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A kinetic model of rat proximal tubule transport-load-dependent bicarbonate reabsorption along the tubule

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Abstract

A model is presented of solute and water reabsorption along the proximal tubule of the rat kidney based on kinetic descriptions of the main membrane transport systems, in order to assess the extent to which these kinetics suffice to explain certain aspects of the global transport behaviour in this segment, especially with respect to bicarbonate reabsorption. The model includes in the apical membrane, an active proton pump, Na+/H+ antiport, Na-coupled transport of organic solutes, Cl−/formate exchange with formic acid recycling, and membrane conductances to protons and K+. In the baso-lateral membrane, besides the Na+/K+ pump, the model includes Na+-3HCO −3 and electroneutral K+-Cl− cotransporters, and membrane conductances for K+, H+, and, optionally, for Cl−. Appropriate passive diffusional pathways were included in both cell membranes and in the paracellular pathway. Using mass balance and electoneutrality constraints, these transport systems were built into an epithelial model which was then integrated (by finite difference approximation) into a model of a longitudinal tubule. Simulated cellular solute concentrations and luminal concentration profiles were in good agreement with reported experimental observations. We show that, given the reported transport kinetics for the Na+/H+ antiporter, a hitherto unexplained observation concerning load-dependent bicarbonate reabsorption can be shown mainly to result from the nonlinear longitudinal concentration profile for bicarbonate and pH. We also discuss problems of transcellular Cl− transport in the light of recent reports of basolateral Cl− conductance and observations relevant to apical Cl−/formate (or other base) exchange.

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Abbreviations

o, c, b:

used as subscripts or superscripts to indicate luminal, intracellular, or blood (peritubular) compartments, respectively

[x] i ,(x) i :

concentration, [·], or activity, (·), of solutex in compartmenti (mM)

J x :

transmembrane flux of speciesx (pmol min−1 mm−1)

V xmax :

maximum rate of transport in equations forJ x (pmol min−1 mm−1, unless noted otherwise)

k x i :

dissociation constant for speciesx in compartmenti (mM)

ψ ap :

apical membrane potentialψ o−ψ c (mV)

ψ 12 :

transmembrane potential,ψ 1−ψ 2, between any two (mV) compartments 1 and 2

P x :

permeability constant for solutex (nl min−1 mm−1)

σ x :

reflection coefficient for solutex

z x :

ionic valence of solutex

L p :

water filtration coefficient (nl min−1 mm−1 mmHg−1)

ΔCOP:

colloid oncotic pressure difference (lumen-blood) (mmHg)

Δp :

hydrostatic pressure difference (lumen-blood) (mmHg)

R, T, and ℱ:

universal gas constant, temperature (K), and Faraday constant

GFR and SNGFR:

glomerular filtration rate and single nephron glomerular filtration rate Activity coefficients for ionic solutes were taken to be 0.75 (Edelmanet al., 1978)

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Authors and Affiliations

  1. Faculté de Médecine Necker, INSERM U.323, Paris, France

    S. Randall Thomas & George Dagher

  2. Laboratoire de Physiologie Cellulaire, Collège de France, Paris, France

    S. Randall Thomas & George Dagher

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Thomas, S.R., Dagher, G. A kinetic model of rat proximal tubule transport-load-dependent bicarbonate reabsorption along the tubule. Bltn Mathcal Biology 56, 431–458 (1994). https://doi.org/10.1007/BF02460466

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