Na+ Recirculation and Isosmotic Transport

The Na(+) recirculation theory for solute-coupled fluid absorption is an expansion of the local osmosis concept introduced by Curran and analyzed by Diamond & Bossert. Based on studies on small intestine the theory assumes that the observed recirculation of Na(+) serves regulation of the osmolarity of the absorbate. Mathematical modeling reproducing bioelectric and hydrosmotic properties of small intestine and proximal tubule, respectively, predicts a significant range of observations such as isosmotic transport, hyposmotic transport, solvent drag, anomalous solvent drag, the residual hydraulic permeability in proximal tubule of AQP1 (-/-) mice, and the inverse relationship between hydraulic permeability and the concentration difference needed to reverse transepithelial water flow. The model reproduces the volume responses of cells and lateral intercellular space (lis) following replacement of luminal NaCl by sucrose as well as the linear dependence of volume absorption on luminal NaCl concentration. Analysis of solvent drag on Na(+) in tight junctions provides explanation for the surprisingly high metabolic efficiency of Na(+) reabsorption. The model predicts and explains low metabolic efficiency in diluted external baths. Hyperosmolarity of lis is governed by the hydraulic permeability of the apical plasma membrane and tight junction with 6-7 mOsm in small intestine and < or = 1 mOsm in proximal tubule. Truly isosmotic transport demands a Na(+) recirculation of 50-70% in small intestine but might be barely measurable in proximal tubule. The model fails to reproduce a certain type of observations: The reduced volume absorption at transepithelial osmotic equilibrium in AQP1 knockout mice, and the stimulated water absorption by gallbladder in diluted external solutions. Thus, it indicates cellular regulation of apical Na(+) uptake, which is not included in the mathematical treatment.     

Analysis of standing droplets in rat proximal tubules

Volume, osmolality, and concentrations for Na, Cl, and raffinose have been measured as a function of time in standing droplets within rat intermediate and late proximal tubules. Standing droplet reabsorption proceeds without the development of a measurable osmotic difference across the epithelium. After 140 s of tubular exposure, droplet-to- plasma concentration differences are observed for raffinose, Na, and Cl with the observed Na concentration difference, usually referred to as limiting gradient, being approximately 9 mM. It is possible that a smaller or even no limiting difference would be attained with longer exposure times. Previous values measured for the limiting Na concentration in the rat proximal tubule were determined before the attainment of constant concentrations. Assuming that the Na concentration we measured is the limiting value, we estimate that active NaCl transport accounts for a very small fraction, less than 6%, of the volume reabsorption; using an alternative approach of fitting a theoretical model to our experimental data, active NaCl transport is again estimated to account for only 6% of the total reabsorbate. The previous interpretation that a limiting Na concentration gradient constitutes the most direct evidence for active Na transport may be in error; the gradient we measure can be modeled without incorporating active NaCl transport.     

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 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.     

The Mechanism of Isotonic Water Transport

The mechanism by which active solute transport causes water transport in isotonic proportions across epithelial membranes has been investigated. The principle of the experiments was to measure the osmolarity of the transported fluid when the osmolarity of the bathing solution was varied over an eightfold range by varying the NaCl concentration or by adding impermeant non-electrolytes. An in vitro preparation of rabbit gall bladder was suspended in moist oxygen without an outer bathing solution, and the pure transported fluid was collected as it dripped off the serosal surface. Under all conditions the transported fluid was found to approximate an NaCl solution isotonic to whatever bathing solution used. This finding means that the mechanism of isotonic water transport in the gall bladder is neither the double membrane effect nor co-diffusion but rather local osmosis. In other words, active NaCl transport maintains a locally high concentration of solute in some restricted space in the vicinity of the cell membrane, and water follows NaCl in response to this local osmotic gradient. An equation has been derived enabling one to calculate whether the passive water permeability of an organ is high enough to account for complete osmotic equilibration of actively transported solute. By application of this equation, water transport associated with active NaCl transport in the gall bladder cannot go through the channels for water flow under passive conditions, since these channels are grossly too impermeable. Furthermore, solute-linked water transport fails to produce the streaming potentials expected for water flow through these passive channels. Hence solute-linked water transport does not occur in the passive channels but instead involves special structures in the cell membrane, which remain to be identified.     

A mathematical model of proximal tubule absorption

A previous model of the mechanisms of flow through epithelia was modified and extended to include hydrostatic and osmotic pressures in the cells and in the peritubular capillaries. The differential equations for flow and concentration in each region of the proximal tubule were derived. The equations were solved numerically by a finite difference method. The principal conclusions are: (i) Cell NaCl concentration remains essentially isotonic over the pressure variations considered; (ii) channel NaCl concentration varies only a few mosmol from isotonicity, and the hydrostatic and osmotic pressure differences across the cell wall are of the same order of magnitude; (iii) both reabsorbate osmolality and pressure-induced flow are relatively insensitive to the geometry of the system; (iv) a strong equilibrating mechanism exists in the sensitivity of the reabsorbate osmolality to luminal osmolality; this mechanism is far more significant than any other parameter change.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

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.     

Standing-gradient osmotic flow. A mechanism for coupling of water and solute transport in epithelia

At the ultrastructural level, epithelia performing solute-linked water transport possess long, narrow channels open at one end and closed at the other, which may constitute the fluid transport route (e.g., lateral intercellular spaces, basal infoldings, intracellular canaliculi, and brush-border microvilli). Active solute transport into such folded structures would establish standing osmotic gradients, causing a progressive approach to osmotic equilibrium along the channel's length. The behavior of a simple standing-gradient flow system has therefore been analyzed mathematically because of its potential physiological significance. The osmolarity of the fluid emerging from the channel's open end depends upon five parameters: channel length, radius, and water permeability, and solute transport rate and diffusion coefficient. For ranges of values of these parameters encountered experimentally in epithelia, the emergent osmolarity is found by calculation to range from isotonic to a few times isotonic; i.e., the range encountered in epithelial absorbates and secretions. The transported fluid becomes more isotonic as channel radius or solute diffusion coefficient is decreased, or as channel length or water permeability is increased. Given appropriate parameters, a standing-gradient system can yield hypertonic fluids whose osmolarities are virtually independent of transport rate over a wide range, as in distal tubule and avian salt gland. The results suggest that water-to-solute coupling in epithelia is due to the ultrastructural geometry of the transport route.     

Water movement across split frog skin.

A net inward fluid reabsorption (salt-linked flow) has been observed in isolated skin epithelium (split skin) with the same magnitude as in whole skin when identical NaCl Ringer solutions were used to bathe both sides. Split skins also respond to a hyperosmotic sucrose solution bathing the outer (epithelial) surface by generating an outward osmotic flow. A non-linear relationship between osmotic flow and the osmotic gradient has been found in split skin similar to that found in whole skin.     

Role of the Paracellular Pathway in Isotonic Fluid Movement Across the Renal Tubule

Evidence for a highly permeable paracellular shunt in the proximal tubule is reviewed. The paracellular pathway is described as a crucial site for the regulation of net absorption and for solute-solvent interaction. Available models for the coupling of salt and water transport are assessed with respect to the problem of isotonic water movement. Two new models are proposed taking into account that the tight junctions are permeable to salt and water and that active transport sites for sodium are distributed uniformly along the lateral cell membrane. The first model (continuous model) is a modification of Diamond and Bossert''s proposal using different assumptions and boundary conditions. No appreciable standing gradients are predicted by this model. The second model (compartmental model) is an expansion of Curran''s double membrane model by including additional compartments and driving forces. Both models predict a reabsorbate which is not isosmotic. For the particular case of the proximal tubule it is shown that in the presence of a leaky epithelium these deviations from isotonicity might have escaped experimental observation.     

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.     

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.     

A Model of Peritubular Capillary Control of Isotonic Fluid Reabsorption by the Renal Proximal Tubule

A mathematical model of peritubular transcapillary fluid exchange has been developed to investigate the role of the peritubular environment in the regulation of net isotonic fluid transport across the mammalian renal proximal tubule. The model, derived from conservation of mass and the Starling transcapillary driving forces, has been used to examine the quantitative effects on proximal reabsorption of changes in efferent arteriolar protein concentration and plasma flow rate. Under normal physiological conditions, relatively small perturbations in protein concentration are predicted to influence reabsorption more than even large variations in plasma flow, a prediction in close accord with recent experimental observations in the rat and dog. Changes either in protein concentration or plasma flow have their most pronounced effects when the opposing transcapillary hydrostatic and osmotic pressure differences are closest to equilibrium. Comparison of these theoretical results with variations in reabsorption observed in micropuncture studies makes it possible to place upper and lower bounds on the difference between interstitial oncotic and hydrostatic pressures in the renal cortex of the rat.     

Some aspects of osmoregulation in a stenohaline freshwater catfish, Heteropneustes fossilis (Bloch), in different salinities

Transfer of the catfish, Heteropneustes fossilis , to 10% sea water (101 mosmol l⁻¹) or to 0·4% NaCl (140 mosmol l⁻¹) does not evoke any change in plasma osmolarity from the normal freshwater values. There is, however, a reduction in urine flow rate (UFR) and increase in urine osmolarity without any change in the rate of osmolar clearance. In isosmotic (25% sea water or 0·7% NaCl) and in hyperosmotic (30% sea water or 1·1% NaCl) media there is a significant increase in plasma osmolarity accompanied by marked reduction in glomerular filtration rate (GFR), UFR and free water clearance. The results suggest that the catfish cannot effectively osmoregulate in isosmotic or hyperosmotic media and that the inability of the renal tubules to increase reabsorption of water and to reduce free water clearance may account for the restricted range of salinity tolerance of this catfish. Also, in the hyperosmotic media, plasma levels of cortisol are lowered while in the proximal pars distalis the corticotrophs appear active, suggesting increased utilization and clearance of cortisol. Prolactin-secreting cells, however, are degranulated and chromophobic in catfish maintained in hyperosmotic environment.     

The physico-chemical mechanism of mediated transport. II. Osmotic and isosmotic volume flow

The process of volume change of cells subject to osmotic shocks or isosmotic entrance of permeant solute is formulated on the basis of the accepted structure for the plasma membrane and a physico-chemical approach similar to that recently developed. The effect of relevant parameters is discussed and theoretical equilibrium values for the variables are calculated in connection with water and permeant solute permeability determinations. Although a sorption-diffusional mechanism for solute and/or water volume flow within the membrane is assumed in both cases, the kinetics of volume change is shown to be totally different between them. In the isosmotic process a fixed relationship, given by the total solute concentration, is shown to exist between the permeant solute and volume fluxes to the cell, thereby implying a definite value for the volume fraction of water in the migration pathway, higher than 90%. The bi-phase osmotic regulatory response caused by permeant solute is simulated on the basis of an osmotic and isosmotic processes in series, showing good agreement with general behavior. Finally, an explanation to the problem of volume flow and forces in connection with a diffusional mechanism in biological and artificial membranes, is presented.     

The Drosophila inebriated-encoded neurotransmitter/osmolyte transporter: dual roles in the control of neuronal excitability and the osmotic stress response

Water reabsorption by organs such as the mammalian kidney and insect Malpighian tubule/hindgut requires a region of hypertonicity within the organ. To balance the high extracellular osmolarity, cells within these regions accumulate small organic molecules called osmolytes. These osmolytes can accumulate to a high level without toxic effects on cellular processes. Here we provide evidence consistent with the possibility that the two protein isoforms encoded by the inebriated (ine) gene, which are members of the Na+/Cl--dependent neurotransmitter/osmolyte transporter family, perform osmolyte transport within the Malpighian tubule and hindgut. We show that ine mutants lacking both isoforms are hypersensitive to osmotic stress, which we assayed by maintaining flies on media containing NaCl, KCl, or sorbitol, and that this hypersensitivity is completely rescued by high-level ectopic expression of the ine-RB isoform. We provide evidence that this hypersensitivity represents a role for ine that is distinct from the increased neuronal excitability phenotype of ine mutants. Finally, we show that each ine genotype exhibits a "threshold" [NaCl]: long-term maintenance on NaCl-containing media above, but not below, the threshold causes lethality. Furthermore, this threshold value increases with the amount of ine activity. These data suggest that ine mutations confer osmotic stress sensitivity by preventing osmolyte accumulation within the Malpighian tubule and hindgut.     

Hormonal control of renal functions in insects

Insect Malpighian tubules secrete an isosmotic, KCl-rich primary urine containing low concentrations of most other blood solutes. Neuropeptide diuretic hormones (DH), possibly related to vasopressin, stimulate tubular fluid secretion by 2- to 200-fold in response to water loading, e.g., feeding. DH acts on tubules through cyclic AMP (cAMP) to stimulate salt transport without measurable change in osmotic permeability. Changes in composition of tubular secretion after stimulation and the possible control of DH release are discussed. Most of the water, ions, and metabolites in tubular secretion are normally reabsorbed by active mechanisms in the rectum, where the urine may finally become either hyposmotic or strongly hyperosmotic to the blood. A newly discovered neuropeptide, chloride transport-stimulating hormone, controls (via cAMP) reabsorption of the principal salt by stimulating K-dependent, electrogenic transport of Cl- across the apical cell border. Passive net absorption of K+ is thereby enhanced. Diuretic and antidiuretic factors may control osmotic permeability of the rectal wall and thereby influence the osmotic concentrations of the rectal absorbate and final urine. The increased recycling of a KCl-rich fluid through the Malpighian tubule-rectal system after feeding probably serves to clear the body of unwanted substances ingested with, and produced by, metabolism of the meal.     

Mechanisms of salt and water transport in proximal tubule as measured by split drop

A mathematical analysis of split drop experiments indicates that the isosmotic flow assumption is naturally embedded in the system equations. The analysis is applied to the experimental data reported by Maude (1970), who used a polyethylene glycol (PEG 1000) and sodium chloride perfusate in rat proximal tubule. In addition to a value of the permeability coefficient of the slowly permeating species (PEG 1000) which is in accord with Maude's findings, upper limits for the values of sodium and water permeability coefficients are calculated. In particular, it was found that the sodium permeability coefficient is, at most, three times larger than that of PEG 1000. A good fit to the data is provided by a passive transport model.     

Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop

We used a simple mathematical model of rat thick ascending limb (TAL) of the loop of Henle to predict the impact of spatially inhomogeneous NaCl permeability, spatially inhomogeneous NaCl active transport, and spatially inhomogeneous tubular radius on luminal NaCl concentration when sustained, sinusoidal perturbations were superimposed on steady-state TAL flow. A mathematical model previously devised by us that used homogeneous TAL transport and fixed TAL radius predicted that such perturbations result in TAL luminal fluid NaCl concentration profiles that are standing waves. That study also predicted that nodes in NaCl concentration occur at the end of the TAL when the tubular fluid transit time equals the period of a periodic perturbation, and that, for non-nodal periods, sinusoidal perturbations generate non-sinusoidal oscillations (and thus a series of harmonics) in NaCl concentration at the TAL end. In the present study we find that the inhomogeneities transform the standing waves and their associated nodes into approximate standing waves and approximate nodes. The impact of inhomogeneous NaCl permeability is small. However, for inhomogeneous active transport or inhomogeneous radius, the oscillations for non-nodal periods tend to be less sinusoidal and more distorted than in the homogeneous case and to thus have stronger harmonics. Both the homogeneous and non-homogeneous cases predict that the TAL, in its transduction of flow oscillations into concentration oscillations, acts as a low-pass filter, but the inhomogeneities result in a less effective filter that has accentuated non-linearities.