A model of calcium transport along the rat nephron

How the kidney regulates magnesium: a modelling study

The kidneys are crucial for maintaining Mg2+ homeostasis. Along the proximal tubule and thick ascending limb, Mg2+ is reabsorbed paracellularly, while along the distal convoluted tubule (DCT), Mg2+ is reabsorbed transcellularly via transient receptor potential melastatin 6 (TRPM6). TRPM6 and other renal transporter expressions are regulated by sex hormones. To investigate renal Mg2 handling, we have developed sex-specific computational models of electrolyte transport along rat superficial nephron. Model simulations indicated that along the proximal tubule and thick ascending limb, Mg2+ and Na+ transport occur parallelly, but they are dissociated along the DCT. In addition, our models predicted higher paracellular Mg2+ permeability in females to attain similar cortical thick ascending limb fractional Mg2+ reabsorption in both sexes. Furthermore, DCT fractional Mg2+ reabsorption is higher in females than in males, allowing females to better fine-tune Mg2+ excretion. We validated our models by simulating the administration of three classes of diuretics. The model predicted significantly increased, marginally increased and significantly decreased Mg2+ excretions for loop, thiazide and K-sparing diuretics, respectively, aligning with experimental findings. The models can be used to conduct in silico studies on kidney adaptations to Mg2+ homeostasis alterations during conditions such as pregnancy, diabetes and chronic kidney disease.

Mathematical modeling of calcium homeostasis in female rats: An analysis of sex differences and maternal adaptations

Calcium plays a vital role in various biological processes, including muscle contractions, blood clotting, skeletal mineralization, and cell signaling. While extracellular calcium makes up less than 1% of total body calcium, it is tightly regulated since too high or too low extracellular calcium concentration can have dangerous effects on the body. Mathematical modeling is a well-suited approach to investigate the complex physiological processes involved in calcium regulation. While mathematical models have been developed to study calcium homeostasis in male rats, none have been used to investigate known sex differences in hormone levels nor the unique physiological states of pregnancy and lactation. Calcitriol, the active form of vitamin D, plays a key role in intestinal calcium absorption, renal calcium reabsorption, and bone remodeling. It has been shown that, when compared to age-matched male rats, females have significantly lower calcitriol levels. In this study we first seek to investigate the impact of this difference as well as other known sex differences on calcium homeostasis using mathematical modeling. Female bodies differ from male bodies in that during their lifetime they may undergo massive adaptations during pregnancy and lactation. Indeed, maternal adaptations impact calcium regulation in all mammals. In pregnant rodents, intestinal absorption of calcium is massively increased in the mother's body to meet the needs of the developing fetus. In a lactating rodent, much of the calcium needs of milk are met by bone resorption, intestinal absorption, and renal calcium reabsorption. Given these observations, the goal of this project is to develop multi-scale whole-body models of calcium homeostasis that represents (1) how sex differences impact calcium homeostasis in female vs. male rats and (2) how a female body adapts to support the excess demands brought on by pregnancy and lactation. We used these models to quantify the impact of individual sex differences as well as maternal adaptations during pregnancy and lactation. Additionally, we conducted "what if" simulations to test whether sex differences in calcium regulation may enable females to better undergo maternal adaptations required in pregnancy and lactation than males.

Claudin-2 deficiency associates with hypercalciuria in mice and human kidney stone disease

The major risk factor for kidney stone disease is idiopathic hypercalciuria. Recent evidence implicates a role for defective calcium reabsorption in the renal proximal tubule. We hypothesized that claudin-2, a paracellular cation channel protein, mediates proximal tubule calcium reabsorption. We found that claudin-2-null mice have hypercalciuria due to a primary defect in renal tubule calcium transport and papillary nephrocalcinosis that resembles the intratubular plugs in kidney stone formers. Our findings suggest that a proximal tubule defect in calcium reabsorption predisposes to papillary calcification, providing support for the vas washdown hypothesis. Claudin-2-null mice were also found to have increased net intestinal calcium absorption, but reduced paracellular calcium permeability in the colon, suggesting that this was due to reduced intestinal calcium secretion. Common genetic variants in the claudin-2 gene were associated with decreased tissue expression of claudin-2 and increased risk of kidney stones in 2 large population-based studies. Finally, we describe a family in which males with a rare missense variant in claudin-2 have marked hypercalciuria and kidney stone disease. Our findings indicate that claudin-2 is a key regulator of calcium excretion and a potential target for therapies to prevent kidney stones.

Claudins in Renal Physiology and Pathology

Claudins are integral proteins expressed at the tight junctions of epithelial and endothelial cells. In the mammalian kidney, every tubular segment express a specific set of claudins that give to that segment unique properties regarding permeability and selectivity of the paracellular pathway. So far, 3 claudins (10b, 16 and 19) have been causally traced to rare human syndromes: variants of CLDN10b cause HELIX syndrome and variants of CLDN16 or CLDN19 cause familial hypomagnesemia with hypercalciuria and nephrocalcinosis. The review summarizes our current knowledge on the physiology of mammalian tight junctions and paracellular ion transport, as well as on the role of the 3 above-mentioned claudins in health and disease. Claudin 14, although not having been causally linked to any rare renal disease, is also considered, because available evidence suggests that it may interact with claudin 16. Some single-nucleotide polymorphisms of CLDN14 are associated with urinary calcium excretion and/or kidney stones. For each claudin considered, the pattern of expression, the function and the human syndrome caused by pathogenic variants are described.

Nanoscale Analysis of Randall's Plaques by Electron Energy Loss Spectromicroscopy: Insight in Early Biomineral Formation in Human Kidney

Idiopathic kidney stones originate mainly from calcium phosphate deposits at the tip of renal papillae, known as Randall's plaques (RPs), also detected in most human kidneys without stones. However, little is known about the mechanisms involved in RP formation. The localization and characterization of such nanosized objects in the kidney remain a real challenge, making their study arduous. This study provides a nanoscale analysis of the chemical composition and morphology of incipient RPs, characterizing in particular the interface between the mineral and the surrounding organic compounds. Relying on data gathered from a calculi collection, the morphology and chemical composition of incipient calcifications in renal tissue were determined using spatially resolved electron energy-loss spectroscopy. We detected microcalcifications and individual nanocalcifications found at some distance from the larger ones. Strikingly, concerning the smaller ones, we show that two types of nanocalcifications coexist: calcified organic vesicles and nanometric mineral granules mainly composed of calcium phosphate with carbonate in their core. Interestingly, some of these nanocalcifications present similarities with those reported in physiological bone or pathological cardiovascular biominerals, suggesting possible common formation mechanisms. However, the high diversity of these nanocalcifications suggests that several mechanisms may be involved (nucleation on a carbonate core or on organic compounds). In addition, incipient RPs also appear to present specific features at larger scales, revealing secondary calcified structures embedded in a fibrillar organic material. Our study proves that analogies exist between physiological and pathological biominerals and provides information to understand the physicochemical processes involved in pathological calcification formation.

On the role of the epithelium in a model of sodium exchange in renal tubules

In this study we present a mathematical model describing the transport of sodium in a fluid circulating in a counter-current tubular architecture, which constitutes a simplified model of Henle's loop in a kidney nephron. The model explicitly takes into account the epithelial layer at the interface between the tubular lumen and the surrounding interstitium. In a specific range of parameters, we show that explicitly accounting for transport across the apical and basolateral membranes of epithelial cells, instead of assuming a single barrier, affects the axial concentration gradient, an essential determinant of the urinary concentrating capacity. We present the solution related to the stationary system, and we perform numerical simulations to understand the physiological behaviour of the system. We prove that when time grows large, our dynamic model converges towards the stationary system at an exponential rate. In order to prove rigorously this global asymptotic stability result, we study eigen-problems of an auxiliary linear operator and its dual.

Pseudoxanthoma Elasticum, Kidney Stones and Pyrophosphate: From a Rare Disease to Urolithiasis and Vascular Calcifications

Pseudoxanthoma elasticum is a rare disease mainly due to ABCC6 gene mutations and characterized by ectopic biomineralization and fragmentation of elastic fibers resulting in skin, cardiovascular and retinal calcifications. It has been recently described that pyrophosphate (a calcification inhibitor) deficiency could be the main cause of ectopic calcifications in this disease and in other genetic disorders associated to mutations of ENPP1 or CD73. Patients affected by Pseudoxanthoma Elasticum seem also prone to develop kidney stones originating from papillary calcifications named Randall’s plaque, and to a lesser extent may be affected by nephrocalcinosis. In this narrative review, we summarize some recent discoveries relative to the pathophysiology of this mendelian disease responsible for both cardiovascular and renal papillary calcifications, and we discuss the potential implications of pyrophosphate deficiency as a promoter of vascular calcifications in kidney stone formers and in patients affected by chronic kidney disease.

Vitamin D and Calcium Supplementation Accelerates Randall's Plaque Formation in a Murine Model

Most kidney stones are made of calcium oxalate crystals. Randall's plaque, an apatite deposit at the tip of the renal papilla, is considered to at the origin of these stones. Hypercalciuria may promote Randall's plaque formation and growth. We analyzed whether long-term exposure of Abcc6^-/- mice (a murine model of Randall's plaque) to vitamin D supplementation, with or without a calcium-rich diet, would accelerate the formation of Randall's plaque. Eight groups of mice (including Abcc6^-/- and wild type) received vitamin D alone (100,000 UI/kg every 2 weeks), a calcium-enriched diet alone (calcium gluconate 2 g/L in drinking water), both vitamin D supplementation and a calcium-rich diet, or a standard diet (controls) for 6 months. Kidney calcifications were assessed by 3-dimensional microcomputed tomography, μ-Fourier transform infrared spectroscopy, field emission-scanning electron microscopy, transmission electron microscopy, and Yasue staining. At 6 months, Abcc6^-/- mice exposed to vitamin D and calcium supplementation developed massive Randall's plaque when compared with control Abcc6^-/- mice (P < 0.01). Wild-type animals did not develop significant calcifications when exposed to vitamin D. Combined administration of vitamin D and calcium significantly accelerates Randall's plaque formation in a murine model. This original model raises concerns about the cumulative risk of vitamin D supplementation and calcium intakes in Randall's plaque formation.

A model of calcium transport and regulation in the proximal tubule

The objective of this study was to examine theoretically how Ca²⁺ reabsorption in the proximal tubule (PT) is modulated by Na⁺ and water fluxes, parathyroid hormone (PTH), Na⁺-glucose cotransporter (SGLT2) inhibitors, and acetazolamide. We expanded a previously published mathematical model of water and solute transport in the rat PT (Layton AT, Vallon V, Edwards A. Am J Physiol Renal Physiol 308: F1343–F1357, 2015) that did not include Ca²⁺. Our results indicate that Ca²⁺ reabsorption in the PT is primarily driven by the transepithelial Ca²⁺ concentration gradient that stems from water reabsorption, which is itself coupled to Na⁺ reabsorption. Simulated variations in permeability or transporter activity elicit opposite changes in paracellular and transcellular Ca²⁺ fluxes, whereas a simulated decrease in filtration rate lowers both fluxes. The model predicts that PTH-mediated inhibition of the apical Na⁺/H⁺ exchanger NHE3 reduces Na⁺ and Ca²⁺ transport to a similar extent. It also suggests that acetazolamide- and SGLT2 inhibitor-induced calciuria at least partly stems from reduced Ca²⁺ reabsorption in the PT. In addition, backleak of phosphate (PO₄) across tight junctions is predicted to reduce net PO₄ reabsorption by ~20% under normal conditions. When transcellular PO₄ transport is substantially reduced by PTH, paracellular PO₄ flux is reversed and contributes significantly to PO₄ reabsorption. Furthermore, PTH is predicted to exert an indirect impact on PO₄ reabsorption via its inhibitory action on NHE3. This model thus provides greater insight into the mechanisms that modulate Ca²⁺ and PO₄ reabsorption in the PT.

High frequency and wide range of human kidney papillary crystalline plugs

Most of kidney stones are supposed to originate from Randall's plaque at the tip of the papilla or from papillary tubular plugs. Nevertheless, the frequency and the composition of crystalline plugs remain only partly described. The objective was to assess the frequency, the composition and the topography of papillary plugs in human kidneys. A total of 76 papillae from 25 kidneys removed for cancer and without stones were analysed by immunohistochemistry combined with Yasue staining, field emission-scanning electron microscopy and Fourier transformed infrared micro-spectroscopy. Papillary tubular plugs have been observed by Yasue staining in 23/25 patients (92%) and 52/76 papillae (68%). Most of these plugs were made of calcium phosphate, mainly carbonated apatite and amorphous calcium phosphate, and rarely octacalcium phosphate pentahydrate. Calcium and magnesium phosphate (whitlockite) have also been observed. Based upon immunostaining coupled to Yasue coloration, most of calcium phosphate plugs were located in the deepest part of the loop of Henle. Calcium oxalate monohydrate and dihydrate tubular plugs were less frequent and stood in collecting ducts. At last, we observed calcium phosphate plugs deforming and sometimes breaking adjacent collecting ducts. Papillary tubular plugging, which may be considered as a potential first step toward kidney stone formation, is a very frequent setting, even in kidneys of non-stone formers. The variety in their composition and the distal precipitation of calcium oxalate suggest that plugs may occur in various conditions of urine supersaturation. Plugs were sometimes associated with collecting duct deformation.

Topography, Composition and Structure of Incipient Randall Plaque at the Nanoscale Level

PURPOSE

Randall identified calcium phosphate plaques in renal papillae as the origin of kidney stones. However, little is known about the early steps of Randall plaque formation preceding the onset of urolithiasis. Our objective was to characterize the composition and the initial formation site of incipient Randall plaque in nonstone forming, living patients.

MATERIALS AND METHODS

Median patient age was 67.7 years. A total of 54 healthy papillae from kidneys removed for cancer and without stones were analyzed by immunohistochemistry and von Kossa staining, field emission-scanning electron microscopy with energy dispersive x-ray analysis, μ-Fourier transform infrared spectroscopy, cryo-transmission electron microscopy coupled to selected area electron diffraction and electron energy loss spectroscopy.

RESULTS

Incipient Randall plaque was observed in 72.7% of kidneys. As expected, carbonated apatite was the main component of microcalcifications but amorphous calcium phosphate and whitlockite were identified in 80% and 40% of papillae, respectively. Incipient plaques were noted in the deepest part of the papillae around the loop of Henle tip as well as around the vasa recta, representing 62.4% and 37.2% of microcalcifications, respectively. Plaques were rarely close to collecting ducts. At the nanoscale level incipient calcifications were often composed of several nanocrystals in organic material that looked like microvesicles.

CONCLUSIONS

Incipient Randall plaque is frequent. It appears not only at the extreme tip of the renal papillae around the hairpin structure of the loop of Henle but also around the vasa recta. Nanoscale analyses suggest a local nucleation process promoting nanocrystal growth in a supersaturated milieu. In addition, plaques contain various calcium and magnesium phosphates, and not only carbonated apatite.

Mathematical modeling of urea transport in the kidney

Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

Regulation of calcium reabsorption along the rat nephron: a modeling study

We expanded a mathematical model of transepithelial transport along the rat nephron to include the transport of Ca2+ and probe the impact of calcium-sensing mechanisms on Ca2+ reabsorption. The model nephron extends from the medullary thick ascending limb (mTAL) to the inner medullary collecting duct (IMCD). Our model reproduces several experimental findings, such as measurements of luminal Ca2+ concentrations in cortical tubules, and the effects of furosemide or deletion of the transient receptor potential channel vanilloid subtype 5 (TRPV5) on urinary Ca2+ excretion. In vitro microperfusion of rat TAL has demonstrated that activation of the calcium-sensing receptor CaSR lowers the TAL permeability to Ca2+, PCaTAL (Loupy A, Ramakrishnan SK, Wootla B, Chambrey R, de la Faille R, Bourgeois S, Bruneval P, Mandet C, Christensen EI, Faure H, Cheval L, Laghmani K, Collet C, Eladari D, Dodd RH, Ruat M, Houillier P. J Clin Invest 122: 3355, 2012). Our results suggest that this regulatory mechanism significantly impacts renal Ca2+ handling: when plasma Ca2+ concentration ([Ca2+]) is raised by 10%, the CaSR-mediated reduction in PCaTAL per se is predicted to enhance urinary Ca2+ excretion by ∼30%. If high [Ca2+] also induces renal outer medullary potassium (ROMK) inhibition, urinary Ca2+ excretion is further raised. In vitro, increases in luminal [Ca2+] have been shown to activate H+-ATPase pumps in the outer medullary CD and to lower the water permeability of IMCD. Our model suggests that if these responses exhibit the sigmoidal dependence on luminal [Ca2+] that is characteristic of CaSR, then the impact of elevated Ca2+ levels in the CD on urinary volume and pH remains limited. Finally, our model suggests that CaSR inhibitors could significantly reduce urinary Ca2+ excretion in hypoparathyroidism, thereby reducing the risk of calcium stone formation.

Three-dimensional reconstruction of the rat nephron

This study gives a three-dimensional (3D) structural analysis of rat nephrons and their connections to collecting ducts. Approximately 4,500 2.5-μm-thick serial sections from the renal surface to the papillary tip were obtained from each of 3 kidneys of Wistar rats. Digital images were recorded and aligned into three image stacks and traced from image to image. Short-loop nephrons (SLNs), long-loop nephrons (LLNs), and collecting ducts (CDs) were reconstructed in 3D. We identified a well-defined boundary between the outer stripe and the inner stripe of the outer medulla corresponding to the transition of descending thick limbs to descending thin limbs and between the inner stripe and the inner medulla, i.e., the transition of ascending thin limbs into ascending thick limbs of LLNs. In all nephrons, a mosaic pattern of proximal tubule (PT) cells and descending thin limb (DTL) cells was observed at the transition between the PT and the DTL. The course of the LLNs revealed tortuous proximal "straight" tubules and winding of the DTLs within the outer half of the inner stripe. The localization of loop bends of SLNs in the inner stripe of the outer medulla and the bends of LLNs in the inner medulla reflected the localization of their glomeruli; i.e., the deeper the glomerulus, the deeper the bend. Each CD drained approximately three to six nephrons with a different pattern than previously established in mice. This information will provide a basis for evaluation of structural changes within nephrons as a result of physiological or pharmaceutical intervention.