A mathematical model of the urine concentrating mechanism in the rat renal medulla. I. Formulation and base-case results

A new, region-based mathematical model of the urine concentrating mechanism of the rat renal medulla was used to investigate the significance of transport and structural properties revealed in anatomic studies. The model simulates preferential interactions among tubules and vessels by representing concentric regions that are centered on a vascular bundle in the outer medulla (OM) and on a collecting duct cluster in the inner medulla (IM). Particularly noteworthy features of this model include highly urea-permeable and water-impermeable segments of the long descending limbs and highly urea-permeable ascending thin limbs. Indeed, this is the first detailed mathematical model of the rat urine concentrating mechanism that represents high long-loop urea permeabilities and that produces a substantial axial osmolality gradient in the IM. That axial osmolality gradient is attributable to the increasing urea concentration gradient. The model equations, which are based on conservation of solutes and water and on standard expressions for transmural transport, were solved to steady state. Model simulations predict that the interstitial NaCl and urea concentrations in adjoining regions differ substantially in the OM but not in the IM. In the OM, active NaCl transport from thick ascending limbs, at rates inferred from the physiological literature, resulted in a concentrating effect such that the intratubular fluid osmolality of the collecting duct increases ~2.5 times along the OM. As a result of the separation of urea from NaCl and the subsequent mixing of that urea and NaCl in the interstitium and vasculature of the IM, collecting duct fluid osmolality further increases by a factor of ~1.55 along the IM.     

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.     

Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney

It has become widely accepted that the osmolality gradient along the corticomedullary axis of the mammalian outer medulla is generated and sustained by a process of countercurrent multiplication: active NaCl absorption from thick ascending limbs is coupled with the counterflow configuration of the descending and ascending limbs of the loops of Henle to generate an axial osmolality gradient along the outer medulla. However, aspects of anatomic structure (e.g., the physical separation of the descending limbs of short loops of Henle from contiguous ascending limbs), recent physiologic experiments (e.g., those that suggest that the thin descending limbs of short loops of Henle have a low osmotic water permeability), and mathematical modeling studies (e.g., those that predict that water-permeable descending limbs of short loops are not required for the generation of an axial osmolality gradient) suggest that countercurrent multiplication may be an incomplete, or perhaps even erroneous, explanation. We propose an alternative explanation for the axial osmolality gradient: we regard the thick limbs as NaCl sources for the surrounding interstitium, and we hypothesize that the increasing axial osmolality gradient along the outer medulla is primarily sustained by an increasing ratio, as a function of increasing medullary depth, of NaCl absorption (from thick limbs) to water absorption (from thin descending limbs of long loops of Henle and, in antidiuresis, from collecting ducts). We further hypothesize that ascending vasa recta that are external to vascular bundles will carry, toward the cortex, an absorbate that at each medullary level is hyperosmotic relative to the adjacent interstitium.     

Role of UTB Urea Transporters in the Urine Concentrating Mechanism of the Rat Kidney

A mathematical model of the renal medulla of the rat kidney was used to investigate urine concentrating mechanism function in animals lacking the UTB urea transporter. The UTB transporter is believed to mediate countercurrent urea exchange between descending vasa recta (DVR) and ascending vasa recta (AVR) by facilitating urea transport across DVR endothelia. The model represents the outer medulla (OM) and inner medulla (IM), with the actions of the cortex incorporated via boundary conditions. Blood flow in the model vasculature is divided into plasma and red blood cell compartments. In the base-case model configuration tubular dimensions and transport parameters are based on, or estimated from, experimental measurements or immunohistochemical evidence in wild-type rats. The base-case model configuration generated an osmolality gradient along the cortico-medullary axis that is consistent with measurements from rats in a moderately antidiuretic state. When expression of UTB was eliminated in the model, model results indicated that, relative to wild-type, the OM cortico-medullary osmolality gradient and the net urea flow through the OM were little affected by absence of UTB transporter. However, because urea transfer from AVR to DVR was much reduced, urea trapping by countercurrent exchange was significantly compromised. Consequently, urine urea concentration and osmolality were decreased by 12% and 8.9% from base case, respectively, with most of the reduction attributable to the impaired IM concentrating mechanism. These results indicate that the in vivo urine concentrating defect in knockout mouse, reported by Yang et al. (J Biol Chem 277(12), 10633–10637, 2002), is not attributable to an OM concentrating mechanism defect, but that reduced urea trapping by long vasa recta plays a significant role in compromising the concentrating mechanism of the IM. Moreover, model results are in general agreement with the explanation of knockout renal function proposed by Yang et al.     

Functional morphology of the avian medullary cone

The organization of the renal medulla of the Gambel's quail, Callipepla gambelii, kidney was examined to determine the number of loops of Henle and collecting ducts and the surface area occupied by the different nephron segments as a function of distance down the medullary cones. Eleven medullary cones were dissected from the kidneys of four birds, and the tissue was processed and sectioned for light microscopy. In addition, individual nephrons were isolated on which total loop thin descending segment and thick prebend segment lengths were measured. The results show no correlation between the absolute number of loops of Henle and the length of the medullary cones. The number of thick and thin limbs of Henle and collecting ducts decrease exponentially with distance toward the apex of the cones and the rate of decrease is similar for cones of different lengths. Initially there is a rapid decrease in the number of thin limbs of Henle, indicating that most nephrons do not penetrate the cones a great distance. Thick descending limbs of Henle (prebend segment) ranged in length from 50 to 770 microm, and there was little correlation with the total length of the loop of Henle. However, the length of the thin limb of Henle correlated well with total loop length. The cell surface areas of the limbs of the loop of Henle and the collecting ducts decreased toward the apex of the cones.     

Ultrastructural localization of Na+,K+-ATPase in rat and rabbit kidney medulla

Na+,K+-ATPase was localized at the ultrastructural level in rat and rabbit kidney medulla. The cytochemical method for the K+-dependent phosphatase component of the enzyme, using p-nitrophenylphosphate (NPP) as substrate, was employed to demonstrate the distribution of Na+, K+- ATPase in tissue-chopped sections from kidneys perfusion-fixed with 1% paraformaldehyde-0.25% glutaraldehyde. In other outer medulla of rat kidney, ascending thick limbs (MATL) were sites of intense K+-dependent NPPase (K+-NPPase) activity, whereas descending thick limbs and collecting tubules were barely reactive. Although descending thin limbs (DTL) of short loop nephrons were unstained, DTL from long loop nephrons in outer medulla were sites of moderate K+-NPPase activity. In rat inner medulla, DTL and ascending thin limbs (ATL) were unreactive for K+-NPPase. In rabbit medulla, only MATL were sites of significant K+-NPPase activity. The specificity of the cytochemical localization of Na+,K+-ATPase at reactive sites in rat and rabbit kidney medulla was demonstrated by K+-dependence of reaction product deposition, localization of reaction product (precipitated phosphate hydrolyzed from NPP) to the cytoplasmic side of basolateral plasma membranes, insensitivity of the reaction to inhibitors of nonspecific alkaline phosphatase, and, in the glycoside-sensitive rabbit kidney, substantial inhibition of staining by ouabain. The observed pattern of distribution of the sodium transport enzyme in kidney medulla is particularly relevant to current models for urine concentration. The presence of substantial Na+,K+-ATPase in MATL is consistent with the putative role of this segment as the driving force for the countercurrent multiplication system in the outer medulla. The absence of significant activity in inner medullary ATL and DTL, however, implies that interstitial solute accumulation in this region probably occurs by passive processes. The localization of significant Na+,K+-ATPase in outer medullary DTL of long loop nephrons in the rat suggests that solute addition in this segment may occur in part by an active salt secretory mechanism that could ultimately contribute to the generation of inner medullary interstitial hypertonicity and urine concentration.     

Architecture of kangaroo rat inner medulla: segmentation of descending thin limb of Henle's loop

We hypothesize that the inner medulla of the kangaroo rat Dipodomys merriami, a desert rodent that concentrates its urine to more than 6,000 mosmol/kgH(2)O water, provides unique examples of architectural features necessary for production of highly concentrated urine. To investigate this architecture, inner medullary nephron segments in the initial 3,000 μm below the outer medulla were assessed with digital reconstructions from physical tissue sections. Descending thin limbs of Henle (DTLs), ascending thin limbs of Henle (ATLs), and collecting ducts (CDs) were identified by immunofluorescence using antibodies that label segment-specific proteins associated with transepithelial water flux (aquaporin 1 and 2, AQP1 and AQP2) and chloride flux (the chloride channel ClC-K1); all tubules and vessels were labeled with wheat germ agglutinin. In the outer 3,000 μm of the inner medulla, AQP1-positive DTLs lie at the periphery of groups of CDs. ATLs lie inside and outside the groups of CDs. Immunohistochemistry and reconstructions of loops that form their bends in the outer 3,000 μm of the inner medulla show that, relative to loop length, the AQP1-positive segment of the kangaroo rat is significantly longer than that of the Munich-Wistar rat. The length of ClC-K1 expression in the prebend region at the terminal end of the descending side of the loop in kangaroo rat is about 50% shorter than that of the Munich-Wistar rat. Tubular fluid of the kangaroo rat DTL may approach osmotic equilibrium with interstitial fluid by water reabsorption along a relatively longer tubule length, compared with Munich-Wistar rat. A relatively shorter-length prebend segment may promote a steeper reabsorptive driving force at the loop bend. These structural features predict functionality that is potentially significant in the production of a high urine osmolality in the kangaroo rat.     

Histotopography and ultrastructure of the thin limbs of the loop of Henle in the hamster

Summary In the kidney of the Syrian hamster the descending thin limbs of both the short and long loops of Henle are not spatially separated from each other and descend between the vascular bundles.Ultrastructurally, five different epithelial types are distinguished in the thin limbs of the short and long loops of Henle. Short loops possess only a descending thin limb with a simply organized epithelium (type 1). Long loops comprise an upper and a lower part of the descending thin limb and the ascending thin limb. The upper part of the long descending thin limb is equipped with a complex and highly interdigitating epithelium with shallow junctions (type 2), which gradually transforms into the simple noninterdigitating type-3 epithelium of the lower part. In a minor portion of long descending thin limbs, however, the upper part begins with an even more complexly organized epithelium (type 2a) than type 2. Type-2a epithelium is conspicuously thicker and possesses a more elaborate mode of cellular interdigitation. Along the descent of this tubular part through the inner stripe of the outer medulla, type-2a epithelium transforms into type-2 epithelium. It is suggested that the long descending thin limbs, which start with type-2a epithelium, belong to the longest loops. The type-4 epithelium of the ascending thin limbs is characterized by flat and extensively interdigitating cells with shallow junctions.The unique pattern of the type-2 a epithelium favors the assumption that solute secretion essentially contributes to the increase in concentration of tubular fluid in long descending thin limbs.This investigation was supported by the Deutsche Forschungsgemeinschaft; project Kr 546 Henlesche Schleife     

The theory of urine formation in water diuresis with implications for antidiuresis

We investigate a model of the renal medulla in which active NaCl transport is restricted to the thick ascending limb of Henle's loop. The model contains a vas rectum, a loop of Henle, salt, and water. The model generates interstitial osmolality curves consonant with the known functioning of the kidney in water diuresis. Using data from the white rat and the curves generated by the model, one can predict the permeability of the thin limb of Henle's loop to NaCl and the percentage of total renal blood flow entering the inner medulla. In this model interstitial osmolality at the papilla can be about twice plasma osmolality, so that NaCl transport restricted to the outer medulla can contribute significantly to the work required in producing a hypertonic urine. However, the interstitial osmolality monotonically decreases proceeding from the junction of the outer and inner medulla to the papilla, and the maximum interstitial osmolality in the outer medulla is greater than the maximum interstitial osmolality in the inner medulla. Thus we infer that a source of active transport located in the inner medulla is needed to explain the high osmolalities observed in hydropenia. A sketch of an alternative model, a “lineal multiplication mechanism”, for the renal concentrating process is presented in which active transport in the inner medulla is restricted to active salt transport by the collecting duct. The lineal multiplication mechanism makes no use of counter-current multipliers in the inner medulla. The research of this author was supported in part by NIH Grant AM06864-03 and a Career Scientist Award from the Health Research Council of New York City, Contr. No. 1391. The research of this author was supported in part by the Office of Naval Research, U.S. Navy under Contr. N(onr) 595(17). The research of this author was supported in part by Grant NSF GP-2067 from the National Science Foundation and was performed at the University of Maryland.     

Maximum Urine Concentrating Capability in a Mathematical Model of the Inner Medulla of the Rat Kidney

In a mathematical model of the urine concentrating mechanism of the inner medulla of the rat kidney, a nonlinear optimization technique was used to estimate parameter sets that maximize the urine-to-plasma osmolality ratio (U/P) while maintaining the urine flow rate within a plausible physiologic range. The model, which used a central core formulation, represented loops of Henle turning at all levels of the inner medulla and a composite collecting duct (CD). The parameters varied were: water flow and urea concentration in tubular fluid entering the descending thin limbs and the composite CD at the outer-inner medullary boundary; scaling factors for the number of loops of Henle and CDs as a function of medullary depth; location and increase rate of the urea permeability profile along the CD; and a scaling factor for the maximum rate of NaCl transport from the CD. The optimization algorithm sought to maximize a quantity E that equaled U/P minus a penalty function for insufficient urine flow. Maxima of E were sought by changing parameter values in the direction in parameter space in which E increased. The algorithm attained a maximum E that increased urine osmolality and inner medullary concentrating capability by 37.5% and 80.2%, respectively, above base-case values; the corresponding urine flow rate and the concentrations of NaCl and urea were all within or near reported experimental ranges. Our results predict that urine osmolality is particularly sensitive to three parameters: the urea concentration in tubular fluid entering the CD at the outer-inner medullary boundary, the location and increase rate of the urea permeability profile along the CD, and the rate of decrease of the CD population (and thus of CD surface area) along the cortico-medullary axis.     

Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla

Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, ɛ, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting ɛ to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L⁻¹ can be generated by forces of the order of 20 mosm L⁻¹. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.     

Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney

The glomerular filtration rate in the kidney is controlled, in part, by the tubuloglomerular feedback (TGF) system, which is a negative feedback loop that mediates oscillations in tubular fluid flow and in fluid NaCl concentration of the loop of Henle. In this study, we developed a mathematical model of the TGF system that represents NaCl transport along a short loop of Henle with compliant walls. The proximal tubule and the outer-stripe segment of the descending limb are assumed to be highly water permeable; the thick ascending limb (TAL) is assumed to be water impermeable and have active NaCl transport. A bifurcation analysis of the TGF model equations was performed by computing parameter boundaries, as functions of TGF gain and delay, that separate differing model behaviors. The analysis revealed a complex parameter region that allows a variety of qualitatively different model equations: a regime having one stable, time-independent steady-state solution and regimes having stable oscillatory solutions of different frequencies. A comparison with a previous model, which represents only the TAL explicitly and other segments using phenomenological relations, indicates that explicit representation of the proximal tubule and descending limb of the loop of Henle lowers the stability of the TGF system. Model simulations also suggest that the onset of limit-cycle oscillations results in increases in the time-averaged distal NaCl delivery, whereas distal fluid delivery is not much affected.     

Cellular basis of an avian countercurrent multiplier system

A kidney from the budgerigar (budgie, parakeet; Melopsittacus undulatus) is composed of cortical reptilian-type nephrons (without loops of Henle) and mammalian-type nephrons (with loops) grouped together in medullary cones. The loop of the mammalian-type nephrons has a descending segment composed of thin and highly interdigitated cells. These thin limb cells have few mitochondria (15% of cell volume), undetectable Na+,K(+)-ATPase activity, and virtually no basolateral surface amplification. Prior to the hairpin turn, the descending limb thickens, but the cells continue to lack basolateral amplification. Cells just prior to and within the hairpin turn resemble cells of the entire ascending limb. These cells are thick (there is no thin ascending segment in the avian loop), with extensive infoldings of the basolateral membrane surrounding numerous mitochondria (45% of cell volume). The area of basolateral membrane is 25 times that of the apical membrane. The basolateral membrane (but not the apical membrane) is enriched in Na+,K(+)-ATPase activity. The structure of the avian mammalian-type nephron (as epitomized by the budgie nephron) and the fact that NaCl accounts for over 90% of the osmotic activity of avian urine leads to the conclusion that the countercurrent multiplier of the avian kidney functions by active NaCl transport from the entire ascending limb. No explanation is offered for the transport specializations found in the thick descending segment of the loop, just prior to the hairpin turn.     

Tubular changes in obstructed kidney of adult mice evaluated using immunohistochemistry for segment-specific marker

The main focus of the present investigation is to examine obstructed kidneys due to unilateral ureteral obstruction (UUO) model in adult mice using segment-specific tubular marker and to confirm the detailed morphological evaluation of UUO that is a typical model for the tubulointerstitial fibrosis which is an endpoint outcome of chronic renal diseases. Adult mice were subjected to UUO, and kidneys were harvested 1, 3, 7 days after surgical operation. Expansion of interstitial space both in the cortex and the medulla was confirmed 3 days after UUO by HE- and azan-staining. Interstitial fibrosis developed especially around dilated tubules. Immunohistochemistry for segment-specific antibodies revealed that the proximal tubules and the descending limb of Henle's loop did not dilate until 7 days after UUO, whereas initial dilation of the ascending limb of Henle's loop appeared to occur one day after surgery. The segment from the distal tubules to the collecting ducts began dilating one day after surgery and afterward significantly dilated. The downstream segment of nephron was involved in dilating earlier than the upstream of nephron in obstructed kidney examined in the present study. Moreover, the tubules accompanying apoptosis of tubular epithelia significantly dilated compared with those without apoptotic tubular epithelia. From the above-mentioned findings, we conclude that tubular dilatation of distal segment (from the ascending limb of Henle's loop to the collecting ducts) of nephron develops tubular epithelial apoptosis caused by accumulated urine, which would link to tubular disappearance and its replacement with fibrous tissue in UUO kidney of adult mice.     

The ultrastructural localization of membrane ATPase in rat thin limbs of the loop of Henle.

The cytochemical distribution of nonspecific membrane ATPase activity in the epithelial membranes of the thin limbs of the loops of Henle of rat nephrons was studied at the ultrastructural level. Membrane ATPase activity was localized in the luminal, lateral, and (to a lesser extent) basal membranes of only the outer medullary segment of the thin descending limbs of long nephrons (Type II epithelium). The reaction product was lacking in the thin limb of short nephrons (Type I epithelium) as well as in the inner medullary descending (Type III epithelium) and ascending (Type IV epithelium) segments of the thin limbs of long nephrons. These data reinforce the concept of thin limb heterogeneity and may indicate a specialized role for the outer medullary segment of thin descending limbs of long nephrons in the concentrating mechanism.     

Countercurrent exchange in the inner renal medulla: Vasa recta-descending limb system

A model of countercurrent exchange has been developed to simulate transport of salt, urea and water among vasa recta and descending limbs of the loop of Henle in the inner medulla. These vessels are abstracted as three concentric cylinders: the inne one represents descending vasa recta, the middle one represents ascending vasa recta and the outer one represents descending limbs. The capillary plexus, which connects the ascending and descending vasa recta, is modeled as a series of well-mixe compartments. Multicomponent transport equations for the sytem are derived from steady state mass balances and simple passive flux relations. The resulting set of nonlinear equations are solved numerically by an iterative Gauss-Seidel algorithm with under-relaxation. Simulations yield the salt and urea concentrations as well as volume flow rates in all tubes and compartments. The simulations indicate that solute concentrations can increase monotonically toward the papillae even if all transport processes within the exchanger are passive and source fluxes decrease monotonically toward the papillae.     

Ultrastructural organization of the hamster renal pelvis.

The renal pelvis of the hamster has been studied by light microscopy (epoxy resin sections), transmission electron microscopy, and morphometric analysis of electron micrographs. Three morphologically distinct epithelia line the pelvis, and each covers a different zone of the kidney. A thin epithelium covering the outer medulla (OM) consists of two cell types: (1) granular cells are most numerous and have apically positioned granules which stain intensely with toluidine blue, are membrane-bound, and contain a fine particulate matter that stains light grey to black in electron micrographs. (2) Basal cells do not have granules, are confined to the basal lamina region, and do not reach the mucosal epithelial surface. The inner medulla (IM) is covered by a pelvic epithelium morphologically similar to collecting duct epithelium of IM. Some cells in this portion of the pelvic epithelium (IM) stain intensely dark with toluidine blue, osmium tetroxide, lead, and uranyl acetate. Transitional epithelium, which separates cortex (C) from pelvic urine, has an asymmetric luminal plasma membrane and discoid vesicles, each of which is similar to those previously observed in mammalian ureter and urinary bladder epithelia. Based on morphological comparisons with other epithelia, the IM and OM pelvic epithelia would appear permeable to solutes and/or water, while the transitional epithelium covering the C appears relatively impermeable. It would also appear that the exchange of solutes and water between pelvic urine and OM would involve capillaries, primarily, since morphometric analysis showed that both fenestrated and continuous capillaries of the OM were extremely abundant (greater than 60% of OM pelvic surface area) just under the thin pelvic epithelium.     

Effect of varying salt and urea permeabilities along descending limbs of Henle in a model of the renal medullary urine concentrating mechanism

Modelling studies have played an important role in research on the mechanism of urine concentration and dilution by the medulla of the kidney ever since Hargitay and Kuhn (1951,Z. Elektrochem. 55, 539–558) first proposed that the parallel tubular structures in the kidney medulla must function as a “countercurrent multiplication” system. Present-day models, in keeping with our considerably improved understanding of most aspects of medullary structure-function relationships, have evolved into rather sophisticated systems of parallel tubes. In spite of this increasing complexity, it has remained the case that “model medullas” do not concentrate as well as the real kidney, especially in the inner medulla where only passive, diffusional transport occurs. Inasmuch as these models take into account the majority of contemporary ideas making up our global hypothesis about the functioning of this system, their failure to behave physiologically indicates that our understanding remains incomplete. The purpose of the present modelling study was to evaluate the implications of some recent measurements showing that permeabilities of NaCl (P _s ) and urea (P _u ) vary along the length of the descending thin limbs of Henle (Imaiet al., 1988,Am. J. Physiol. 254, F323–F328), rather than being constant throughout this segment as had been assumed earlier. It was hoped that these newly measured values might explain, by a passive, diffusional process, the net solute addition at the bend of Henle’s loop observed under some circumstances and heretofore attributed (though without any supporting experimental evidence) to active transport into the descending limb. The results of the present study show that whereas incorporation of the new values forP _s andP _u in the descending limbs of short nephrons does indeed improve the concentrating power of the model, these new values are nonetheless not sufficient to allow the model to build an osmolarity gradient that increases all the way through the inner medulla. This failing, which is common to virtually all modelling studies to date using measured values from rat kidneys, probably points to a key role for preferential exchange supposed by some to exist among certain tubule segments within vascular bundles in species whose kidneys have the highest concentrating power.     

Polyol determination along the rat nephron

The polyols sorbitol and inositol were determined in single freshly microdissected tubule segments of rat kidney. Twenty different structures were separated from six different kidney zones reaching from cortex to papillary tip. Picomol amounts of sorbitol and inositol were quantitated by use of an enzymatic bioluminescence procedure. Experimental conditions (700 mosmol/kg, 4 degrees C) were chosen to assure constant polyol concentrations over 3 h dissection period. Sorbitol exhibited a concentration gradient in the collecting duct system from the outer/inner medullary border (3.9 +/- 0.5 pmol/mm) to the papillary tip (78.8 +/- 6.9 pmol/mm). In the same region descending and ascending limbs of Henle's loop contained 1.5 +/- 0.5 to 5.3 +/- 1.6 pmol/mm and 2.5 +/- 0.8 to 8.35 +/- 1.5 pmol/mm, respectively. In contrast, all outer medullary and cortical structures had lower sorbitol concentrations. Inositol amounts increased continuously in the collecting duct from cortex (5.3 +/- 0.5 pmol/mm) to inner medulla (30.7 +/- 3.8 pmol/mm). This polyol was also found in thick ascending limb of Henle's loop (6.2 +/- 1.1 pmol/mm in cortex to 11.2 +/- 1.4 pmol/mm in outer medulla) and in proximal tubules (5.6 +/- 1.2 pmol/mm in S1 and 4.5 +/- 1.5 pmol/mm in S3). When related to cellular volume measured by planimetry, intracellular sorbitol concentration was calculated to be 51 mmol/l in papillary collecting duct and inositol 28 mmol/l in outer medullary thick ascending limb cells. These data confirm the role of sorbitol in the renal concentrating process in papilla. Inositol seems to have additional function in thick ascending limb of Henle's loop and the proximal tubule.