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A MATHEMATICAL ANALYSIS OF THE ROLE OF PASSIVE DIFFUSION IN THE RENAL RE ABSORPTION OF AMINO ACIDS AND OTHER ORGANIC COMPOUNDS UNDER FREE FLOW CONDITIONS
Author(s) -
Lingard JM,
Cook DI,
Young JA
Publication year - 1978
Publication title -
australian journal of experimental biology and medical science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.999
H-Index - 104
eISSN - 1440-1711
pISSN - 0004-945X
DOI - 10.1038/icb.1978.45
Subject(s) - reabsorption , solvent drag , chemistry , diffusion , saturation (graph theory) , permeability (electromagnetism) , flux (metallurgy) , thermodynamics , sodium , biochemistry , crystallography , membrane , physics , organic chemistry , microstructure , mathematics , combinatorics , grain boundary
Summary An equation has has developed to describe reabsorption and concentration profiles of organic compounds, such as amino acids and glucose, in the proximal kidney tubule under free‐flow conditions. Reabsorption is described in terms of a constant volume flux (J v ), an active: transport function showing saturation kinetics (with parameters J max , the maximum transport rate, and K i , the half‐saturation constant), a passive diffusion term obeying Fick's Law (with permeability coefficient. P) and a solvent drag term (depending on the volume flux, J v and the reflection coefficient δ). It was assumed, in general, that active transport and volume flux were related to tubule length rather than surface area and that transport rates were the same in the pars recta as in the pars concoluta. In the analysis, particular attention was paid to an assessment of the contribution of passive diffusion to the net transport rate off organic substances. It was found that, under normal conditions, the transport rates of most amino acids are set sufficiently high relative to the rate of water reabsorption that the value of the permeability coefficient can be charmed over a range of more than two orders of magnitude without causing substantial changes in the extent of net reabsorption attained by the end of the proximal convolution. Passive movement appears to play a very important role in stabilizing the value of net reabsorption since its effect balances that of active transport. In contrast, in cases where active transport rates are low, net reabsorption is determined largely by the magnitude of water Hux relative to the solute permeability so that the absolute permeability values become critical in determining the extent of reabsorption of a given solute. The effect of changes in plasma amino acid concentration on net reabsorption also varies according to the rate of active transport. If the plasma concentration is very low relative to the half‐saturation constant of the active transport mechanism, then net reabsorption remains relatively independent of plasma concentration and no saturation is observed. However, when this is not the case, net reabsorption becomes very sensitive to changes in plasma concentration.