Computer simulation of renal countercurrent systems

The history of mathematical modeling of renal countercurrent systems is briefly outlined. Several examples are cited and discussed. These include efforts at parameter estimation and experimental design with models. The goal of this work was the evaluation of hypotheses of hypertonic urine formation. The argument is made that computer simulation with reasonably isomorphic models can be used in a variety of ways, but that one indispensable role for this approach is to provide a test of the quantitative sufficiency of hypotheses. Hypotheses of hypertonic urine formation that do not consider active transport in thin ascending limbs do not pass this test. A new proposal is suggested in which the energy for NaCl reabsorption from thin ascending limbs is derived from dissipation of a urea gradient via an antiport.     

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

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.     

Saturation-transfer electron spin resonance studies on the mobility of spin-labeled sodium and potassium ion activated adenosinetriphosphatase in membranes from Squalus acanthias

The sodium and potassium ion activated adenosinetriphosphatase [(Na+,K+)-ATPase] in membranous preparations from Squalus acanthias has been spin-labeled on sulfhydryl groups after prelabeling with N-ethylmaleimide. Saturation-transfer electron spin resonance spectroscopy has been used to study the rotational motions of the labeled protein on the microsecond time scale. Effective rotational correlation times deduced from the diagnostic line-height ratios in the second-harmonic, 90 degrees out-of-phase (V2') spectra are much larger than those deduced from the spectral integrals, indicating the presence of large-scale segmental motions, in addition to rotation of the protein as a whole. Experiments involving controlled cross-linking of the protein by glutaraldehyde, as well as measurements of the line broadening of the conventional electron spin resonance spectra, support this interpretation. Both the spectral integrals and diagnostic line-height ratios are found to increase irreversibly with time on incubation at temperatures greater than 20 degrees C, corresponding to a decrease in the segmental motion of the protein and probably also in the overall protein rotation. The native enzyme displays a marked nonlinearity in the Arrhenius temperature dependence of the activity at temperatures above 20 degrees C, and the activity decreases with a half-life of ca. 70 min on incubation at 37 degrees C (but not on incubation at low temperature), paralleling the time- and temperature-dependent changes in the saturation-transfer spectra of the labeled protein. Both of these observations suggest that the changes observed in the molecular dynamics could correspond to functional properties of the protein.(ABSTRACT TRUNCATED AT 250 WORDS)