Isosmotic volume reabsorption in rat proximal tubule

A theoretical model incorporation both active and passive forces has been developed for fluid reabsorption from split oil droplets in rat intermediate and late proximal tubule. Of necessity, simplifying assumptions have been introduced; we have assumed that the epithelium can be treated as a single membrane and that the membrane "effective" HCO3 permeability is near zero. Based on this model with its underlying assumptions, the following conclusions are drawn. Regardless of the presence or absence of active NaCl transport, fluid reabsorption from the split oil droplet is isosmotic. The reabsorbate osmolarity can be affected by changes in tubular permeability parameters and applied forces but is not readily altered from an osmolarity essentially equal to that of plasma. In a split droplet, isosmotic flow need not be a special consequence of active Na transport, is not the result of a particular set of permeability properties, and is not merely a trivial consequence of a very high hydraulic conductivity; isosmotic flow can be obtained with hydraulic conductivity nearly an order of magnitude lower than that previously measured in the rat proximal convoluted tubule. Isosmotic reabsorption is, in part, the result of the interdependence of salt and water flows, their changing in parallel, and thus their ratio, the reabsorbate concentration being relatively invariant. Active NaCl transport can cause osmotic water flow by reducing the luminal fluid osmolarity. In the presence of passive forces the luminal fluid can be hypertonic to plasma, and active NaCl transport can still exert its osmotic effect on volume flow. There are two passive forces for volume flow: the Cl gradient and the difference in effective osmotic pressure; they have an approximately equivalent effect on volume flow. Experimentally, we have measured volume changes in a droplet made hyperosmotic by the addition of 50 mM NaCl; the experimental results are predicted reasonably well by our theoretical model.     

Fluid reabsorption by the ductuli efferentes testis of the rat is dependent on both sodium and chlorine

The role of Na(+) and Cl(-) in fluid reabsorption by the efferent ducts was examined by perfusing individual ducts in vivo with preparations of 160 mM NaCl in which the ions were replaced, together or individually, with organic solutes while maintaining the osmolality at 300 mmol/kg. Progressively replacing NaCl with mannitol reduced net reabsorption of water and the ions in a concentration-dependent manner, and caused net movement into the lumen at concentrations of NaCl less than 80 mM. The net rates of flux were lower for Na(+) than for Cl(-). In collectates, [Na(+)] was greater than [Cl(-)], indicating that Cl(-) transport is probably linked with another anion. Replacing either Na(+) or Cl(-) in perfusates (with choline and isethionate, respectively) while maintaining the other inorganic ion at 160 mM also reduced net rates of reabsorption in a concentration-dependent manner to zero when either ion was completely replaced. There were no significant differences in the osmolality of perfusate and collectate, and collectates contained a mean of 3.4 mM K(+), indicating a backflux of K(+) into the lumen. It is concluded that fluid reabsorption from the efferent ducts is dependent on the transport of both Na(+) and Cl(-) from the lumen (from a luminal concentration of at least 70-80 mM), and that Cl(-) transport is dependent on another anion. The epithelium is permeable to K(+) and has a higher permeability to a range of organic solutes (mannitol, choline, and isethionate) than epithelium in the proximal kidney tubules.     

Regulation of renal proximal and distal tubule transport: sodium, chloride and organic anions

Renal tubular transport and its regulation are reviewed for Na(+) (and Cl(-)), and for fluid and organic anions (including urate). Filtered Na(+) (and Cl(-)) is reabsorbed along the tubules but only in mammals and birds does most reabsorption occur in the proximal tubules. Reabsorption involves active transport of Na(+) and passive reabsorption of Cl(-). The active Na(+) step always involves Na-K-ATPase at the basolateral membrane, but the entry step at luminal membrane varies among tubule segments and among vertebrate classes (except for Na(+)-2Cl(-)-K(+) cotransporter in diluting segment). Regulation can involve intrinsic, neural and endocrine factors. Proximal tubule fluid reabsorption is dependent on Na(+) reabsorption in all vertebrates studied, except ophidian reptiles. Fluid secretion occurs in glomerular and aglomerular fishes, reptiles and even mammals, but its significance is not always clear. A non-specific transport system for net secretion of organic anions (OAs) exists in the proximal renal tubules of almost all vertebrates. Net transepithelial secretion involves: (1) transport into the cells at the basolateral side against an electrochemical gradient by a tertiary active transport process, in which the final step involves OA/alpha-ketoglutarate exchange and (2) movement out of the cells across the luminal membrane down an electrochemical gradient by unknown carrier-mediated process(es). Regulation may involve protein kinase C and mitogen-activated protein kinase. Urate is net secreted in the proximal tubules of birds and reptiles. This process is urate-specific in reptiles but in birds, it may involve both a urate-specific system and the general OA system.     

Na, Cl, and Water Transport by Rat Colon

Segments of the colon of anesthetized rats have been perfused in vivo with isotonic NaCl solutions and isotonic mixtures of NaCl and mannitol. Unidirectional and net fluxes of Na and Cl and the net fluxes of water and mannitol have been measured. Net water transport was found to depend directly on the rate of net Na transport. There was no water absorption from these isotonic solutions in the absence of net solute transport, indicating that water transport in the colon is entirely a passive process. At all NaCl concentrations studied, the lumen was found to be electrically negative to the surface of the colon by 5 to 15 mv. Na fluxes both into and out of the lumen were linear functions of NaCl concentration in the lumen. Net Na absorption from lumen to plasma has been observed to take place against an electrochemical potential gradient indicating that Na is actively transported. This active Na transport has been interpreted in terms of a carrier model system. Cl transport has been found to be due almost entirely to passive diffusion.     

Sodium chloride transport by rabbit gallbladder. Direct evidence for a coupled NaCl influx process

The results of the present study that NaCl transport by in vitro rabbit gallbladder must be a consequence of a neutral coupled carrier-mediated mechanism that ultimately results in the active absorption of both ions; pure electrical coupling between the movements of Na and Cl can be excluded on the grounds of electrphysiologic considerations. Studies on the unidirectional influxes of Na and Cl have localized the site of this coupled mechanism to the mucosal membranes. Studies on the intracellular ion concentrations and the intracellular electrical potential are consistent with the notion that (a) the coupled NaCl influx process results in the movement of Cl from the mucosal solution into the cell against an apparent electrochemical potential difference; (b) the energy for the uphill movement of Cl is derived from the Na gradient across the mucosal membrane which is maintained by an active Na extrusion mechanism located at the basolateral membranes; and (c) Cl exit from the cell across the basolateral membranes is directed down an electrochemical potential gradient and may be diffusional. Finally, as for the case of rabbit ileum, the coupled NaCl influx process is inhibited by elevated intracellular levels of cyclic 3',5'-adenosine monophosphate. A working model for transcellular and paracellular NaCl transport by in vitro rabbit gallbladder is proposed.     

Intracellular ionic activities and transmembrane electrochemical potential differences in gallbladder epithelium

Summary Intracellular ion activities inNecturus gallbladder epithelium were measured with liquid ion-exchanger microelectrodes. Mean values for K, Cl and Na activities were 87, 35 and 22mm, respectively. The intracellular activities of both K and Cl are above their respective equilibrium values, whereas the Na activity is far below. This indicates that K and Cl are transported uphill toward the cell interior, whereas Na is extruded against its electrochemical gradient. The epithelium transports NaCl from mucosa to serosa. From the data presented and the known Na and Cl conductances of the cell membranes, we conclude that neutral transport driven by the Na electrochemical potential difference can account for NaCl entry at the apical membrane. At the basolateral membrane, Na is actively transported. Because of the low Cl conductance of the membrane, only a small fraction of Cl transport can be explained by diffusion. These data suggest that Cl transport across the basolateral membrane is a coupled process which involves a neutral NaCl pump, downhill KCl transport, or a Cl-anion exchange system.     

Is there a role for renal alpha 2-adrenoceptors in the pathogenesis of hypertension?

Current information suggests that alpha 2-adrenoceptors do not directly influence vascular resistance or Na reabsorption in the rat kidney. To reexamine the effects of alpha 2-agonists we used isolated rat kidneys perfused at 37.5 degrees C with precise measurement of renal artery pressure and flow. The recirculating perfusate contained pyruvate as the sole metabolic substrate which enabled us to use gluconeogenesis as an index of proximal tubular alpha 1-responses. Clonidine and guanfacine in 100 nM concentrations decreased phosphate excretion without altering Na, Cl, or K reabsorption or gluconeogenesis; 500 nM concentrations increased vascular resistance and decreased glomerular filtration rate and Na, Cl, and K excretion with no significant effect on gluconeogenesis. Prior thyroparathyroidectomy prevented the antiphosphaturic but not the antinatriuretic or vascular responses. Clonidine, an alpha 2-agonist with some alpha 1-activity, was a more potent vasoconstrictor than methoxamine or guanfacine. In the presence of prazosin (1 microM), norepinephrine (60 nM) stimulated phosphate reabsorption; norepinephrine alone did not stimulate phosphate reabsorption which indicates alpha 1-antagonism of this alpha 2-response to NE. These results and a literature review suggest that increased renal alpha 2-adrenoceptors could raise renal vascular resistance, reduce renin secretion, and antagonize parathyroid hormone effects on Pi, Ca, HCO3, and Na reabsorption to produce a low renin type of hypertension with increased proximal Na reabsorption and abnormal Ca and Pi excretion.     

Sodium gradient-stimulated transport of L-carnitine into renal brush border membrane vesicles: kinetics, specificity, and regulation by dietary carnitine

L-Carnitine transport by rat renal brush border membrane vesicles was stimulated by a Na+ gradient (extravesicular greater than intravesicular). Total carnitine entry was 2.7 and 3.2 times higher at 15 S in the presence of a 100 mM NaCl gradient than when the vesicles were incubated isoosmotically in buffered 100 mM KCl or buffered mannitol, respectively. Specific carnitine transport (total entry minus contribution from diffusion) was stimulated 3.6- and 5.7-fold, respectively. An "overshoot" was observed for total carnitine entry in the presence of a Na+ gradient but not in the presence of a K+ gradient or in the absence of an ion gradient. L-Carnitine transport was saturable. KT and Vmax for total carnitine transport were 0.11 mM and 11.6 pmol S-1 mg protein-1, respectively, and for Na+-gradient-dependent carnitine transport, 0.055 mM and 5.09 pmol S-1 mg protein-1, respectively. The transport process was structure-specific for a quaternary nitrogen and carboxyl groups attached by a 4- to 6-carbon chain, but without other charged functional groups. Other evidence for a carrier-mediated process included trans-stimulation of transport by intravesicular carnitine and a peak of activity at near physiological temperature. Kinetic data derived from this study, coupled with data from previous physiological studies from this laboratory, suggests that carnitine transport by the brush border membrane is not limiting for carnitine reabsorption. Dietary carnitine (1% of diet for 10 days) reduced by 52% the rate of carnitine transport across the brush border membrane in vitro, without affecting rates of D-glucose, L-lysine, L-glutamic acid, or L-alanine transport. Down-regulation of carnitine transport may prevent excessive or toxic accumulation of L-carnitine in renal tubular cells exposed to high extracellular carnitine concentrations.     

Sodium Movement across Single Perfused Proximal Tubules of Rat Kidneys

Using perfusion techniques in single proximal tubule segments of rat kidney, the relationship between net sodium movement and active transport of ions, as measured by the short-circuit method, has been studied. In addition, the role of the colloid-osmotic pressure gradient in proximal transtubular fluid and sodium movement has been considered. Furthermore, the limiting concentration gradient against which sodium movement can occur and the relationship between intratubular sodium concentration and fluid transfer have been investigated. Comparison of the short-circuit current with the reabsorptive movement of sodium ions indicates that this process is largely, perhaps exclusively, active in nature. No measurable contribution of the normally existing colloid-osmotic pressure gradient to transtubular water movement was detected. On the other hand, fluid movement across the proximal tubular epithelium is dependent upon the transtubular sodium gradient and is abolished when a mean concentration difference of 50 mEq/liter is exceeded.     

Regulation of glomerulotubular balance. I. Impact of dopamine on flow-dependent transport

In response to volume expansion, locally generated dopamine decreases proximal tubule reabsorption by reducing both Na/H-exchanger 3 (NHE3) and Na-K-ATPase activity. We have previously demonstrated that mouse proximal tubules in vitro respond to changes in luminal flow with proportional changes in Na(+) and HCO(3)(-) reabsorption and have suggested that this observation underlies glomerulotubular balance. In the present work, we investigate the impact of dopamine on the sensitivity of reabsorptive fluxes to changes in luminal flow. Mouse proximal tubules were microperfused in vitro at low and high flow rates, and volume and HCO(3)(-) reabsorption (J(v) and J(HCO3)) were measured, while Na(+) and Cl(-) reabsorption (J(Na) and J(Cl)) were estimated. Raising luminal flow increased J(v), J(Na), and J(HCO3) but did not change J(Cl). Luminal dopamine did not change J(v), J(Na), and J(HCO3) at low flow rates but completely abolished the increments of Na(+) absorption by flow and partially inhibited the flow-stimulated HCO(3)(-) absorption. The remaining flow-stimulated HCO(3)(-) absorption was completely abolished by bafilomycin. The DA1 receptor blocker SCH23390 and the PKA inhibitor H89 blocked the effect of exogenous dopamine and produced a two to threefold increase in the sensitivity of proximal Na(+) reabsorption to luminal flow rate. Under the variety of perfusion conditions, changes in cell volume were small and did not always parallel changes in Na(+) transport. We conclude that 1) dopamine inhibits flow-stimulated NHE3 activity by activation of the DA1 receptor via a PKA-mediated mechanism; 2) dopamine has no effect on flow-stimulated H-ATPase activity; 3) there is no evidence of flow stimulation of Cl(-) reabsorption; and 4) the impact of dopamine is a coordinated modulation of both luminal and peritubular Na(+) transporters.     

A search for a defect of proximal transport in denervated kidneys of conscious dogs

The influence of renal nerves on proximal Na+ reabsorption was studied in clearance experiments with unilaterally renal-denervated conscious dogs prepared by surgical bladder division. Two types of experiments were made : A. maximal water diuresis, and B. Total blockade of distal NaCl reabsorption with ethacrynic acid and chlorothiazide. In maximal water diuresis CH2O + CNa was used as a measure of fluid delivery to the distal nephron. At similar GFR on both sides, the proximal reabsorption estimated as GFR--(CH2O + CNa) was 38.4 +/- 5.6 ml/min for the intact and 35.9 +/- 4.2 ml/min for the denervated kidney (n = 6, difference NS). After distal tubular blockade, proximal Na+ reabsorption calculated as filtered load minus urinary excretion was 3.84 +/- 0.43 mmol/min for the intact and 3.91 +/- 0.36 mmol/min for the denervated kidney (n = 6, difference NS). The fractional reabsorption of NA+ was 64.9 +/- 1.0% for the intact and 66.9 +/- 1.1% for the denervated kidney (difference NS). In contrast to data from renal denervation studies with anaesthetized animals, the present experiments did not show any difference in proximal reabsorption between the innervated- and denervated kidney. We conclude that in absence of anaesthesia renal efferent nerves have no major effect on NaCl transport in dog proximal tubule.     

Kinetics of Na(+) transport in necturus proximal tubule

The dependence of proximal tubular sodium and fluid readsorption on the Na(+) concentration of the luminal and peritubular fluid was studied in the perfused necturus kidney. Fluid droplets, separated by oil from the tubular contents and identical in composition to the vascular perfusate, were introduced into proximal tubules, reaspirated, and analyzed for Na(+) and [(14)C]mannitol. In addition, fluid transport was measured in short-circuited fluid samples by observing the rate of change in length of the split droplets in the tubular lumen. Both reabsorptive fluid and calculated Na fluxes were simple, storable functions of the perfusate Na(+) concentration (K(m) = 35-39 mM/liter, V(max) = 1.37 control value). Intracellular Na(+), determined by tissue analysis, and open-circuit transepithelial electrical potential differences were also saturable functions of extracellular Na(+). In contrast, net reabsorptive fluid and Na(+) fluxes were linearly dependent on intracellular Na(+) and showed no saturation, even at sharply elevated cellular sodium concentrations. These concentrations were achieved by addition of amphotericin B to the luminal perfusate, a maneuver which increased the rate of Na(+) entry into the tubule cells and caused a proportionate rise in net Na(+) flux. It is concluded that active peritubular sodium transport in proximal tubule cells of necturus is normally unsaturated and remains so even after amphotericin-induced enhancement of luminal Na(+) entry. Transepithelial movement of NaCl may be described by a model with a saturable luminal entry step of Na(+) or NaCl into the cell and a second, unsaturated active transport step of Na(+) across the peritubular cell boundary.     

Radial transport of sodium and chloride into tomato root xylem

Transport of Na and Cl across exuding tomato (Lycopersicon esculentum Mill.) roots was determined as a function of ambient NaCl concentrations in the ranges of both systems 1 and 2. Kinetics of radial transport under steady-state conditions and the effect of dinitrophenol indicate that Na and Cl were transported by two different mechanisms. Sodium was neither accumulated against a concentration gradient nor directly inhibited by dinitrophenol from diffusing into the xylem. Chloride was accumulated in the xylem and its transport was nearly completely blocked by dinitrophenol. A comparison of the radial transport isotherms for Na and Cl for intact and decapitated plants indicates that the separate mechanisms were not unique to excised roots. It is concluded that radial Na transport in tomatoes was facilitated by a passive convective type process with the rate-limiting barrier located at the outer cortical plasmalemma. Chloride transport in both concentration ranges involved, either directly or indirectly, a metabolic mechanism. Absorption and retention of Na in the root tissue was negligible. Chloride was accumulated by the tissue but was unaffected by dinitrophenol.     

Hypoxia decreases proteins involved in epithelial electrolyte transport in A549 cells and rat lung

Fluid reabsorption from alveolar space is driven by active Na reabsorption via epithelial Na channels (ENaCs) and Na-K-ATPase. Both are inhibited by hypoxia. Here we tested whether hypoxia decreases Na transport by decreasing the number of copies of transporters in alveolar epithelial cells and in lungs of hypoxic rats. Membrane fractions were prepared from A549 cells exposed to hypoxia (3% O(2)) as well as from whole lung tissue and alveolar type II cells from rats exposed to hypoxia. Transport proteins were measured by Western blot analysis. In A549 cells, alpha(1)- and beta(1)-Na-K-ATPase, Na/K/2Cl cotransport, and ENaC proteins decreased during hypoxia. In whole lung tissue, alpha(1)-Na-K-ATPase and Na/K/2Cl cotransport decreased. alpha- and beta-ENaC mRNAs also decreased in hypoxic lungs. Similar results were seen in alveolar type II cells from hypoxic rats. These results indicate a slow decrease in the amount of Na-transporting proteins in alveolar epithelial cells during exposure to hypoxia that also occurs in vivo in lungs from hypoxic animals. The reduced number of transporters might account for the decreased transport activity and impaired edema clearance in hypoxic lungs.     

New evidence for active sodium transport from fluid-filled rat lungs

The hypothesis that fluid reabsorption from the air spaces is mediated at least in part by active transport of Na+ was investigated in six sets of experiments conducted in isolated fluid-filled rat lungs. Fluid reabsorption was monitored by following the changes in the air space concentration of labeled albumin. We found that incorporation of bicarbonate rather than a nonvolatile buffer (N-2-hydroxy-ethylpiperazine-N'-2-ethanesulfonic acid) in the air space solution more than doubled the rate of fluid reabsorption. Addition of 10(-4) M amiloride to the air space solution reduced the rate of fluid reabsorption over a 2-h experiment from 1.2 +/- 0.1 to 0.7 +/- 0.1 ml and decreased reabsorption of both labeled and unlabeled Na+ from the air spaces. To show that Na+ could be reabsorbed from the air spaces even if the concentrations of Na+ in the perfusate increased above those in the air space, mannitol (150 mM) was added to the perfusate and air space solutions and the concentrations of Na+ and Cl- were reduced to 90 and 60 mM, respectively. Mannitol diffuses across the pulmonary epithelium very slowly, and it osmotically restrained the movement of water out of the air spaces. Na+ concentrations in the perfusate increased by 10 +/- 2 mM, but concentrations in the air space remained unchanged. Despite an increasingly unfavorable concentration gradient for Na+, 0.2 mmol Na+ and 0.6 ml water were reabsorbed from the air spaces in 2 h. Ouabain (10(-4) M) did not appear to slow fluid reabsorption in the presence of mannitol, but it reduced K+ secretion into the air spaces and increased K+ appearance in the perfusate in a manner consistent with inhibition of Na+-K+-adenosinetriphosphatase at the basolateral surface of the epithelial cells. Fluid reabsorption was not altered when the lungs were exposed to a hypotonic solution (185 mM), but secretion of K+ into the air spaces was accelerated and K+ was lost from the perfusate. These experiments are consistent with active Na+ transport from the air spaces.     

Chloride reabsorption by renal proximal tubules of necturus

Summary Movement of Cl from the lumen ofNecturus proximal tubule into the cells is mediated and dependent on the presence of luminal Na. Intracellular Cl activity was monitored with ion selective microelectrodes. In Cl Ringer's perfused kidneys, cell Cl activity was 24.5±1.1mm, 2 to 3 times higher than that predicted for passive distribution. When luminal NaCl was partially replaced by mannitol (capillaries perfused with Cl Ringer's) cell Cl decreased showing a sigmoidal dependence on luminal NaCl. Peritubular membrane potential was unaltered. Sulfate Ringer's perfusion of the kidneys washed out all cell Cl but did not alter peritubular membrane potential. Chloride did not enter the cell when the tubule lumen was perfused with 100mm KCl, LiCl, or tetramethylammonium Cl. Luminal perfusion of NaCl caused cell Cl to rise rapidly to the same value as the controls in the Cl Ringer's experiments. Perfusion of the tubule lumen with mixtures of NaCl and Na₂SO₄, while the capillaries contained sulfate Ringer's yielded a sigmoidal dependence of cell Cl on luminal NaCl activity. Chloride movement from the lumen into the proximal tubule cells required approximately equal concentrations of Na and Cl. Current clamp experiments indicated that intracellular chloride activity was insensitive to alterations in liminal membrane potential, suggesting that chloride entry was electrically neutral. The transcellular chloride flux was calculated to constitute about one half of the normal chloride reabsorption rate. We conclude that the cell Cl activity is primarily determined by the NaCl concentration in the tubule lumen and that Cl entry across the luminal membrane is mediated.     

Pantothenate-sodium cotransport in renal brush-border membranes

The mechanism of pantothenate transport into rabbit renal brush-border membrane vesicles was studied. Under voltage-clamped conditions, an inward NaCl gradient induced the transient accumulation of pantothenate against its concentration gradient, indicating Na+/pantothenate cotransport. K+, Rb+, Li+, NH4+, and choline+ were ineffective in replacing Na+. Pantothenate analogs, D-glucose, and various carboxylic acids did not inhibit Na+-dependent pantothenate transport, suggesting that this system is specific for pantothenate. Kinetic analysis of the Na+-dependent pantothenate uptake revealed a single transport system which obeyed Michaelis-Menten kinetics (Km = 16 microM and Vmax = 6.7 pmol X mg-1 X 10 s-1). Imposition of an inside-negative membrane potential caused net uphill pantothenate accumulation in the presence of Na+ but absence of a Na+ gradient, indicating that Na+/pantothenate cotransport is electrogenic. The relationship between extravesicular Na+ concentration and pantothenate transport measured under voltage-clamped conditions was sigmoidal: a Hill coefficient (napp) of 2 and a [Na+]0.5 of 55 mM were calculated. It is suggested that an anionic pantothenate1- molecule is cotransported with two Na+ to give a net charge of +1. The coupling of pantothenate transport to the Na+ electrochemical gradient may provide an efficient mechanism for reabsorption of pantothenate in the kidney.     

Effect of luminal Na+ on the kinetics of intestinal absorption of sugars in vivo

The effect of sodium concentration on the absorption kinetics of glucose, galactose and 3-o-methyl-glucose in rat and hamster jejunum in vivo has been studied. In consecutive 1 min periods the total absorption and absorption in presence of 0.5 mM phlorizin were measured. The difference between them was taken as the active transport rate. The perfusion rate value was 5.6 ml X min-1 and sugar concentrations in the perfusion solution ranged from 1 to 10 mM. The results for the different sodium concentrations show a nearly common Vmax for the same sugar and animal species, while the apparent KT values increase when the sodium concentration in the lumen decreases, mimicking a pure affinity-type activation system. The absorption of sugar when solutions without Na+ are perfused, is greater than that entering passively in the presence of phlorizin. An explanation may be that appreciable amounts of endogenous Na+ find their way to the intestinal lumen in favour of the gradient, making Na+-sugar cotransport possible.     

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.     

A mathematical model of the urine concentrating mechanism in the rat renal medulla. II. Functional implications of three-dimensional architecture

In a companion study [Layton AT. A mathematical model of the urine concentrating mechanism in the rat renal medulla. I. Formulation and base-case results. Am J Physiol Renal Physiol. (First published November 10, 2010). 10.1152/ajprenal.00203.2010] a region-based mathematical model was formulated for the urine concentrating mechanism in the renal medulla of the rat kidney. In the present study, we investigated model sensitivity to some of the fundamental structural assumptions. An unexpected finding is that the concentrating capability of this region-based model falls short of the capability of models that have radially homogeneous interstitial fluid at each level of only the inner medulla (IM) or of both the outer medulla and IM, but are otherwise analogous to the region-based model. Nonetheless, model results reveal the functional significance of several aspects of tubular segmentation and heterogeneity: 1) the exclusion of ascending thin limbs that reach into the deep IM from the collecting duct clusters in the upper IM promotes urea cycling within the IM; 2) the high urea permeability of the lower IM thin limb segments allows their tubular fluid urea content to equilibrate with the surrounding interstitium; 3) the aquaporin-1-null terminal descending limb segments prevent water entry and maintain the transepithelial NaCl concentration gradient; 4) a higher thick ascending limb Na(+) active transport rate in the inner stripe augments concentrating capability without a corresponding increase in energy expenditure for transport; 5) active Na(+) reabsorption from the collecting duct elevates its tubular fluid urea concentration. Model calculations predict that these aspects of tubular segmentation and heterogeneity promote effective urine concentrating functions.