Mosaic expression of claudins in thick ascending limbs of Henle results in spatial separation of paracellular Na+ and Mg2+ transport.

The thick ascending limb (TAL) of Henle's loop drives paracellular Na+, Ca2+, and Mg2+ reabsorption via the tight junction (TJ). The TJ is composed of claudins that consist of four transmembrane segments, two extracellular segments (ECS1 and -2), and one intracellular loop. Claudins interact within the same (cis) and opposing (trans) plasma membranes. The claudins Cldn10b, -16, and -19 facilitate cation reabsorption in the TAL, and their absence leads to a severe disturbance of renal ion homeostasis. We combined electrophysiological measurements on microperfused mouse TAL segments with subsequent analysis of claudin expression by immunostaining and confocal microscopy. Claudin interaction properties were examined using heterologous expression in the TJ-free cell line HEK 293, live-cell imaging, and Förster/FRET. To reveal determinants of interaction properties, a set of TAL claudin protein chimeras was created and analyzed. Our main findings are that (i) TAL TJs show a mosaic expression pattern of either cldn10b or cldn3/cldn16/cldn19 in a complex; (ii) TJs dominated by cldn10b prefer Na+ over Mg2+, whereas TJs dominated by cldn16 favor Mg2+ over Na+; (iii) cldn10b does not interact with other TAL claudins, whereas cldn3 and cldn16 can interact with cldn19 to form joint strands; and (iv) further claudin segments in addition to ECS2 are crucial for trans interaction. We suggest the existence of at least two spatially distinct types of paracellular channels in TAL: a cldn10b-based channel for monovalent cations such as Na+ and a spatially distinct site for reabsorption of divalent cations such as Ca2+ and Mg2.

Salt stress in the renal tubules is linked to TAL-specific expression of uromodulin and an upregulation of heat shock genes.

Previously, our comprehensive cardiovascular characterization study validated Uromodulin as a blood pressure gene. Uromodulin is a glycoprotein exclusively synthesized at the thick ascending limb of the loop of Henle and is encoded by the Umod gene. Umod-/- mice have significantly lower blood pressure than Umod+/+ mice, are resistant to salt-induced changes in blood pressure, and show a leftward shift in pressure-natriuresis curves reflecting changes of sodium reabsorption. Salt stress triggers transcription factors and genes that alter renal sodium reabsorption. To date there are no studies on renal transcriptome responses to salt stress. Here we aimed use RNA-Seq to delineate salt stress pathways in tubules isolated from Umod+/+ mice (a model of sodium retention) and Umod-/- mice (a model of sodium depletion) ± 300 mosmol sodium chloride ( n = 3 per group). In response to salt stress, the tubules of Umod+/+ mice displayed an upregulation of heat shock transcripts. The greatest changes occurred in the expression of: Hspa1a (Log2 fold change 4.35, P = 2.48 e-12) and Hspa1b (Log2 fold change 4.05, P = 2.48 e-12). This response was absent in tubules of Umod-/- mice. Interestingly, seven of the genes discordantly expressed in the Umod-/- tubules were electrolyte transporters. Our results are the first to show that salt stress in renal tubules alters the transcriptome, increasing the expression of heat shock genes. This direction of effect in Umod+/+ tubules suggest the difference is due to the presence of Umod facilitating greater sodium entry into the tubule cell reflecting a specific response to salt stress.

Role of renal transporters and novel regulatory interactions in the TAL that control blood pressure.

Hypertension (HTN), a major public health issue is currently the leading factor in the global burden of disease, where associated complications account for 9.4 million deaths worldwide every year. Excessive dietary salt intake is among the environmental factors that contribute to HTN, known as salt sensitivity. The heterogeneity of salt sensitivity and the multiple mechanisms that link high salt intake to increases in blood pressure are of upmost importance for therapeutic application. A continual increase in the kidney's reabsorption of sodium (Na+) relies on sequential actions at various segments along the nephron. When the distal segments of the nephron fail to regulate Na+, the effects on Na+ homeostasis are unfavorable. We propose that the specific nephron region where increased active uptake occurs as a result of variations in Na+ reabsorption is at the thick ascending limb of the loop of Henle (TAL). The purpose of this review is to urge the consideration of the TAL as contributing to the pathophysiology of salt-sensitive HTN. Further research in this area will enable development of a therapeutic application for targeted treatment.

Paracellular transport and energy utilization in the renal tubule.

PURPOSE OF REVIEW: Paracellular transport across the tight junction is a general mechanism for transepithelial transport of solutes in epithelia, including the renal tubule. However, why paracellular transport evolved, given the existence of a highly versatile system for transcellular transport, is unknown. RECENT FINDINGS: Recent studies have identified the paracellular channel, claudin-2, that is responsible for paracellular reabsorption of sodium in the proximal renal tubule. Knockout of claudin-2 in mice impairs proximal sodium and fluid reabsorption but is compensated by upregulation of sodium reabsorption in the loop of Henle. This occurs at the expense of increased renal oxygen consumption, hypoxia of the outer medulla and increased susceptibility to ischemic kidney injury. SUMMARY: Paracellular transport can be viewed as a mechanism to exploit the potential energy in existing electrochemical gradients to drive passive transepithelial transport without consuming additional energy. In this way, it enhances the efficiency of energy utilization by transporting epithelia.

Genetic causes of hypomagnesemia, a clinical overview.

Magnesium is essential to the proper functioning of numerous cellular processes. Magnesium ion (Mg2+) deficits, as reflected in hypomagnesemia, can cause neuromuscular irritability, seizures and cardiac arrhythmias. With normal Mg2+ intake, homeostasis is maintained primarily through the regulated reabsorption of Mg2+ by the thick ascending limb of Henle's loop and distal convoluted tubule of the kidney. Inadequate reabsorption results in renal Mg2+ wasting, as evidenced by an inappropriately high fractional Mg2+ excretion. Familial renal Mg2+ wasting is suggestive of a genetic cause, and subsequent studies in these hypomagnesemic families have revealed over a dozen genes directly or indirectly involved in Mg2+ transport. Those can be classified into four groups: hypercalciuric hypomagnesemias (encompassing mutations in CLDN16, CLDN19, CASR, CLCNKB), Gitelman-like hypomagnesemias (CLCNKB, SLC12A3, BSND, KCNJ10, FYXD2, HNF1B, PCBD1), mitochondrial hypomagnesemias (SARS2, MT-TI, Kearns-Sayre syndrome) and other hypomagnesemias (TRPM6, CNMM2, EGF, EGFR, KCNA1, FAM111A). Although identification of these genes has not yet changed treatment, which remains Mg2+ supplementation, it has contributed enormously to our understanding of Mg2+ transport and renal function. In this review, we discuss general mechanisms and symptoms of genetic causes of hypomagnesemia as well as the specific molecular mechanisms and clinical phenotypes associated with each syndrome.

A mathematical model of rat proximal tubule and loop of Henle.

Proximal tubule and loop of Henle function are coupled, with proximal transport determining loop fluid composition, and loop transport modulating glomerular filtration via tubuloglomerular feedback (TGF). To examine this interaction, we begin with published models of the superficial rat proximal convoluted tubule (PCT; including flow-dependent transport in a compliant tubule), and the rat thick ascending Henle limb (AHL). Transport parameters for this PCT are scaled down to represent the proximal straight tubule (PST), which is connected to the thick AHL via a short descending limb. Transport parameters for superficial PCT and PST are scaled up for a juxtamedullary nephron, and connected to AHL via outer and inner medullary descending limbs, and inner medullary thin AHL. Medullary interstitial solute concentrations are specified. End-AHL hydrostatic pressure is determined by distal nephron flow resistance, and the TGF signal is represented as a linear function of end-AHL cytosolic Cl concentration. These two distal conditions required iterative solution of the model. Model calculations capture inner medullary countercurrent flux of urea, and also suggest the presence of an outer medullary countercurrent flux of ammonia, with reabsorption in AHL and secretion in PST. For a realistically strong TGF signal, there is the expected homeostatic impact on distal flows, and in addition, a homeostatic effect on proximal tubule pressure. The model glycosuria threshold is compatible with rat data, and predicted glucose excretion with selective 1Na(+):1glucose cotransporter (SGLT2) inhibition comports with observations in the mouse. Model calculations suggest that enhanced proximal tubule Na(+) reabsorption during hyperglycemia is sufficient to activate TGF and contribute to diabetic hyperfiltration.

Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis.

We present a lumped-nephron model that explicitly represents the main features of the underlying physiology, incorporating the major hormonal regulatory effects on both tubular and vascular function, and that accurately simulates hormonal regulation of renal salt and water excretion. This is the first model to explicitly couple glomerulovascular and medullary dynamics, and it is much more detailed in structure than existing whole organ models and renal portions of multiorgan models. In contrast to previous medullary models, which have only considered the antidiuretic state, our model is able to regulate water and sodium excretion over a variety of experimental conditions in good agreement with data from experimental studies of the rat. Since the properties of the vasculature and epithelia are explicitly represented, they can be altered to simulate pathophysiological conditions and pharmacological interventions. The model serves as an appropriate starting point for simulations of physiological, pathophysiological, and pharmacological renal conditions and for exploring the relationship between the extrarenal environment and renal excretory function in physiological and pathophysiological contexts.

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.

Insulin-like growth factor-1 (IGF-1) inhibits the basolateral Cl channels in the thick ascending limb of the rat kidney.

The aim of the present study is to test the hypothesis that insulin-like-growth factor-1 (IGF-1) plays a role in the regulation of basolateral Cl channels in the thick ascending limb (TAL). The patch-clamp experiments demonstrated that application of IGF-I or insulin inhibited the basolateral 10-pS Cl channels. However, the concentration of insulin required for the inhibition of the Cl channels by 50% (K(1/2)) was ten times higher than those of IGF-1. The inhibitory effect of IGF-I on the 10-pS Cl channels was blocked by suppressing protein tyrosine kinase or by blocking phosphoinositide 3-kinase (PI3K). In contrast, inhibition of phospholipase C (PLC) failed to abolish the inhibitory effect of IGF-1 on the Cl channels in the TAL. Western blot analysis demonstrated that IGF-1 significantly increased the phosphorylation of phospholipid-dependent kinase (PDK) at serine residue 241 (Ser(241)) and AKT at Ser(473) in the isolated medullary TAL. Moreover, inhibition of PI3K with LY294002 abolished the effect of IGF-1 on the phosphorylation of PDK and AKT. The notion that the effect of IGF-1 on the 10-pS Cl channels was induced by stimulation of PDK-AKT-mTOR pathway was further suggested by the finding that rapamycin completely abolished the effect of IGF-1 on the 10-pS Cl channels in the TAL. We conclude that IGF-1 inhibits the basolateral Cl channels by activating PI3K-AKT-mTOR pathways. The inhibitory effect of IGF-1 on the Cl channels may play a role in ameliorating the ischemia-induced renal injury through IGF-1 administration.

Mitochondrial proteomic analysis reveals deficiencies in oxygen utilization in medullary thick ascending limb of Henle in the Dahl salt-sensitive rat.

The renal medullary thick ascending limb (mTAL) of the Dahl salt-sensitive (SS) rat is the site of enhanced NaCl reabsorption and excess superoxide production. In the present studies we isolated mitochondria from mTAL of SS and salt-resistant control strain SS.13(BN) rats on 0.4 and 8% salt diet for 7 days and performed a proteomic analysis. Purity of mTAL and mitochondria isolations exceeded 93.6 and 55%, respectively. Using LC/MS spectral analysis techniques we identified 96 mitochondrial proteins in four biological mTAL mitochondria samples, run in duplicate, as defined by proteins with a false discovery rate <5% and scan count ≥2. Seven of these 96 proteins, including IDH2, ACADM, SCOT, Hsp60, ATPA, EFTu, and VDAC2 were differentially expressed between the two rat strains. Oxygen consumption and high-resolution respirometry analyses showed that mTAL cells and the mitochondria in the outer medulla of SS rats fed high-salt diet exhibited lower rates of oxygen utilization compared with those from SS.13(BN) rats. These studies advance the conventional proteomic paradigm of focusing exclusively upon whole tissue homogenates to a focus upon a single cell type and specific subcellular organelle. The results reveal the importance of a largely unexplored role for deficiencies of mTAL mitochondrial metabolism and oxygen utilization in salt-induced hypertension and renal medullary oxidative stress.

Signal transduction in a compliant thick ascending limb.

In several previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model, which represents the TAL as a rigid tube, predicts that TGF signal transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to constant intratubular fluid flow, the time interval required for an element of tubular fluid to traverse the TAL, as a function of time, is oscillatory and periodic but not sinusoidal. As a consequence, NaCl concentration in tubular fluid alongside the macula densa will be nonsinusoidal and thus contain harmonics of the original sinusoidal frequency. We hypothesized that the complexity found in power spectra based on in vivo time series of key TGF variables arises in part from those harmonics and that nonlinearities in TGF-mediated oscillations may result in increased NaCl delivery to the distal nephron. To investigate the possibility that a more realistic model of the TAL would damp the harmonics, we have conducted new studies in a model TAL that has compliant walls and thus a tubular radius that depends on transmural pressure. These studies predict that compliant TAL walls do not damp, but instead intensify, the harmonics. In addition, our results predict that mean TAL flow strongly influences the shape of the NaCl concentration waveform at the macula densa. This is a consequence of the inverse relationship between flow speed and transit time, which produces asymmetry between up- and downslopes of the oscillation, and the nonlinearity of TAL NaCl absorption at low flow rates, which broadens the trough of the oscillation relative to the peak. The dependence of waveform shape on mean TAL flow may be the source of the variable degree of distortion, relative to a sine wave, seen in experimental recordings of TGF-mediated oscillations.

Isolated interstitial nodal spaces may facilitate preferential solute and fluid mixing in the rat renal inner medulla.

Recent anatomic findings indicate that in the upper inner medulla of the rodent kidney, tubules, and vessels are organized around clusters of collecting ducts (CDs). Within CD clusters, CDs and some of the ascending vasa recta (AVR) and ascending thin limbs (ATLs), when viewed in transverse sections, form interstitial nodal spaces, which are arrayed at structured intervals throughout the inner medulla. These spaces, or microdomains, are bordered on one side by a single CD, on the opposite side by one or more ATLs, and on the other two sides by AVR. To study the interactions among these CDs, ATLs, and AVR, we have developed a mathematical compartment model, which simulates steady-state solute exchange through the microdomain at a given inner medullary level. Fluid in all compartments contains Na(+), Cl(-), urea and, in the microdomain, negative fixed charges that represent macromolecules (e.g., hyaluronan) balanced by Na(+). Fluid entry into AVR is assumed to be driven by hydraulic and oncotic pressures. Model results suggest that the isolated microdomains facilitate solute and fluid mixing among the CDs, ATLs, and AVR, promote water withdrawal from CDs, and consequently may play an important role in generating the inner medullary osmotic gradient.

Increase of sodium delivery stimulates the mitochondrial respiratory chain H2O2 production in rat renal medullary thick ascending limb.

The mitochondria-rich epithelial cells of the renal medullary thick ascending limb (mTAL) reabsorb nearly 25% of filtered sodium (Na(+)) and are a major source of cellular reactive oxygen species. Although we have shown that delivery of Na(+) to the mTAL of rats increases superoxide (O(2)(·-)) production in mTAL, little is known about H(2)O(2) production, given the lack of robust and selective fluorescent indicators for determining changes within the whole cell, specifically in the mitochondria. The present study determined the effect of increased tubular flow and Na(+) delivery to mTAL on the production of mitochondrial H(2)O(2) in mTAL. H(2)O(2) responses were determined in isolated, perfused mTAL of Sprague-Dawley rats using a novel mitochondrial selective fluorescent H(2)O(2) indicator, mitochondria peroxy yellow 1, and a novel, highly sensitive and stable cytosolic-localized H(2)O(2) indicator, peroxyfluor-6 acetoxymethyl ester. The results showed that mitochondrial H(2)O(2) and cellular fluorescent signals increased progressively over a period of 30 min following increased tubular perfusion (5-20 nl/min), reaching levels of statistical significance at ∼10-12 min. Responses were inhibited with rotenone or antimycin A (inhibitors of the electron-transport chain), polyethylene glycol-catalase and by reducing Na(+) transport with furosemide or ouabain. Inhibition of membrane NADPH-oxidase with apocynin had no effect on mitochondrial H(2)O(2) production. Cytoplasmic H(2)O(2) (peroxyfluor-6 acetoxymethyl ester) increased in parallel with mitochondrial H(2)O(2) (mitochondria peroxy yellow 1) and was partially attenuated (∼65%) by rotenone and completely inhibited by apocynin. The present data provide clear evidence that H(2)O(2) is produced in the mitochondria in response to increased flow and delivery of Na(+) to the mTAL, and that whole cell H(2)O(2) levels are triggered by the mitochondrial reactive oxygen species production. The mitochondrial production of H(2)O(2) may represent an important target for development of more effective antioxidant therapies.

The betaine-GABA transporter (BGT1, slc6a12) is predominantly expressed in the liver and at lower levels in the kidneys and at the brain surface.

The Na(+)- and Cl(-)-dependent GABA-betaine transporter (BGT1) has received attention mostly as a protector against osmolarity changes in the kidney and as a potential controller of the neurotransmitter GABA in the brain. Nevertheless, the cellular distribution of BGT1, and its physiological importance, is not fully understood. Here we have quantified mRNA levels using TaqMan real-time PCR, produced a number of BGT1 antibodies, and used these to study BGT1 distribution in mice. BGT1 (protein and mRNA) is predominantly expressed in the liver (sinusoidal hepatocyte plasma membranes) and not in the endothelium. BGT1 is also present in the renal medulla, where it localizes to the basolateral membranes of collecting ducts (particularly at the papilla tip) and the thick ascending limbs of Henle. There is some BGT1 in the leptomeninges, but brain parenchyma, brain blood vessels, ependymal cells, the renal cortex, and the intestine are virtually BGT1 deficient in 1- to 3-mo-old mice. Labeling specificity was assured by processing tissue from BGT1-deficient littermates in parallel as negative controls. Addition of 2.5% sodium chloride to the drinking water for 48 h induced a two- to threefold upregulation of BGT1, tonicity-responsive enhancer binding protein, and sodium-myo-inositol cotransporter 1 (slc5a3) in the renal medulla, but not in the brain and barely in the liver. BGT1-deficient and wild-type mice appeared to tolerate the salt treatment equally well, possibly because betaine is one of several osmolytes. In conclusion, this study suggests that BGT1 plays its main role in the liver, thereby complementing other betaine-transporting carrier proteins (e.g., slc6a20) that are predominantly expressed in the small intestine or kidney rather than the liver.

An improved method of renal tissue engineering, by combining renal dissociation and reaggregation with a low-volume culture technique, results in development of engineered kidneys complete with loops of Henle.

BACKGROUND: Tissue engineering of functional kidney tissue is an important goal for clinical restoration of renal function in patients damaged by infectious, toxicological, or genetic disease. One promising approach is the use of the self-organizing abilities of embryonic kidney cells to arrange themselves, from a simply reaggregated cell suspension, into engineered organs similar to fetal kidneys. The previous state-of-the-art method for this results in the formation of a branched collecting duct tree, immature nephrons (S-shaped bodies) beside and connected to it, and supportive stroma. It does not, though, result in the significant formation of morphologically detectable loops of Henle - anatomical features of the nephron that are critical to physiological function. METHODS: We have combined the best existing technique for renal tissue engineering from cell suspensions with a low-volume culture technique that allows intact kidney rudiments to make loops of Henle to test whether engineered kidneys can produce these loops. RESULTS: The result is the formation of loops of Henle in engineered cultured 'fetal kidneys', very similar in both morphology and in number to those formed by intact organ rudiments. CONCLUSION: This brings the engineering technique one important step closer to production of a fully realistic organ.

Renal outer medullary potassium channel knockout models reveal thick ascending limb function and dysfunction.

The renal outer medullary potassium channel (ROMK) is an adenosine triphosphate-sensitive inward-rectifier potassium channel (Kir1.1 or KCNJ1) highly expressed in the cortical and medullary thick ascending limbs (TAL), connecting segment (CNT) and cortical collecting duct (CCD) in the mammalian kidney, where it serves to recycle potassium (K(+)) across the apical membrane in TAL and to secrete K(+) in the CNT and CCD. ROMK channel mutations cause type II Bartter's syndrome with salt wasting and dehydration, and ROMK knockout mice display a similar phenotype of Bartter's syndrome in humans. Studies from ROMK null mice indicate that ROMK is required to form both the small-conductance (30pS, SK) K channels and the 70pS (IK) K channels in the TAL. The availability of ROMK(-/-) mice has made it possible to study electrolyte transport along the nephron in order to understand the TAL function under physiological conditions and the compensatory mechanisms of salt and water transport under the conditions of TAL dysfunction. This review summarizes previous progress in the study of K(+) channel activity in the TAL and CCD, ion transporter expression and activities along the nephron, and renal functions under physiological and pathophysiological conditions using ROMK(-/-) mice.

Hypoxia-inducible transcription factors stabilization in the thick ascending limb protects against ischemic acute kidney injury.

Hypoxia-inducible transcription factors (HIF) protect cells against oxygen deprivation, and HIF stabilization before ischemia mitigates tissue injury. Because ischemic acute kidney injury (AKI) often involves the thick ascending limb (TAL), modulation of HIF in this segment may be protective. Here, we generated mice with targeted TAL deletion of the von Hippel-Lindau protein (Vhl), which mediates HIF degradation under normoxia, using Tamm-Horsfall protein (Thp)-driven Cre expression. These mice showed strong expression of HIF-1α in TALs but no changes in kidney morphology or function under control conditions. Deficiency of Vhl in the TAL markedly attenuated proximal tubular injury and preserved TAL function following ischemia-reperfusion, which may be partially a result of enhanced expression of glycolytic enzymes and lactate metabolism. These results highlight the importance of the thick ascending limb in the pathogenesis of AKI and suggest that pharmacologically targeting the HIF system may have potential to prevent and mitigate AKI.

[Magnesium homeostasis and its disturbances].

Magnesium homeostasis is maintained through normal functions of the kidney, intestine, and bone. In the kidney, approximately 80% magnesium is filtered by the glomeruli. In general, 95% filtered magnesium is collectively reabsorbed in the proximal tubule (15%-20%) , thick ascending limb of Henle (TAL, 65%-75%) , and the distal convoluted tubule (DCT, 5%-10%) . In the TAL, magnesium reabsorption regulated by the paracellular pathway via claudin-16 is driven by electrochemical voltage. Chloride channel Kb and renal outer medullary potassium channels control this lumen-positive voltage. In the DCT, the transcellular pathway via transient receptor potential melastatin 6 (TRPM6) plays a fundamental role in the final 5%-10% magnesium reabsorption. The functions of TRPM6 depend on Na-Cl co-transporters and Na( + )-K( + )-ATPase. Defects in these regulatory proteins may cause inherited or drug-induced disorders of magnesium metabolism. Recently, some proteins have been confirmed to be responsible for magnesium homeostasis ; however, further research is required to elucidate the mechanisms underlying the maintenance of magnesium homeostasis.

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.