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.     

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.     

An Optimization Algorithm for a Distributed-Loop Model of an Avian Urine Concentrating Mechanism

To better understand how the avian kidney’s morphological and transepithelial transport properties affect the urine concentrating mechanism (UCM), an inverse problem was solved for a mathematical model of the quail UCM. In this model, a continuous, monotonically decreasing population distribution of tubes, as a function of medullary length, was used to represent the loops of Henle, which reach to varying levels along the avian medullary cones. A measure of concentrating mechanism efficiency – the ratio of the free-water absorption rate (FWA) to the total NaCl active transport rate (TAT) – was optimized by varying a set of parameters within bounds suggested by physiological experiments. Those parameters include transepithelial transport properties of renal tubules, length of the prebend enlargement of the descending limb (DL), DL and collecting duct (CD) inflows, plasma Na⁺ concentration, length of the cortical thick ascending limbs, central core solute diffusivity, and population distribution of loops of Henle and of CDs along the medullary cone. By selecting parameter values that increase urine flow rate (while maintaining a sufficiently high urine-to-plasma osmolality ratio (U/P)) and that reduce TAT, the optimization algorithm identified a set of parameter values that increased efficiency by ∼60% above base-case efficiency. Thus, higher efficiency can be achieved by increasing urine flow rather than increasing U/P. The algorithm also identified a set of parameters that reduced efficiency by ∼70% via the production of a urine having near-plasma osmolality at near-base-case TAT.In separate studies, maximum efficiency was evaluated as selected parameters were varied over large ranges. Shorter cones were found to be more efficient than longer ones, and an optimal loop of Henle distribution was found that is consistent with experimental findings.     

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.     

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.     

Localization of thyroxine 5'-monodeiodinase activity in the renal proximal tubules in rabbits and rats

To determine the localization of T4 5'-monodeiodinase activity in rabbit and rat nephron segments, the formation of tri-iodothyronine (T3) from thyroxine (T4) was measured in kidney homogenate and in isolated nephron segments obtained by the microdissection method. In order of decreasing activity, homogenates of rabbit renal cortex, outer medulla and inner medulla were capable of converting T4 to T3. In the isolated nephron segments of the rabbit cortex, the activities were noted in both proximal convoluted and proximal straight tubules. On the other hand, the activities were not detected in segments including the cortical thick ascending limb of Henle's loop, the distal convoluted tubule, the connecting tubule, and the cortical collecting tubule. It is concluded that both the convoluted and the straight tubules are the sites of T3 production in the kidney.     

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.     

Role of vasopressin in the modifications of renal function during aging]

In the course of aging, the renal concentrating ability is markedly reduced. This defect may result from an inappropriate synthesis of antidiuretic hormone in the central nervous system or may be due to an impaired renal response to vasopressin. The two hypotheses have been studied in vivo in rats and in vitro in mice. The results of these studies indicated that: 1) dehydration induces a comparable release of vasopressin along the hypothalamo-hypophysial axis in 10, 20 and 30 month-old rats; 2) there is no change with age of the number of nephrons, single nephron filtration rate or transport capacity of Henle's loop of cortical nephrons which could account for an impaired renal response to vasopressin; 3) the reduced concentrating ability of the kidney appears to be linked to a decreased response of the medullary thick ascending limb of Henle's loop which in part is responsible for the cortico-papillary gradient of solutes within the kidney.     

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.     

Urinary concentrating defect in glutathione-depleted rats

The effect of an acute depletion of glutathione by diethyl maleate injection on renal concentrating function was examined in rats. The parameters tested were the concentration and dilution of urine, applying conventional clearance techniques. Tissue osmolality and Na+-K+ ATPase activity were also measured. Diethyl maleate treated rats showed a diminished renal glutathione concentration and an impairment in the glomerular filtration rate and in electrolyte and water excretion. Treated rats also showed a diminished urine-to-plasma osmolality ratio as compared with controls. The studies on free water formation revealed a marked difference between groups; these data were supported with a diminished medullary Na+-K+ ATPase and a diminished corticomedullary osmolality gradient in the treated rats. The studies suggest that one area of target cells of glutathione depletion is that of the ascending limb of Henle's loop.     

Tubuloglomerular Feedback Signal Transduction in a Short Loop of Henle

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

Role of renal prostaglandins in the fall in urine osmolality after papillary micropuncture

The effect of micropuncture of the renal papilla through an intact ureter on urinary concentrating ability of rats was examined. Micropuncture of the renal papilla caused a fall in urine osmolality in the punctured kidney from 1718 +/- 106 to 1035 +/- 79 mosmol/kg X H2O. In order to investigate the role of renal prostaglandins in this process, PGE2 excretion was measured and found to increase from 63.4 +/- 14.0 to 205.5 +/- 57.1 pg/min. Urine osmolality and PGE2 excretion from the contralateral kidney were not significantly altered. In animals given meclofenamate (2 mg/kg X hr), renal PGE2 excretion was reduced to 22.3 +/- 5.1 pg/min prior to micropuncture and it remained low at 8.9 +/- 1.8 pg/min after papillary micropuncture. Meclofenamate also blocked the fall in urine osmolality caused by micropuncture of the renal papilla, with urine osmolality averaging 1940 +/- 122 before and 1782 +/- 96 mosmol/kg X H2O after the micropuncture. These results indicated that papillary micropuncture through an intact ureter increased renal PGE2 excretion and that a rise in renal production of PGE2 or some other prostanoid is associated with a fall in urine concentrating ability.     

Characterization and localization of ouabain-insensitive Na-dependent ATPase activities along the rat nephron.

Single segments of rat nephron contain two distinct ouabain-insensitive, K-independent, Na-dependent ATPase activities: a Na-stimulated ATPase and a Na-inhibited ATPase. Na-inhibited ATPase activity is found in the proximal tubule and the thick ascending limb of Henle's loop but is absent in the collecting tubule whereas Na-stimulated ATPase is exclusively located in the proximal convoluted tubule. Na-inhibited ATPase, but not Na-stimulated ATPase, is totally abolished in the presence of 100 microM Ca2+. Conversely, Na-stimulated ATPase, but not Na-inhibited ATPase, is curtailed when nephron segments are preincubated at pH 7.2 whereas it is activated at pH 7.8. Finally, Na-stimulated ATPase displays an apparent Km for Na+ of approximately 10 mM, and is dose-dependently inhibited by the diuretic triflocin (IC50 approximately 6 x 10(-6) M).     

Lack of inhibition of vasopressin-stimulated NA+K+ATPase by atrial natriuretic factor in the rat renal medullary thick ascending limb of Henle's loop

The anti-diuretic hormone, arginine vasopressin (AVP) stimulates the activity of Na+K+ATPase in the rat renal medullary thick ascending limb of Henle's loop (mTAL). Atrial natriuretic factor (ANF) has been suggested to exert a tubular effect on the mammalian nephron, perhaps in part, by interacting with other hormones. In the present study, we investigated the effect of rat ANF with and without AVP upon mTAL Na+K+ATPase activity using cytochemical methods. ANF alone failed to inhibit or stimulate Na+K+ATPase activity in mTAL at any of the concentrations tested (10 nmol-0.1 pmol l-1). Unlike the rat hypothalamic digitalis-like factor, ANF (10 nmol-10 fmol l-1) did not inhibit Na+K+ATPase activity after stimulation with AVP (1 fmol l-1) for either 4 or 10 min. The results suggest that ANF does not exert an effect on mTAL, either alone or in conjunction with AVP.     

mPGES-1 deletion potentiates urine concentrating capability after water deprivation

PGE(2) plays an important role in the regulation of fluid metabolism chiefly via antagonizing vasopressin-induced osmotic permeability in the distal nephron, but its enzymatic sources remain uncertain. The present study was undertaken to investigate the potential role of microsomal PGE synthase (mPGES)-1 in the regulation of urine concentrating ability after water deprivation (WD). Following 24-h WD, wild-type (WT) mice exhibited a significant reduction in urine volume, accompanied by a significant elevation in urine osmolality compared with control groups. In contrast, in response to WD, mPGES-1 knockout (KO) mice had much less urine volume and higher urine osmolality. Analysis of plasma volume by measurement of hematocrit and by using a nanoparticle-based method consistently demonstrated that dehydrated WT mice were volume depleted, which was significantly improved in the KO mice. WD induced a twofold increase in urinary PGE(2) output in WT mice, which was completely blocked by mPGES-1 deletion. At baseline, the KO mice had a 20% increase in V(2) receptor mRNA expression in the renal medulla but not the cortex compared with WT controls; the expression was unaffected by WD irrespective of the genotype. In response to WD, renal medullary aquaporin-2 (AQP2) mRNA exhibited a 60% increase in WT mice, and this increase was greater in the KO mice. Immunoblotting demonstrated increased renal medullary AQP2 protein abundance in both genotypes following WD, with a greater increase in the KO mice. Similar results were obtained by using immunohistochemistry. Paradoxically, plasma AVP response to WD seen in WT mice was absent in the KO mice. Taken together, these results suggest that mPGES-1-derived PGE(2) reduces urine concentrating ability through suppression of renal medullary expression of V(2) receptors and AQP2 but may enhance it by mediating the central AVP response.     

Osmoregulation of natriuretic peptide receptor signaling in inner medullary collecting duct. A requirement for p38 MAPK.

In the inner medullary collecting duct of the terminal nephron, the type A natriuretic peptide receptor (NPR-A) plays a major role in determining urinary sodium content. This nephron segment, by virtue of its medullary location, is subject to very high levels of extracellular tonicity. We have examined the ability of medium tonicity to regulate the activity and expression of this receptor in cultured rat inner medullary collecting duct cells. We found that NaCl (75 mm) and sucrose (150 mm), but not urea (150 mm), increased natriuretic peptide receptor activity, gene expression, and promoter activity. The osmotic stimulus also activated extracellular signal-regulated kinase (ERK), c-Jun NH(2)-terminal kinase (JNK), and p38 mitogen-activated protein kinase (p38 MAPK). In the latter instance the beta isoform was selectively activated. Inhibition of p38 MAPK with SB203580 blocked the osmotic induction of receptor activity and expression, as well as receptor gene promoter activity, whereas inhibition of ERK with PD98059 had no effect. Cotransfection of p38 beta MAPK together with the receptor gene promoter resulted in amplification of the osmotic stimulation of the latter, whereas cotransfection of dominant negative MKK6, but not dominant-negative MEK, completely blocked the osmotic induction of receptor promoter activity. Collectively, the data indicate that extracellular osmolality stimulates receptor activity and receptor gene expression through a specific p38 beta-dependent mechanism, raising the possibility that changes in medullary tonicity could play an important role in the regulation of renal sodium handling in the terminal nephron.     

A Standardized Test of Renal Concentrating Capacity in Adults with Some Results in Essential Hypertension

Three groups of patients: A with normal glomerular filtration rate, B with moderate and C with advanced renal damage, were dehydrated and fasted for 30 hours. At regular intervals measurements were taken of urine osmolality, urine specific gravity and serum osmolality. The time required to reach maximum urine osmolality varies with the degree of dehydration and inversely with the severity of kidney damage. In patients with normal glomerular filtration rate, maximum urine osmolality is not attained by 30 hours of dehydration. Thus, for shorter periods, all “normal ranges” of concentrating capacity must be related to specific durations of dehydration. Carefully measured urine specific gravities parallel urine osmolalities closely, especially when proteinuria and glucosuria are absent. The measurement of U/P osmolality ratio offers no clinical advantage in the assessment of renal concentration capacity over the measurement of urine osmolality alone. In Group A, hypertensives achieved higher urine concentrations than did the nonhypertensives under identical test conditions. A normal range for renal concentrating capacity has been presented.     

Urinary Concentrating Ability in Women with Asymptomatic Bacteriuria in Pregnancy

The incidence of impaired renal concentrating ability in pregnant women with asymptomatic significant bacteriuria is significantly less than previously reported when osmolality readings are performed on every urine specimen obtained during the 24 hours'' deprivation of fluids. The concentrating defect is more considerable as pregnancy progresses. The lower the maximum urinary osmolality the more difficult is the treatment of the patient, and the higher the incidence of acute pyelonephritis.     

Ultrastructure of the nephron of the one-humped camel, Camelus dromedarius

The nephron of the one-humped camel Camelus dromedarius was investigated by light and transmission electron microscopy. Besides the many features common to other mammalian kidneys, the nephron of the camel is unique in having an unusually thick basal lamina underlying the epithelial cells of the nephron, the thickest being found in part of the parietal layer of Bowman's capsule and the thin limb of the loop of Henle. In the latter, the membrane usually appears lamellated and contains numerous tiny vesicles. In other parts of the nephron, the basal lamina usually has a homogenous appearance. The possible significance of the thickening of the basal lamina is discussed in relation to the general high renal efficiency of the camel.