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

Aquaporins in Urinary System

There are at least eight aquaporins (AQPs) expressed in the kidney. Including AQP1 expressed in proximal tubules, thin descending limb of Henle and vasa recta; AQP2, AQP3, AQP4, AQP5, and AQP6 expressed in collecting ducts; AQP7 expressed in proximal tubules; AQP8 expressed in proximal tubules and collecting ducts; and AQP11 expressed in the endoplasmic reticulum of proximal tubular epithelial cells. Over years, researchers have constructed different AQP knockout mice and explored the effect of AQP knockout on kidney function. Thus, the roles of AQPs in renal physiology are revealed, providing very useful information for addressing fundamental questions about transepithelial water transport and the mechanism of near isoosmolar fluid reabsorption. This chapter introduces the localization and function of AQPs in the kidney and their roles in different kidney diseases to reveal the prospects of AQPs in further basic and clinical studies.

Mathematical models for kidney function focusing on clinical interest

We give an overview of mathematical models of renal physiology and anatomy with the clinician in mind. Beyond the past focus on issues of local transport mechanisms along the nephron and the urine concentrating mechanism, recent models have brought insight into difficult problems such as renal ischemia (oxygen and CO₂ diffusion in the medulla) or calcium and potassium homeostasis. They have also provided revealing 3D reconstructions of the full trajectories of families of nephrons and collecting ducts through cortex and medulla. The recent appearance of sophisticated whole-kidney models representing nephrons and their associated renal vasculature promises more realistic simulation of renal pathologies and pharmacological treatments in the foreseeable future.

Mammalian urine concentration: a review of renal medullary architecture and membrane transporters

Mammalian kidneys play an essential role in balancing internal water and salt concentrations. When water needs to be conserved, the renal medulla produces concentrated urine. Central to this process of urine concentration is an osmotic gradient that increases from the corticomedullary boundary to the inner medullary tip. How this gradient is generated and maintained has been the subject of study since the 1940s. While it is generally accepted that the outer medulla contributes to the gradient by means of an active process involving countercurrent multiplication, the source of the gradient in the inner medulla is unclear. The last two decades have witnessed advances in our understanding of the urine-concentrating mechanism. Details of medullary architecture and permeability properties of the tubules and vessels suggest that the functional and anatomic relationships of these structures may contribute to the osmotic gradient necessary to concentrate urine. Additionally, we are learning more about the membrane transporters involved and their regulatory mechanisms. The role of medullary architecture and membrane transporters in the mammalian urine-concentrating mechanism are the focus of this review.

Modeling glucose metabolism and lactate production in the kidney

The metabolism of glucose provides most of the ATP required for energy-dependent transport processes. In the inner medulla of the mammalian kidney, limited blood flow and O2 supply yield low oxygen tension; therefore, a substantial fraction of the glucose metabolism in that region is anaerobic. Lactate is considered to be a waste product of anaerobic glycolysis, which yields two lactate molecules for each glucose molecule consumed, thereby likely leading to the production and accumulation of a significant amount of lactate in the inner medulla. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed mathematical model of the renal medulla of the rat kidney. The model represents the radial organization of the renal tubules and vessels, which centers around the vascular bundles in the outer medulla and around clusters of collecting ducts in the inner medulla. Model simulations yield significant radial gradients in interstitial fluid oxygen tension and glucose and lactate concentrations in the outer medulla and upper inner medulla. In the deep inner medulla, interstitial fluid concentrations become much more homogeneous, as the radial organization of tubules and vessels is not distinguishable. Using this model, we have identified parameters concerning glucose transport and basal metabolism, as well as lactate production via anaerobic glycolysis, that yield predicted blood glucose and lactate concentrations consistent with experimental measurements in the papillary tip. In addition, simulations indicate that the radial organization of the rat kidney may affect lactate buildup in the inner medulla.

Aquaporins in Urinary System

Several aquaporin (AQP )-type water channels are expressed in kidney: AQP1 in the proximal tubule, thin descending limb of Henle, and vasa recta; AQP2 -6 in the collecting duct; AQP7 in the proximal tubule; AQP8 in the proximal tubule and collecting duct; and AQP11 in the endoplasmic reticulum of proximal tubule cells. AQP2 is the vasopressin-regulated water channel that is important in hereditary and acquired diseases affecting urine-concentrating ability. The roles of AQPs in renal physiology and transepithelial water transport have been determined using AQP knockout mouse models. This chapter describes renal physiologic insights revealed by phenotypic analysis of AQP knockout mice and the prospects for further basic and clinical studies.

Modeling Glucose Metabolism in the Kidney

The mammalian kidney consumes a large amount of energy to support the reabsorptive work it needs to excrete metabolic wastes and to maintain homeostasis. Part of that energy is supplied via the metabolism of glucose. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed model of the renal medulla of the rat kidney. The model represents water and solute flows, transmural fluxes, and biochemical reactions in the luminal fluid of the nephrons and vessels. In particular, the model simulates the metabolism of oxygen and glucose. Using that model, we have identified parameters concerning glucose transport and basal metabolism that yield predicted blood glucose concentrations that are consistent with experimental measurements. The model predicts substantial axial gradients in blood glucose levels along various medullary structures. Furthermore, the model predicts that in the inner medulla, owing to the relatively limited blood flow and low tissue oxygen tension, anaerobic metabolism of glucose dominates.

Mathematical Model of Ammonia Handling in the Rat Renal Medulla

The kidney is one of the main organs that produces ammonia and release it into the circulation. Under normal conditions, between 30 and 50% of the ammonia produced in the kidney is excreted in the urine, the rest being absorbed into the systemic circulation via the renal vein. In acidosis and in some pathological conditions, the proportion of urinary excretion can increase to 70% of the ammonia produced in the kidney. Mechanisms regulating the balance between urinary excretion and renal vein release are not fully understood. We developed a mathematical model that reflects current thinking about renal ammonia handling in order to investigate the role of each tubular segment and identify some of the components which might control this balance. The model treats the movements of water, sodium chloride, urea, NH₃ and NH4+, and non-reabsorbable solute in an idealized renal medulla of the rat at steady state. A parameter study was performed to identify the transport parameters and microenvironmental conditions that most affect the rate of urinary ammonia excretion. Our results suggest that urinary ammonia excretion is mainly determined by those parameters that affect ammonia recycling in the loops of Henle. In particular, our results suggest a critical role for interstitial pH in the outer medulla and for luminal pH along the inner medullary collecting ducts.

Urine-concentrating mechanism in the inner medulla: function of the thin limbs of the loops of Henle

The ability of mammals to produce urine hyperosmotic to plasma requires the generation of a gradient of increasing osmolality along the medulla from the corticomedullary junction to the papilla tip. Countercurrent multiplication apparently establishes this gradient in the outer medulla, where there is substantial transepithelial reabsorption of NaCl from the water-impermeable thick ascending limbs of the loops of Henle. However, this process does not establish the much steeper osmotic gradient in the inner medulla, where there are no thick ascending limbs of the loops of Henle and the water-impermeable ascending thin limbs lack active transepithelial transport of NaCl or any other solute. The mechanism generating the osmotic gradient in the inner medulla remains an unsolved mystery, although it is generally considered to involve countercurrent flows in the tubules and vessels. A possible role for the three-dimensional interactions between these inner medullary tubules and vessels in the concentrating process is suggested by creation of physiologic models that depict the three-dimensional relationships of tubules and vessels and their solute and water permeabilities in rat kidneys and by creation of mathematical models based on biologic phenomena. The current mathematical model, which incorporates experimentally determined or estimated solute and water flows through clearly defined tubular and interstitial compartments, predicts a urine osmolality in good agreement with that observed in moderately antidiuretic rats. The current model provides substantially better predictions than previous models; however, the current model still fails to predict urine osmolalities of maximally concentrating rats.

Advances in Understanding the Urine-Concentrating Mechanism

The renal medulla produces concentrated urine through the generation of an osmotic gradient that progressively increases from the cortico-medullary boundary to the inner medullary tip. In the outer medulla, the osmolality gradient arises principally from vigorous active transport of NaCl, without accompanying water, from the thick ascending limbs of short- and long-looped nephrons. In the inner medulla, the source of the osmotic gradient has not been identified. Recently, there have been important advances in our understanding of key components of the urine-concentrating mechanism, including (a) better understanding of the regulation of water, urea, and sodium transport proteins; (b) better resolution of the anatomical relationships in the medulla; and (c) improvements in mathematical modeling of the urine-concentrating mechanism. Continued experimental investigation of signaling pathways regulating transepithelial transport, both in normal animals and in knockout mice, and incorporation of the resulting information into mathematical simulations may help to more fully elucidate the mechanism for concentrating urine in the inner medulla.

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.

A model of calcium transport along the rat nephron

We developed a mathematical model of calcium (Ca2+) transport along the rat nephron to investigate the factors that promote hypercalciuria. The model is an extension of the flat medullary model of Hervy and Thomas ( Am J Physiol Renal Physiol 284: F65–F81, 2003). It explicitly represents all the nephron segments beyond the proximal tubules and distinguishes between superficial and deep nephrons. It solves dynamic conservation equations to determine NaCl, urea, and Ca2+ concentration profiles in tubules, vasa recta, and the interstitium. Calcium is known to be reabsorbed passively in the thick ascending limbs and actively in the distal convoluted (DCT) and connecting (CNT) tubules. Our model predicts that the passive diffusion of Ca2+ from the vasa recta and loops of Henle generates a significant axial Ca2+ concentration gradient in the medullary interstitium. In the base case, the urinary Ca2+ concentration and fractional excretion are predicted as 2.7 mM and 0.32%, respectively. Urinary Ca2+ excretion is found to be strongly modulated by water and NaCl reabsorption along the nephron. Our simulations also suggest that Ca2+ molar flow and concentration profiles differ significantly between superficial and deep nephrons, such that the latter deliver less Ca2+ to the collecting duct. Finally, our results suggest that the DCT and CNT can act to counteract upstream variations in Ca2+ transport but not always sufficiently to prevent hypercalciuria.

Comparative physiology and architecture associated with the mammalian urine concentrating mechanism: role of inner medullary water and urea transport pathways in the rodent medulla

Comparative studies of renal structure and function have potential to provide insights into the urine-concentrating mechanism of the mammalian kidney. This review focuses on the tubular transport pathways for water and urea that play key roles in fluid and solute movements between various compartments of the rodent renal inner medulla. Information on aquaporin water channel and urea transporter expression has increased our understanding of functional segmentation of medullary thin limbs of Henle's loops, collecting ducts, and vasa recta. A more complete understanding of membrane transporters and medullary architecture has identified new and potentially significant interactions between these structures and the interstitium. These interactions are now being introduced into our concept of how the inner medullary urine-concentrating mechanism works. A variety of regulatory pathways lead directly or indirectly to variable patterns of fluid and solute movements among the interstitial and tissue compartments. Animals with the ability to produce highly concentrated urine, such as desert species, are considered to exemplify tubular structure and function that optimize urine concentration. These species may provide unique insights into the urine-concentrating process.(1)

Urine concentrating mechanism in the inner medulla of the mammalian kidney: role of three-dimensional architecture

The urine concentrating mechanism in the mammalian renal inner medulla (IM) is not understood, although it is generally considered to involve countercurrent flows in tubules and blood vessels. A possible role for the three-dimensional relationships of these tubules and vessels in the concentrating process is suggested by recent reconstructions from serial sections labelled with antibodies to tubular and vascular proteins and mathematical models based on these studies. The reconstructions revealed that the lower 60% of each descending thin limb (DTL) of Henle's loops lacks water channels (aquaporin-1) and osmotic water permeability and ascending thin limbs (ATLs) begin with a prebend segment of constant length. In the outer zone of the IM (i) clusters of coalescing collecting ducts (CDs) form organizing motif for loops of Henle and vasa recta; (ii) DTLs and descending vasa recta (DVR) are arrayed outside CD clusters, whereas ATLs and ascending vasa recta (AVR) are uniformly distributed inside and outside clusters; (iii) within CD clusters, interstitial nodal spaces are formed by a CD on one side, AVR on two sides, and an ATL on the fourth side. These spaces may function as mixing chambers for urea from CDs and NaCl from ATLs. In the inner zone of the IM, cluster organization disappears and half of Henle's loops have broad lateral bends wrapped around terminal CDs. Mathematical models based on these findings and involving solute mixing in the interstitial spaces can produce urine slightly more concentrated than that of a moderately antidiuretic rat but no higher.

Modeling transport in the kidney: investigating function and dysfunction

Mathematical models of water and solute transport in the kidney have significantly expanded our understanding of renal function in both health and disease. This review describes recent theoretical developments and emphasizes the relevance of model findings to major unresolved questions and controversies. These include the fundamental processes by which urine is concentrated in the inner medulla, the ultrastructural basis of proteinuria, irregular flow oscillation patterns in spontaneously hypertensive rats, and the mechanisms underlying the hypotensive effects of thiazides. Macroscopic models of water, NaCl, and urea transport in populations of nephrons have served to test, confirm, or refute a number of hypotheses related to the urine concentrating mechanism. Other macroscopic models focus on the mechanisms, role, and irregularities of renal hemodynamic control and on the regulation of renal oxygenation. At the mesoscale, models of glomerular filtration have yielded significant insight into the ultrastructural basis underlying a number of disorders. At the cellular scale, models of epithelial solute transport and pericyte Ca2+ signaling are being used to elucidate transport pathways and the effects of hormones and drugs. Areas where further theoretical progress is conditional on experimental advances are also identified.

The physiology of urinary concentration: an update

The renal medulla produces concentrated urine through the generation of an osmotic gradient extending from the cortico-medullary boundary to the inner medullary tip. This gradient is generated in the outer medulla by the countercurrent multiplication of a comparatively small transepithelial difference in osmotic pressure. This small difference, called a single effect, arises from active NaCl reabsorption from thick ascending limbs, which dilutes ascending limb flow relative to flow in vessels and other tubules. In the inner medulla, the gradient may also be generated by the countercurrent multiplication of a single effect, but the single effect has not been definitively identified. There have been important recent advances in our understanding of key components of the urine concentrating mechanism. In particular, the identification and localization of key transport proteins for water, urea, and sodium, the elucidation of the role and regulation of osmoprotective osmolytes, better resolution of the anatomical relationships in the medulla, and improvements in mathematic modeling of the urine concentrating mechanism. Continued experimental investigation of transepithelial transport and its regulation, both in normal animals and in knock-out mice, and incorporation of the resulting information into mathematic simulations, may help to more fully elucidate the inner medullary urine concentrating mechanism.

The Mammalian Urine Concentrating Mechanism: Hypotheses and Uncertainties

The urine concentrating mechanism of the mammalian kidney, which can produce a urine that is substantially more concentrated than blood plasma during periods of water deprivation, is one of the enduring mysteries in traditional physiology. Owing to the complex lateral and axial relationships of tubules and vessels, in both the outer and inner medulla, the urine concentrating mechanism may only be fully understood in terms of the kidney’s three-dimensional functional architecture and its implications for preferential interactions among tubules and vessels.

Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla

Recent studies of three-dimensional architecture of rat renal inner medulla (IM) and expression of membrane proteins associated with fluid and solute transport in nephrons and vasculature have revealed structural and transport properties that likely impact the IM urine concentrating mechanism. These studies have shown that 1) IM descending thin limbs (DTLs) have at least two or three functionally distinct subsegments; 2) most ascending thin limbs (ATLs) and about half the ascending vasa recta (AVR) are arranged among clusters of collecting ducts (CDs), which form the organizing motif through the first 3-3.5 mm of the IM, whereas other ATLs and AVR, along with aquaporin-1-positive DTLs and urea transporter B-positive descending vasa recta (DVR), are external to the CD clusters; 3) ATLs, AVR, CDs, and interstitial cells delimit interstitial microdomains within the CD clusters; and 4) many of the longest loops of Henle form bends that include subsegments that run transversely along CDs that lie in the terminal 500 microm of the papilla tip. Based on a more comprehensive understanding of three-dimensional IM architecture, we distinguish two distinct countercurrent systems in the first 3-3.5 mm of the IM (an intra-CD cluster system and an inter-CD cluster system) and a third countercurrent system in the final 1.5-2 mm. Spatial arrangements of loop of Henle subsegments and multiple countercurrent systems throughout four distinct axial IM zones, as well as our initial mathematical model, are consistent with a solute-separation, solute-mixing mechanism for concentrating urine in the IM.

Living history of physiology: Bodil Schmidt-Nielsen

In 2005, The American Physiological Society initiated The Living History of Physiology Project to recognize senior members who have made extraordinary contributions during their career to the advancement of the discipline and profession of physiology. Each physiologist will be interviewed for archival purposes, and the video tape will be available from the American Physiological Society Headquarters. In addition, a biographical profile of the recipient will be published in Advances in Physiology Education.

A model of glucose transport and conversion to lactate in the renal medullary microcirculation

In this study, we modeled mathematically the transport of glucose across renal medullary vasa recta and its conversion to lactate by anaerobic glycolysis. Uncertain parameter values were determined by seeking good agreement between predictions and experimental measurements of lactate generation rates, as well as glucose and lactate concentration ratios between the papilla and the corticomedullary junction; plausible kinetic rate constant and permeability values are summarized in tabular form. Our simulations indicate that countercurrent exchange of glucose from descending (DVR) to ascending vasa recta (AVR) in the outer medulla (OM) and upper inner medulla (IM) severely limits delivery to the deep inner medulla, thereby limiting medullary lactate generation. If the permeability to glucose of OMDVR and IMDVR is taken to be the same and equal to 4 x 10(-4) cm/s, the fraction of glucose that bypasses the IM is calculated as 54%; it is predicted as 37% if the presence of pericytes in OMDVR reduces the glucose permeability of these vessels by a factor of 2 relative to that of IMDVR. Our results also suggest that red blood cells (RBCs) act as a reservoir that reduces the bypass of glucose from DVR to AVR. The rate of lactate generation by anaerobic glycolysis of glucose supplied by blood from glomerular efferent arterioles is predicted to range from 2 to 8 nmol/s, in good agreement with lower estimates obtained from the literature (Bernanke D and Epstein FH. Am J Physiol 208: 541-545, 1965; Bartlett S, Espinal J, Janssens P, and Ross BD. Biochem J 219: 73-78, 1984).

Two modes for concentrating urine in rat inner medulla

We used a mathematical model of the urine concentrating mechanism of rat inner medulla (IM) to investigate the implications of experimental studies in which immunohistochemical methods were combined with three-dimensional computerized reconstruction of renal tubules. The mathematical model represents a distribution of loops of Henle with loop bends at all levels of the IM, and the vasculature is represented by means of the central core assumption. Based on immunohistochemical evidence, descending limb portions that reach into the papilla are assumed to be only moderately water permeable or to be water impermeable, and only prebend segments and ascending thin limbs are assumed to be NaCl permeable. Model studies indicate that this configuration favors the targeted delivery of NaCl to loop bends, where a favorable gradient, sustained by urea absorption from collecting ducts, promotes NaCl absorption. We identified two model modes that produce a significant axial osmolality gradient. One mode, suggested by preliminary immunohistochemical findings, assumes that aquaporin-1-null portions of loops of Henle that reach into the papilla have very low urea permeability. The other mode, suggested by perfused tubule experiments from the literature, assumes that these same portions of loops of Henle have very high urea permeabilities. Model studies were conducted to determine the sensitivity of these modes to parameter choices. Model results are compared with extant tissue-slice and micropuncture studies.

Concentration of solutes in the renal inner medulla: interstitial hyaluronan as a mechano-osmotic transducer

Although the concentrating process in the renal outer medulla is well understood, the concentrating mechanism in the renal inner medulla remains an enigma. The purposes of this review are fourfold. 1) We summarize a theoretical basis for classifying all possible steady-state inner medullary countercurrent concentrating mechanisms based on mass balance principles. 2) We review the major hypotheses that have been proposed to explain the axial osmolality gradient in the interstitium of the renal inner medulla. 3) We summarize and expand on the Schmidt-Nielsen hypothesis that the contractions of the renal pelvocalyceal wall may provide an important energy source for concentration in the inner medulla. 4) We discuss the special properties of hyaluronan, a glycosaminoglycan that is the chief component of a gel-like renal inner medullary interstitial matrix, which may allow it to function as a mechano-osmotic transducer, converting energy from the contractions of the pelvic wall to an axial osmolality gradient in the medulla. These considerations set the stage for renewed experimental investigation of the urinary concentrating process and a new generation of mathematical models of the renal concentrating mechanism, which treat the inner medullary interstitium as a viscoelastic system rather than a purely hydraulic system.

Inner medullary lactate production and accumulation: a vasa recta model

Since anaerobic glycolysis yields two lactates for each glucose consumed and since it is reported to be a major source of ATP for inner medullary (IM) cell maintenance, it is a likely source of "external" IM osmoles. It has long been known that such an osmole source could theoretically contribute to the "single-effect" of the urine concentrating mechanism, but there was previously no suggestion of a plausible source. I used numerical simulation to estimate axial gradients of lactate and glucose that might be accumulated by countercurrent recycling in IM vasa recta (IMVR). Based on measurements in other tissues, anaerobic glycolysis (assumed to be independent of diuretic state) was estimated to consume approximately 20% of the glucose delivered to the IM. IM tissue mass and axial distribution of loops and vasa recta were according to reported values for rat and other rodents. Lactate (P(LAC)) and glucose (P(GLU)) permeabilities were varied over a range of plausible values. The model results suggest that P(LAC) of 100 x 10(-5) cm/s (similar to measured permeabilities for other small solutes) is sufficiently high to ensure efficient lactate recycling. By contrast, it was necessary in the model to reduce P(GLU) to a small fraction of this value (1/25th) to avoid papillary glucose depletion by countercurrent shunting. The results predict that IM lactate production could suffice to build a significant steady-state axial lactate gradient in the IM interstitium. Other modeling studies (Jen JF and Stephenson JL. Bull Math Biol 56: 491-514, 1994; and Thomas SR and Wexler AS. Am J Physiol Renal Fluid Electrolyte Physiol 269: F159-F171, 1995) have shown that 20-100 mosmol/kgH(2)O of unspecified external, interstitial, osmolytes could greatly improve IM concentrating ability. The present study gives several plausible scenarios consistent with accumulation of metabolically produced lactate osmoles, although only to the lower end of this range. For example, if 20% of entering glucose is consumed, the model predicts that papillary lactate would attain about 15 mM assuming vasa recta outflow is increased 30% by fluid absorbed from the nephrons and collecting ducts and that this lactate gradient would double if IM blood flow were reduced by one-half, as may occur in antidiuresis. Several experimental tests of the hypothesis are indicated.

Requirement of aquaporin-1 for NaCl-driven water transport across descending vasa recta

Deletion of AQP1 in mice results in diminished urinary concentrating ability, possibly related to reduced NaCl- and urea gradient-driven water transport across the outer medullary descending vasa recta (OMDVR). To quantify the role of AQP1 in OMDVR water transport, we measured osmotically driven water permeability in vitro in microperfused OMDVR from wild-type, AQP1 heterozygous, and AQP1 knockout mice. OMDVR diameters in AQP1(-/-) mice were 1.9-fold greater than in AQP1(+/+) mice. Osmotic water permeability (P(f)) in response to a 200 mM NaCl gradient (bath > lumen) was reduced about 2-fold in AQP1(+/-) mice and by more than 50-fold in AQP1(-/-) mice. P(f) increased from 1015 to 2527 microm/s in AQP1(+/+) mice and from 22 to 1104 microm/s in AQP1(-/-) mice when a raffinose rather than an NaCl gradient was used. This information, together with p-chloromercuribenzenesulfonate inhibition measurements, suggests that nearly all NaCl-driven water transport occurs by a transcellular route through AQP1, whereas raffinose-driven water transport also involves a parallel, AQP1-independent, mercurial-insensitive pathway. Interestingly, urea was also able to drive water movement across the AQP1-independent pathway. Diffusional permeabilities to small hydrophilic solutes were comparable in AQP1(+/+) and AQP1(-/-) mice but higher than those previously measured in rats. In a mathematical model of the medullary microcirculation, deletion of AQP1 resulted in diminished concentrating ability due to enhancement of medullary blood flow, partially accounting for the observed urine-concentrating defect.

Cycles and separations in a model of the renal medulla

This study gives the first quantitative analysis of net steady-state transmural fluxes of water, urea, and NaCl in a numerical model of the rat renal medulla in antidiuresis, revealing the model's predictions of water, urea, and NaCl cycling patterns. These predictions are compared both to in vivo micropuncture data from the literature and to earlier qualitative proposals (e.g., K. V. Lemley and W. Kriz. Kidney Int. 31: 538-548, 1987) of cycling and exchange patterns based on medullary anatomy and available permeability and transport parameter measurements. The analysis is based on our most recent three-dimensional model [X. Wang, S. R. Thomas, and A. S. Wexler. Am. J. Physiol. 274 (Renal Physiol. 43): F413-F424, 1998]. In general agreement with earlier proposed patterns, this analysis predicts the following: 1) important water short-circuiting from descending structures to ascending vasa recta in most medullary regions, 2) massive urea recycling in the upper inner medulla, 3) a progressive increase of the ratio of urea to total osmoles along the corticopapillary axis, 4) urea dumped from the collecting ducts (CD) into the deep papilla is returned to the cortex essentially via outer medullary short vasa recta, bearing witness to a shift from the long descending limbs and vasa recta of the inner medulla (IM) to short structures in the outer medulla (OM). The analysis also shows that the known radial heterogeneity of the inner stripe (IS) implies unequal osmolalities in long descending limbs, vasa recta, and CDs entering the IM across the OM/IM border and explains the model's unorthodox osmolality profile along the CD. In conflict with micropuncture evidence of a doubling of urea flow in superficial Henle's loops (SHL) between the end proximal and early distal tubule (T. Armsen and H. W. Reinhardt. Pflügers Arch. 326: 270-280, 1971), the model predicts net urea loss from SHL due to the model's inclusion of nonneglible measured urea permeability of medullary thick ascending limbs [M. A. Knepper, Am. J. Physiol. 245 (Renal Fluid Electrolyte Physiol. 14): F634-F639, 1983]. We present a suite of adjusted model permeabilities that improves agreement with the micropuncture data on this point. In conclusion, this modeling analysis of solute and water recycling serves as a quantitative check on qualitative propositions in the literature and allows closer critical comparison of model behavior with published experimental results than was heretofore possible.

Severely impaired urinary concentrating ability in transgenic mice lacking aquaporin-1 water channels

Water channel aquaporin-1 (AQP1) is strongly expressed in kidney in proximal tubule and descending limb of Henle epithelia and in vasa recta endothelia. The grossly normal phenotype in human subjects deficient in AQP1 (Colton null blood group) and in AQP4 knockout mice has suggested that aquaporins (other than the vasopressin-regulated water channel AQP2) may not be important in mammalian physiology. We have generated transgenic mice lacking detectable AQP1 by targeted gene disruption. In kidney proximal tubule membrane vesicles from knockout mice, osmotic water permeability was reduced 8-fold compared with vesicles from wild-type mice. Although the knockout mice were grossly normal in terms of survival, physical appearance, and organ morphology, they became severely dehydrated and lethargic after water deprivation for 36 h. Body weight decreased by 35 +/- 2%, serum osmolality increased to >500 mOsm, and urinary osmolality (657 +/- 59 mOsm) did not change from that before water deprivation. In contrast, wild-type and heterozygous mice remained active after water deprivation, body weight decreased by 20-22%, serum osmolality remained normal (310-330 mOsm), and urine osmolality rose to >2500 mOsm. Urine [Na+] in water-deprived knockout mice was <10 mM, and urine osmolality was not increased by the V2 agonist DDAVP. The results suggest that AQP1 knockout mice are unable to create a hypertonic medullary interstitium by countercurrent multiplication. AQP1 is thus required for the formation of a concentrated urine by the kidney.

Fourfold reduction of water permeability in inner medullary collecting duct of aquaporin-4 knockout mice

Aquaporin (AQP)-3 and AQP4 water channels are expressed at the basolateral membrane of mammalian collecting duct epithelium. To determine the contribution of AQP4 to water permeability in the initial inner medullary collecting duct (IMCD), osmotic water permeability (Pf) was compared in isolated perfused IMCD segments from wild-type and AQP4 knockout mice. The AQP4 knockout mice were previously found to have normal gross appearance, survival, growth, and kidney morphology and a mild urinary concentrating defect (T. Ma, B. Yang, A. Gillespie, E. J. Carlson, C. J. Epstein, and A. S. Verkman, J. Clin. Invest. 100: 957-962, 1997). Transepithelial Pf was measured in microdissected IMCDs after 18-48 h of water deprivation and in the presence of 0.1 nM arginine vasopressin (to make basolateral Pf rate limiting). Pf values (37 degrees C; means +/- SE in cm/s x 10(-3)) were 56.0 +/- 8.5 for wild-type mice (n = 5) and 13.1 +/- 3.7 for knockout mice (n = 6) (P < 0.001). Northern blot analysis of kidney showed that transcript expression of AQP1, AQP2, AQP3, and AQP6 were not affected by AQP4 deletion. Immunoblot analysis indicated no differences in protein expression of AQP1, AQP2, or AQP3, and immunoperoxidase showed no differences in staining patterns. Coexpression of AQP3 and AQP4 in Xenopus laevis oocytes showed additive water permeabilities, suggesting that AQP4 deletion does not affect AQP3 function. These results indicate that AQP4 is responsible for the majority of basolateral membrane water movement in IMCD but that its deletion is associated with a very mild defect in urinary concentrating ability.