An equation for flow in the renal proximal tubule

Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.     

Application of a fiber-matrix model to transport in renal tubules

The effects of tight junction structure on water and solute fluxes across proximal tubular epithelium were examined with fiber-matrix equations previously derived by Curry and Michel (1980. Microvascular Research. 20:96-99). Using plausible estimates of tight junction fiber length and width the model predicts solute (Ps) and water permeability (Lp) coefficients that agree with the measured values. When fiber-matrix and pore models were compared for physiologically relevant ranges of matrix void fraction (80-98%) and pore radii (0-20 A), the fiber-matrix model predicted a 10-fold higher Lp/Ps ratio. Lp/Ps was most sensitive to small changes in tight junction structure when void fractions exceeded 90%. Void fractions of 96.5% and 97.1% predicted previously measured values for Lp and solute permeabilities in rat and rabbit proximal tubules. These values are consistent with void fractions and permeabilities of artificial membranes. The fiber-matrix tight junction model was incorporated into a model of reabsorption from the rat proximal tubule developed by Weinstein (1984). American Journal of Physiology. 247:F848-F862.) A void fraction of 98% predicted the experimental results for isosmotic reabsorption driven by active transport. Changing void fraction over the range of 97-99% produced a 50-75% change in predicted volume reabsorption with active transport. According to the fiber-matrix model: (a) solute permeabilities alone cannot be used to predict Lp, (b) previously measured solute permeabilities in the proximal tubule are compatible with significant water reabsorption through a water-permeable tight junction, and (c) hydraulic and solute permeabilities may be sensitive to small changes in tight junction fiber length and diameter or ionic strength within the tight junction.     

Membrane stress causes inhibition of water channels in brush border membrane vesicles from kidney proximal tubule

Brush border membrane vesicles (BBMV) from rabbit kidney proximal tubule cells, prepared with different internal solute concentrations (cellobiose buffer 13, 18 or 85 mosM) developed an hydrostatic pressure difference across the membrane of 18.7 mosM, that causes a membrane tension close to 5 × 10⁻⁵ N cm⁻¹. When subjected to several hypertonic osmotic shocks an initial delay of osmotic shrinkage (a lag time), corresponding to a very small change in initial volume was apparent. This initial osmotic response, which is significantly retarded, was correlated with the initial period of elevated membrane tension, suggesting that the water permeability coefficient is inhibited by membrane stress. We speculate that this inhibition may serve to regulate cell volume in the proximal tubule.     

Axial heterogeneity and filtered-load dependence of proximal bicarbonate reabsorption.

A theoretical model was developed to examine the role of physical and chemical factors in the control of bicarbonate reabsorption in the renal proximal tubule. Included in the model were axial and radial variations in the concentrations of HCO3-, CO2 and related chemical species in the tubule lumen and epithelial cells. Relations between these concentrations and the solute fluxes across the brush border and basolateral membranes were also included, as were reaction rate and equilibrium expressions to describe the various buffering processes in the lumen and cells. The two most critical membrane parameters, the rate constant for H+ secretion at the brush border and the effective permeability of HCO3- at the basolateral membrane, were evaluated by comparing model predictions with available free-flow micropuncture data in the rat. It was found that the experimental observations could be explained only by decreasing one or both of these membrane parameters with axial position, suggesting a progressive decrease in HCO3- reabsorptive capacity along the tubule. For single nephron filtered loads of HCO3- up to about 1,400 pmol/min, absolute bicarbonate reabsorption was predicted to increase nearly in proportion to filtered load, whereas it was calculated to be relatively constant at higher filtered loads, irrespective of how filtered load was assumed to be varied. These predictions are in excellent agreement with most of the available micropuncture data in rats, as is the prediction that HCO3- reabsorption should change in parallel with CO2 partial pressure in the filtrate, at a given filtered load of HCO3-. Certain discrepancies between the model predictions and experimental observations are evident at very high filtered loads, and the implications of these are discussed in terms of possible adaptive responses of the tubule.     

Biochemical, functional, and morphological characterization of a primary culture of rabbit proximal tubule cells.

Primary cultures of renal rabbit proximal tubule cells were initiated from a pure suspension of proximal tubule fragments. Proximal tubule cells were grown in a hormone-supplemented, serum-free medium containing low concentrations of antibiotics. Confluent monolayers exhibited multicellular dome formation, indicating the presence of transepithelial solute and water transport. Ultrastructural examination revealed a monolayer of polarized epithelial cells with tight junctions and sparse membraneous microvilli facing the culture medium. Time course biochemical characterization was performed using a palette of 12 enzymes, representative of important metabolic functions or pathways. Brush-border-associated enzymes (gamma-glutamyl transpeptidase and alanine aminopeptidase) were moderately reduced throughout the culture whereas alkaline phosphatase was markedly decreased at confluency. Mitochondrial and lysosomal marker enzymes were well preserved over the culture period. Glutathione-S-transferase activity remained stable during the 16-day culture period investigated. Glycolysis enzyme activities (lactate dehydrogenase and hexokinase) were enhanced, as a function of culture age. Na(+)-K(+)-ATPase activity rise was concomitant with the increase of glycolysis marker enzymes. In contrast, the gluconeogenesis marker enzyme, glucose-6-phosphatase, fell dramatically to reach a low level equivalent to 4% of the activity measured in isolated proximal tubules. Primary cultures exhibited several differentiated functions of the proximal tubule cell: (a) PTH alone was able to induce a significant stimulation of adenylate cyclase activity, unlike isoproterenol, thyrocalcitonin, and arginine vasopressin, and (b) sodium-dependent alpha-methylglucoside (AMG) transport was detected. This AMG uptake was selectively inhibited by phlorizin (5 X 10(-3) M), which is a competitive inhibitor of glucose uptake at the apical membrane. Complete characterization made it possible to investigate hitherto unexplored aspects of in vitro cultured proximal tubule cells. This primary culture model could provide a useful and reliable tool to investigate in vitro renal proximal tubule function, under normal conditions or after a drug-induced toxicity.     

Control and Modulation of Fluid Flow in the Rat Kidney

We have developed a mathematical model of the rat’s renal hemodynamics in the nephron level, and used that model to study flow control and signal transduction in the rat kidney. The model represents an afferent arteriole, glomerular filtration, and a segment of a short-loop nephron. The model afferent arteriole is myogenically active and represents smooth muscle membrane potential and electrical coupling. The myogenic mechanism is based on the assumption that the activity of nonselective cation channels is shifted by changes in transmural pressure, such that elevation in pressure induces vasoconstriction, which increases resistance to blood flow. From the afferent arteriole’s fluid delivery output, glomerular filtration rate is computed, based on conservation of plasma and plasma protein. Chloride concentration is then computed along the renal tubule based on solute conservation that represents water reabsorption along the proximal tubule and the water-permeable segment of the descending limb, and chloride fluxes driven by passive diffusion and active transport. The model’s autoregulatory response is predicted to maintain stable renal blood flow within a physiologic range of blood pressure values. Power spectra associated with time series predicted by the model reveal a prominent fundamental peak at ～165 mHz arising from the afferent arteriole’s spontaneous vasomotion. Periodic external forcings interact with vasomotion to introduce heterodynes into the power spectra, significantly increasing their complexity.     

Convective paracellular solute flux. A source of ion-ion interaction in the epithelial transport equations

An electrolyte model of an epithelium (a cell and a tight junction in parallel, both in series with a lateral interspace basement membrane) is analyzed using the formalism of nonequilibrium thermodynamics. It is shown that if the parallel structures are heteroporous (i.e., reflection coefficients for two ion species differ between the components), then a cross-term will appear in the overall transport equations of the epithelium. Formally, this cross-term represents an ion-ion interaction. With respect to the rat proximal tubule, data indicating epithelial ionic reflection coefficients less than unity, together with the assumption of no transcellular solvent drag, imply the presence of convective paracellular solute flux. This means that a model applicable to a heteroporous structure must be used to represent the tubule, and, in particular, the cross-terms for ion-ion interaction must also be evaluated in permeability determinations. A series of calculations is presented that permits the estimation of the Na-Cl interaction for rat proximal tubule from available experimental data. One consequence of tubule heteroporosity is that an electrical potential may be substantially less effective than an equivalent concentration gradient in driving reabsorptive ion fluxes.     

Effect of ACE inhibition on glomerular permselectivity and tubular albumin concentration in the renal ablation model

Despite the central role of tubular plasma proteins that characterize progressive kidney diseases, protein concentrations along the nephron in pathological conditions have not been quantified so far. We combined experimental techniques and theoretical analysis to estimate glomerular and tubular levels of albumin in the experimental model of 5/6 nephrectomy (Nx) in the rat, with or without angiotensin-converting enzyme (ACE) inhibition. We measured glomerular permselectivity by clearance of fluorescent Ficoll and albumin and used theoretical analysis to estimate tubular albumin. As expected, 5/6 Nx induced an elevation of the fractional clearance of the largest Ficoll molecules (radii >56 ?, P < 0.05), increasing the importance of the shunt pathway of the glomerular membrane and the albumin excretion rate (119 ± 41 vs. 0.6 ± 0.2 mg/24 h, P < 0.01). ACE inhibition normalized glomerular permselectivity and urinary albumin (0.5 ± 0.3 mg/24 h). Theoretical analysis indicates that with 5/6 Nx, an increased albumin filtration overcomes proximal tubule reabsorption, with a massive increase in average albumin concentration along the tubule, reaching the highest value of >2,500 μg/ml at the end of the collecting duct. ACE inhibition improved glomerular permselectivity, limiting albumin filtration under proximal tubule reabsorption capacity, with low albumin concentration along the entire nephron, averaging <13 μg/ml at the end of the collecting duct. These results reinforce our understanding of the mechanisms of renal disease progression and the effects of angiotensin II antagonism. They also suggest that evaluation of tubular protein concentration levels could help to identify patients at risk of kidney disease progression and to improve clinical management.     

Intrarenal Renin Angiotensin System Revisited: ROLE OF MEGALIN-DEPENDENT ENDOCYTOSIS ALONG THE PROXIMAL NEPHRON

The existence of a local renin angiotensin system (RAS) of the kidney has been established. Angiotensinogen (AGT), renin, angiotensin-converting enzyme (ACE), angiotensin receptors, and high concentrations of luminal angiotensin II have been found in the proximal tubule. Although functional data have documented the relevance of a local RAS, the dualism between biosynthesis and endocytotic uptake of its components and their cellular processing has been incompletely understood. To resolve this, we have selectively analyzed their distribution, endocytosis, transcytosis, and biosynthesis in the proximal tubule. The presence of immunoreactive AGT, restricted to the early proximal tubule, was due to its retrieval from the ultrafiltrate and storage in endosomal and lysosomal compartments. Cellular uptake was demonstrated by autoradiography of radiolabeled AGT and depended on intact endocytosis. AGT was identified as a ligand of the multiple ligand-binding repeats of megalin. AGT biosynthesis was restricted to the proximal straight tubule, revealing substantial AGT mRNA expression. Transgenic AGT overexpression under the control of an endogenous promoter was also restricted to the late proximal tubule. Proximal handling of renin largely followed the patterns of AGT, whereas its local biosynthesis was not significant. Transcytotic transport of AGT in a proximal cell line revealed a 5% recovery rate after 1 h. ACE was expressed along late proximal brush-border membrane, whereas ACE2 was present along the entire segment. Surface expression of ACE and ACE2 differed as a function of endocytosis. Our data on the localization and cellular processing of RAS components provide new aspects of the functional concept of a “self-contained” renal RAS.     

Kinetic transport model for cellular regulation of pH and solute concentration in the renal proximal tubule.

An open circuit kinetic model was developed to calculate the time course of proximal tubule cell pH, solute concentrations, and volume in response to induced perturbations in luminal or peritubular fluid composition. Solute fluxes were calculated from electrokinetic equations containing terms for known carrier saturabilities, allosteric dependences, and ion coupling ratios. Apical and basolateral membrane potentials were determined iteratively from the requirements of cell electroneutrality and equal opposing transcellular and paracellular currents. The model converged to membrane potentials accurate to 0.05% in one to four iterations. Model variables included cell concentrations of Na, K, HCO3, glucose, pH (uniform CO2), volume, and apical and basolateral membrane potentials. The basic model contained passive apical membrane transport of Na/H, Na/glucose, H and K, basolateral transport of Na/3HCO3, K, H, and glucose, and paracellular transport of Na, K, Cl, and HCO3; apical H and basolateral 3Na/2K-ATPases were present. Apical Na/H and basolateral K transport were regulated allosterically by pH. Apical Na/H transport, basolateral Na/3HCO3 transport, and the 3Na/2K-ATPase were saturable. Model parameters were chosen from data in the rat proximal tubule. Model predictions for the magnitude and time course of cell pH, Na, and membrane potential in response to rapid changes in apical and peritubular Na and HCO3 were in excellent agreement with experiment. In addition, the model requires that there exist an apical H-ATPase, basolateral Na/3HCO3 transport saturable with HCO3, and electroneutral basolateral K transport.     

Modeling epithelial cell homeostasis: Steady-state analysis

Critical to epithelial cell viability is the homeostasis of cell volume and composition during changes in transcellular transport. In this study, two previously developed mathematical models (principal cell of the collecting duct and proximal tubule cell) are approximated by their linearizations about a reference condition. This yields matrices which estimate cell volume, cell composition, and transcellular fluxes in response to perturbations of bath conditions and membrane transporter activity. These approximations are themselves extended with the inclusion of linear dependence of membrane transport coefficients on cell variables (e.g., volume, solute concentrations, or electrical potential). This provides cell models with variable permeabilities, which may be homeostatic, and which can be examined systematically: sequentially testing each membrane permeability and its controlling cell variable. In the proximal tubule approximation, volume-mediated increases in peritubular K—Cl or Na—3HCO₃ cotransport, and volume-mediated decreases in Na,K-ATPase activity are homeostatic; modulation of peritubular K permeability has little impact. In the principal cell model, volume homeostasis is afforded by volume-sensitive peritubular Na/H exchange or Cl⁻ conductance. Predictions from the linear analysis are confirmed in the full models. This approach yields a systematic examination of homeostasis in an epithelial model, and identifies candidate control parameters.     

Analysis of proximal tubule salt and water transport in standing droplets.

A mathematical model has been developed describing solute and water movement in the renal proximal tubule standing droplet experiment. The model explicitly incorporates the constraint of isosmotic reabsorption. Solute asymmetry due to the unequal distribution of protein, bicarbonate and other solutes between plasma and the standing droplet is shown to be one of the major reabsorptive forces; however, the introduction of an additional reabsorptive mechanism into the system equations is required in order to obtain a quantitative fit with experimental observations. The model demonstrates that limiting concentration gradients can be obtained in the absence of active transport and that their magnitudes will vary inversely with the permeability of the poorly permeant solute. Conversely, situations can occur where active transport will not elicit a limiting gradient. Consequently, previous interpretations of the meaning of limiting gradients and their magnitudes need to be reconsidered. The model further predicts that the technique for measuring non-electrolyte permeability using standing droplet experiments is likely to underestimate the true permeability. Finally, it is shown that a previous theoretical model of standing droplets, which does not explicitly include the constraint of isomotic reabsorption, cannot fit experimental data from proximal tubules.     

Flash photolysis of caged nitric oxide inhibits proximal tubular fluid reabsorption in free-flow nephron

A nonobstructing optical method was developed to measure proximal tubular fluid reabsorption in rat nephron at 0.25 Hz. The effects of uncaging luminal nitric oxide (NO) on proximal tubular reabsorption were investigated with this method. Proximal fluid reabsorption rate was calculated as the difference of tubular flow measured simultaneously at two locations (0.8-1.8 mm apart) along a convoluted proximal tubule. Tubular flow was estimated on the basis of the propagating velocity of fluorescent dextran pulses in the lumen. Changes in local tubular flow induced by intratubular perfusion were detected simultaneously along the proximal tubule, indicating that local tubular flow can be monitored in multiple sites along a tubule. The estimated tubular reabsorption rate was 5.52 +/- 0.38 nl.min(-1).mm(-1) (n = 20). Flash photolysis of luminal caged NO (potassium nitrosylpentachlororuthenate) was induced with a 30-Hz UV nitrogen-pulsed laser. Release of NO from caged NO into the proximal tubule was confirmed by monitoring intracellular NO concentration using a cell-permeant NO-sensitive fluorescent dye (DAF-FM). Emission of DAF-FM was proportional to the number of laser pulses used for uncaging. Photolysis of luminal caged NO induced a dose-dependent inhibition of proximal tubular reabsorption without activating tubuloglomerular feedback, whereas uncaging of intracellular cGMP in the proximal tubule decreased tubular flow. Coupling of this novel method to measure reabsorption with photolysis of caged signaling molecules provides a new paradigm to study tubular reabsorption with ambient tubular flow.     

Progressive enzyme changes within anatomically defined segments of rabbit nephron: demonstration with a new technique

The kidney is an extremely heterogeneous organ, with morphological, physiological, and metabolic changes occurring from segment to segment along each nephron. To determine the heterogeneity that might exist within discrete anatomical segments of rabbit nephron, we developed a technique for making quantitative enzyme assays in serial samples, about 100 micron long, along identified segments of the nephron. Results for three enzymes in proximal convoluted and straight tubules show that adenylate kinase, an enzyme of high-energy phosphate metabolism, gradually decreases along the S1 and S2 segments of the proximal tubule, with no abrupt changes. Fructose bisphosphatase, a gluconeogenic enzyme, is high along the major portion of the proximal tubule but plummets along the final millimeter of S3. Conversely, phosphofructokinase, a glycolytic enzyme, is very low along the proximal tubule but increases sharply within the final millimeter. These data underscore the biochemical heterogeneity of the nephron, illustrating the enzyme levels may change markedly even within anatomically defined regions. They also suggest the importance of further studies of this type and demonstrate a practical means for such studies.     

Neuropeptide Y inhibits cAMP accumulation in renal proximal convoluted tubules

The effect of neuropeptide Y (NPY) on cAMP accumulation in various segments of the rabbit nephron was examined. NPY inhibited parathyroid hormone-stimulated cAMP accumulation in the proximal convoluted tubule in a concentration-dependent manner. NPY also inhibited forskolin-stimulated cAMP production in this segment of the nephron. In contrast, NPY had no effect on parathyroid hormone or forskolin-stimulated cAMP accumulation in the proximal straight tubule. Similarly, NPY had no effect on forskolin-stimulated cAMP levels along the rest of the nephron. These results are consistent with previous studies which have localized NPY receptors to the proximal convoluted tubule, and suggest that NPY via its effects on cAMP metabolism may play a role in proximal tubule transport.     

Solvent drag measurement of transcellular and basolateral membrane NaCl reflection coefficient in kidney proximal tubule

The NaCl reflection coefficient in proximal tubule has important implications for the mechanisms of near isosmotic volume reabsorption. A new fluorescence method was developed and applied to measure the transepithelial (sigma NaClTE) and basolateral membrane (sigma NaClcl) NaCl reflection coefficients in the isolated proximal straight tubule from rabbit kidney. For sigma NaClTE measurement, tubules were perfused with buffers containing 0 Cl, the Cl-sensitive fluorescent indicator 6-methoxy-N-[3-sulfopropyl] quinolinium and a Cl-insensitive indicator fluorescein sulfonate, and bathed in buffers of differing cryoscopic osmolalities containing NaCl. The transepithelial Cl gradient along the length of the tubule was measured in the steady state by a quantitative ratio imaging technique. A mathematical model based on the Kedem-Katchalsky equations was developed to calculate the axial profile of [Cl] from tubule geometry, lumen flow, water (Pf) and NaCl (PNaCl) permeabilities, and sigma NaClTE. A fit of experimental results to the model gave PNaCl = (2.25 +/- 0.2) x 10(-5) cm/s and sigma NaClTE = 0.98 +/- 0.03 at 23 degrees C. For measurement of sigma NaClbl, tubule cells were loaded with SPQ in the absence of Cl. NaCl solvent drag was measured from the time course of NaCl influx in response to rapid (less than 1 s) Cl addition to the bath solution. With bath-to-cell cryoscopic osmotic gradients of 0, -60, and +30 mosmol, initial Cl influx was 1.23, 1.10, and 1.25 mM/s; a fit to a mathematical model gave sigma NaClbl = 0.97 +/- 0.04. These results indicate absence of NaCl solvent drag in rabbit proximal tubule. The implications of these findings for water and NaCl movement in proximal tubule are evaluated.     

Cell junctions in the renal tubule of a fresh-water teleost,Salmo gairdneri Rich.

Summary Cell junctions in the renal tubule of the fresh-water rainbow trout were studied with thin-section and freeze-fracture techniques. Gap junctions were restricted to the proximal tubule, which is consistent with other vertebrate classes. Segments I and II of the proximal tubule and the collecting tubule/collecting duct system exhibited a well-developed zonula occludens with anastomosing strands. The distal segment showed a narrow zonula occludens composed of few parallel strands. The structure of the occluding junctions along the renal tubule of this teleost displays several similarities with the pattern of the zonulae occludentes in the amphibian and the mammalian nephron. From these observations, in conjunction with available data from other vertebrate classes, it can be concluded that in the proximal tubule the development of a deep and complex zonula occludens is a general feature of cold-blooded vertebrates.     

Tubuloglomerular Feedback Signal Transduction in a Short Loop of Henle

In previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model does not represent other segments of the nephron, the water, and NaCl transport along which may impact fluid flow rate and NaCl transport along the TAL. To investigate the extent to which those transport processes affect TGF mediation, we have developed a mathematical model for TGF signal transduction in a short loop nephron. The model combines a simple representation of the renal cortex with a highly-detailed representation of the outer medulla (OM). The OM portion of the model is based on an OM urine concentrating mechanism model previously developed by Layton and Layton (Am. J. Renal 289:F1346–F1366, 2005a). When perturbations are applied to intratubular fluid flow at the proximal straight tubule entrance, the present model predicts oscillations in fluid flow and solute concentrations in the cortical TAL and interstitium, and in all tubules, vessels, and interstitium in the OM. Model results suggest that TGF signal transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to constant intratubular fluid flow, the time required for an element of tubular fluid to traverse the TAL is oscillatory, but nonsinusoidal; those results are consistent with our previous studies. As a consequence, oscillations in NaCl concentration in tubular fluid alongside the macula densa (MD) will be nonsinusoidal and contain harmonics of the original sinusoidal frequency. Also, the model predicts that the oscillations in NaCl concentration at the loop-bend fluid are smaller in amplitude than those at the MD, a result that further highlights the crucial role of TAL in the nonlinear transduction of TGF signal from SNGFR to MD NaCl concentration.