relationship between lumen and cell pressures.

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Abbreviations

A :

channel cross-section area, cm2

A max :

maximum channel cross-section area, cm2

α:

volume flow rate, dimensionless

b :

NaCl concentration gradient, (mOsm cm−4)×10−3

β:

NaCl concentration gradient, dimensionless

C :

NaCl concentration, (mOsm cm−3)×10−3

\(\overline C \) :

arithmetic mean NaCl concentration (mOsm cm−3)×10−3

γ:

NaCl concentration, dimensionless

D :

channel NaCl diffusion coefficient, cm2 sec−1

E :

emergent osmolality, (mOsm cm−3)×10−3

k 1 :

channel wall hydraulic permeability, dimensionless

k 2 :

NaCl active transport rate, dimensionless

k 3 :

basement membrane hydraulic permeability, dimensionless

k 4 :

tight junction hydraulic permeability, dimensionless

k 5 :

basement membrane NaCl permeability, dimensionless

k 6 :

tight junction NaCl permeability, dimensionless

k 7 :

NaCl reflection coefficient, tight junction, dimensionless

k 8 :

NaCl reflection coefficient, basement membrane, dimensionless

L :

hydraulic permeability, cm sec−1 mm Hg−1 or NaCl permeability, cm sec−1

λ:

distance, dimensionless

N :

NaCl active transport rate, mOsm cm−2 sec−1

ζ:

compliance parameter, mm Hg−1

p :

hydrostatic pressure, mm Hg

\(\bar p\) :

cell hydrostatic pressure, mm Hg

II :

osmotic pressure, mm Hg

q :

volume flow rate, cm3 sec−1

R :

universal gas constant, mm HgT −1 mol−1

r :

A/A max, dimensionless

S :

channel circumference, cm

σ:

NaCl reflection coefficient

T :

absolute temperature,oK

Φ:

hydrostatic pressure, dimensionless

X :

channel length, cm

x :

distance, cm

z :

pump distribution, dimensionless

B :

basement membrane

BS :

basement membrane, NaCl

IS :

interstitial space

L :

lumen

o :

isotonic

T :

tight junction

TS :

tight junction, NaCl

References

  1. Bank, N.W., Erygar, W.E., Aynedjian, H.S. 1971. A microperfusion study of sucrose movement across the rat proximal tubule during renal vein constriction.J. Clin. Invest. 50:294

    Google Scholar 

  2. Bellman, R.E., Kalaba, R.E. 1965. Quasilinearization and Nonlinear Boundary-Value Problems. American Elsevier, New York

    Google Scholar 

  3. Boulpaep, E.L. 1972. Permeability changes of the proximal tubule ofNecturus during saline loading.Amer. J. Physiol. 222:517

    Google Scholar 

  4. Brenner, B.M., Falchuk, K.H., Keimowitz, R.I., Berliner, R.W. 1969. The relationships between peritubular capillary protein concentration and fluid reabsorption by the proximal tubule.J. Clin. Invest. 48:1519

    Google Scholar 

  5. Brenner, B.M., Galla, J.H. 1971. Influence of post-glomerular hematocrit and protein concentration in rat nephron fluid transfer.Amer. J. Physiol. 220:148

    Google Scholar 

  6. Brenner, B.M., Troy, J.L. 1971. Post-glomerular vascular protein concentration: Evidence for a causal role in governing fluid reabsorption and glomerulotubular balance by the renal proximal tubule.J. Clin. Invest. 50:336

    Google Scholar 

  7. Burg, N.B., Grantham, J.J. 1971. Ion movements in renal tubules.In: Membranes and Ion Transport. E.E. Bittar, editor. Vol. 3, p. 49. Wiley-Interscience, London

    Google Scholar 

  8. Burg, M.B., Orloff, J. 1968. Control of fluid absorption in the renal proximal tubule.J. Clin. Invest. 47:2016

    Google Scholar 

  9. Diamond, J.M. 1974. Tight and leaky junctions of epithelia: A perspective on kisses in the dark.Fed. Proc. 33:2220

    Google Scholar 

  10. Diamond, J., Bossert, W.H. 1967. Standing gradient osmotic flow. A mechanism for coupling of water and solute transport in epithelia.J. Gen. Physiol. 50:2061

    Google Scholar 

  11. DiBona, D.R., Chen, L.C., Sharp, G.W.G. 1974. A study of intercellular spaces in the rabbit jejunum during acute volume expansion and after treatment with cholera toxin.J. Clin. Invest. 53:1300

    Google Scholar 

  12. Frizzell, R.A., Schultz, S.G. 1972. Ionic conductances of extracellular shunt pathway in rabbit ileum. Influence of shunt on transmural sodium transport and electrical potential differences.J. Gen. Physiol. 59:318

    Google Scholar 

  13. Frömter, E. 1972. The route of passive ion movement through the epithelium ofNecturus gallbaldder.J. Membrane Biol. 8:259

    Google Scholar 

  14. Frömter, E., Diamond, J. 1972. Route of passive ion permeability variation in epithelia.Nature, New Biol. 235:9

    Google Scholar 

  15. Gertz, K.H. 1973. Transtubulare Natriumchloridflüsse und Permeabilität für Nichtelektrolyte im proximalen und distalen Convolute der Rattenniere.Pflug. Archiv. 276:336

    Google Scholar 

  16. Green, R., Windhager, E.E., Giebisch, G. 1974. Protein oncotic pressure effects on proximal tubular fluid movement in the rat.Amer. J. Physiol. 226:265

    Google Scholar 

  17. Humphreys, M.H., Earley, L.E. 1971. The mechanism of decreased intestinal sodium and water reabsorption after acute volume expansion in the rat.J. Clin. Invest. 50:2355

    Google Scholar 

  18. Kaye, G.I., Wheeler, H.O., Whitlock, R.T., Lane, N. 1966. Fluid transport in the rabbit gall bladder. A combined physiological and electron microscopic study.J. Cell. Biol. 30:237

    Google Scholar 

  19. Kedem, O., Katchalsky, A. 1958. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes.Biochim. Biophys. Acta 27:229

    Google Scholar 

  20. Lassiter, W.E., Gottschalk, C.W., Mylle, M. 1961. Micropuncture study of net transtubular movement of water and urea in nondiuretic mammalian kidney.Amer. J. Physiol. 200:1139

    Google Scholar 

  21. Lewy, J.E., Windhager, E.E. 1968. Peritubular control of proximal tubular fluid reabsorption in the rat kidney.Amer. J. Physiol. 214:943

    Google Scholar 

  22. Lorentz, W.D., Jr., Lassiter, W.E., Gottschalk, C.W. 1971. Renal tubular permeability during increased intra-renal pressure.J. Clin. Invest. 51:484

    Google Scholar 

  23. Machen, T.E., Diamond, J.M. 1969. An estimate of the salt concentration in the lateral intercellular spaces of rabbit gall-bladder during maximal fluid transport.J. Membrane Biol. 1:194

    Google Scholar 

  24. Martino, J.A., Earley, L.E. 1967. Demonstration of a role of physical factors as determinants of the natriuretic response to volume expansion.J. Clin. Invest. 46:1963

    Google Scholar 

  25. Maunsbach, A.B. 1966. The influence of different fixatives and fixation methods on the ultrastructure of rat kidney and rat proximal tubule cells. I. Comparison on different perfusion fixation methods and of glutaraldehyde formaldehyde and osmium tetroxide fixatives.J. Ultrastruct. Res. 15:242

    Google Scholar 

  26. Robinson, R.A., Stokes, R.H. 1959. Electrolyte Solutions. Butterworth, London

    Google Scholar 

  27. Seely, J.F. 1973. Effects of peritubular oncotic pressure on rat proximal tubule electrical resistance.Kidney Internat. 4:28

    Google Scholar 

  28. Segel, L.A. 1970. Standing gradient flows driven by active solute transport.J. Theoret. Biol. 29:233

    Google Scholar 

  29. Spitzer, A., Windhager, E.E. 1970. Effect of peritubular oncotic pressure changes on proximal tubular fluid reabsorption.Amer. J. Physiol. 218:1188

    Google Scholar 

  30. Spring, K.R. 1973. Current-induced voltage transients inNecturus proximal tubule.J. Membrane Biol. 13:299

    Google Scholar 

  31. Tisher, C.C., Kokko, J.T. 1974. Relationship between peritubular oncotic pressure gradients and morphology in isolated proximal tubules.Kidney Internat. 6:146

    Google Scholar 

  32. Tormey, J.McD., Diamond, J.M. 1967. The ultrastructural route of fluid transport in rabbit gall bladder.J. Gen. Physiol. 50:2031

    Google Scholar 

  33. Ullrich, K.J. 1973. Permeability characteristics of the mammalian nephron.In: Handbook of Physiology. Sec. 8, Renal Physiology. J. Orloff and R.W. Berliner, Editors. p. 377. American Physiol. Society, Washington, D.C.

    Google Scholar 

  34. Ullrich, K.J., Schmidt-Nielsen, B., Odell, R., Jr., Pehling, G., Gottschalk, C.W., Lassiter, W.E., Mylle, M. 1963. Micropuncture study of composition of proximal and distal tubular fluid in rat kidney.Amer. J. Physiol. 204:527

    Google Scholar 

  35. Welling, L.W., Grantham, J.J. 1972. Physical properties of isolated perfused renal tubules and tubular basement membranes.J. Clin. Invest. 51:1063

    Google Scholar 

  36. Whittembury, G., Sugino, N., Solomon, A.K. 1961. Ionic permeability and electrical potential differences inNecturus kidney cells.J. Gen. Physiol. 44:689

    Google Scholar 

  37. Wirz, H. 1956. Der osmotische Druck in den corticalen Tubuli der Rattenniere.Helv. Physiol. Pharmacol. Acta 14:353

    Google Scholar 

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Authors and Affiliations

  1. Biomedical Engineering, Graduate Center for Engineering Sciences, University of Southern California, 90007, Los Angeles, California

    Ronald E. Huss & Donald J. Marsh

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  1. Ronald E. Huss
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Huss, R.E., Marsh, D.J. A model of NaCl and water flow through paracellular pathways of renal proximal tubules. J. Membrain Biol. 23, 305–347 (1975). https://doi.org/10.1007/BF01870256

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  • DOI: https://doi.org/10.1007/BF01870256

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