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A mathematical model of proximal tubule absorption

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Summary

A previous model of the mechanisms of flow through epithelia was modified and extended to include hydrostatic and osmotic pressures in the cells and in the peritubular capillaries. The differential equations for flow and concentration in each region of the proximal tubule were derived. The equations were solved numerically by a finite difference method. The principal conclusions are: (i) Cell NaCl concentration remains essentially isotonic over the pressure variations considered; (ii) channel NaCl concentration varies only a few mosmol from isotonicity, and the hydrostatic and osmotic pressure differences across the cell wall are of the same order of magnitude; (iii) both reabsorbate osmolality and pressure-induced flow are relatively insensitive to the geometry of the system; (iv) a strong equilibrating mechanism exists in the sensitivity of the reabsorbate osmolality to luminal osmolality; this mechanism is far more significant than any other parameter change.

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Abbreviations

A :

Cross-sectional area, cm2

α:

Normalized flow, dimensionless

b :

Solute concentration gradient osmol cm−4

β:

Slope of concentration of proximal tubule reabsorbate as a function of concentration difference between lumen and surrounding interstitium, dimensionless

C :

Solute concentration osmol cm−3

\(\bar C\) :

Average membrane concentration of solute, osmol cm−3

D η :

Diffusion coefficient, cm2 sec−1

δ η :

Dimensionaless membrane parameter, 0 if variable, 1 if fixed

f :

Fractional solute absorption from proximal tubule

F sη :

Axial solute flow, osmol sec−1 cm−1

F vη :

Axial volume flow, cm3 sec−1

γ:

Normalized solute concentration, dimensionless

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Author notes

  1. John L. Stephenson

    Present address: Section on Theoretical Biophysics, National Heart, Lung and Blood Institute, and Mathematical Research Branch, National Institute of Arthritis, Metabolism and Digestive Diseases, National Institutes of Health, Bldg. 31, Room 4B44, 20205, Bethesda, Maryland

Authors and Affiliations

  1. Section on Theoretical Biophysics, National Heart, Lung and Blood Institute, and Mathematical Research Branch, National Institute of Arthritis, Metabolism and Digestive Diseases, National Institutes of Health, Bldg. 31, Room 4B44, 20205, Bethesda, Maryland

    Ronald E. Huss (Chief)

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  1. Ronald E. Huss
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Huss, R.E., Stephenson, J.L. A mathematical model of proximal tubule absorption. J. Membrain Biol. 47, 377–399 (1979). https://doi.org/10.1007/BF01869745

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  • DOI: https://doi.org/10.1007/BF01869745

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