A mathematical model of rat ascending Henle limb. I. Cotransporter function

A brief history of the cortical thick ascending limb: a systems-biology perspective

Here, we review key events in the accrual of knowledge about the cortical thick ascending limb (CTAL) of the kidney, starting with its initial characterization by Maurice Burg in 1973. Burg's work showed that the CTAL actively reabsorbs NaCl and that, because its water permeability is virtually zero, it can lower the luminal NaCl concentration to a "static head" level well below blood levels. This process is central to the kidney's ability to excrete dilute urine in states of high water intake. Following Burg's original observations, Greger and Schlatter, working in the 1980s, identified the membrane transport processes responsible for transepithelial NaCl transport in the CTAL. In the 1990s, several investigators identified the key transporter genes and proteins at a molecular level by cDNA cloning. The successful completion of human and mouse genome sequencing projects at the turn of the century led to the development of transcriptomic and proteomic methodologies that allowed the identification of complete transcriptomes and proteomes of CTAL cells. Knowledge accrual was enhanced by the development of differential equation-based models of transport in the CTAL in the 2010s. Here, we used a simplified mathematical model of NaCl ("salt"), urea, and water transport in the CTAL to address three key questions about CTAL function: 1) What is the mechanism of Burg's "static head" phenomenon? 2) How does the kidney compensate for the very short length of the CTALs of juxtamedullary nephrons? 3) Which of the three isoforms of the apical Na-K-2Cl cotransporter (NKCC2) dominates functionally in the CTAL?NEW & NOTEWORTHY Here, we review key events in the accrual of knowledge about the cortical thick ascending limb (CTAL) of the kidney, starting with its initial characterization by Maurice Burg in 1973, and culminating with the application of systems biology techniques including mathematical modeling.

A mathematical model of the rat kidney. III. Ammonia transport

Ammonia generated within the kidney is partitioned into a urinary fraction (the key buffer for net acid excretion) and an aliquot delivered to the systemic circulation. The physiology of this partitioning has yet to be examined in a kidney model, and that was undertaken in this work. This involves explicit representation of the cortical labyrinth, so that cortical interstitial solute concentrations are computed rather than assigned. A detailed representation of cortical vasculature has been avoided by making the assumption that solute concentrations within the interstitium and peritubular capillaries are likely to be identical and that there is little to no modification of venous composition as blood flows to the renal vein. The model medullary ray has also been revised to include a segment of proximal straight tubule, which supplies ammonia to this region. The principal finding of this work is that cortical labyrinth interstitial ammonia concentration is likely to be several fold higher than systemic arterial ammonia. This elevation of interstitial ammonia enhances ammonia secretion in both the proximal convoluted tubule and distal convoluted tubule, with uptake by Na⁺-K⁺-ATPases of both segments. Model prediction of urinary ammonia excretion was concordant with measured values, but at the expense of greater ammoniagenesis, with high rates of renal venous ammonia flux. This derives from a limited capability of the model medulla to replicate the high interstitial ammonia concentrations that are required to drive collecting duct ammonia secretion. Thus, renal medullary ammonia trapping appears key to diverting ammonia from the renal vein to urine, but capturing the underlying physiology remains a challenge.NEW & NOTEWORTHY This is the first mathematical model to estimate solute concentrations within the kidney cortex. The model predicts cortical ammonia to be several fold greater than in the systemic circulation. This higher concentration drives ammonia secretion in proximal and distal tubules. The model reveals a gap in our understanding of how ammonia generated within the cortex is channeled efficiently into the final urine.

Pulsatile flow through idealized renal tubules: Fluid-structure interaction and dynamic pathologies

Kidney tubules are lined with flow-sensing structures, yet information about the flow itself is not easily obtained. We aim to generate a multiscale biomechanical model for analyzing fluid flow and fluid-structure interactions within an elastic kidney tubule when the driving pressure is pulsatile. We developed a two-dimensional macroscopic mathematical model of a single fluid-filled tubule corresponding to a distal nephron segment and determined both flow dynamics and wall strains over a range of driving frequencies and wall compliances using finite-element analysis. The results presented here demonstrate good agreement with available analytical solutions and form a foundation for future inclusion of elastohydrodynamic coupling by neighboring tubules. Overall, we are interested in exploring the idea of dynamic pathology to better understand the progression of chronic kidney diseases such as Polycystic Kidney Disease.

Physiological roles and molecular mechanisms of K+ -Cl- cotransport in the mammalian kidney and cardiovascular system: where are we?

In the early 80s, renal microperfusion studies led to the identification of a basolateral K⁺ -Cl^- cotransport mechanism in the proximal tubule, thick ascending limb of Henle and collecting duct. More than ten years later, this mechanism was found to be accounted for by three different K⁺ -Cl^- cotransporters (KCC1, KCC3 and KCC4) that are differentially distributed along the renal epithelium. Two of these isoforms (KCC1 and KCC3) were also found to be expressed in arterial walls, the myocardium and a variety of neurons. Subsequently, valuable insights have been gained into the molecular and physiological properties of the KCCs in both the mammalian kidney and cardiovascular system. There is now robust evidence indicating that KCC4 sustains distal renal acidification and that KCC3 regulates myogenic tone in resistance vessels. However, progress in understanding the functional significance of these transporters has been slow, probably because each of the KCC isoforms is not identically distributed among species and some of them share common subcellular localizations with other KCC isoforms or sizeable conductive Cl^- pathways. In addition, the mechanisms underlying the process of K⁺ -Cl^- cotransport are still ill defined. The present review focuses on the knowledge gained regarding the roles and properties of KCCs in renal and cardiovascular tissues.

Molecular features and physiological roles of K+-Cl- cotransporter 4 (KCC4)

A K⁺-Cl^- cotransport system was documented for the first time during the mid-seventies in sheep and goat red blood cells. It was then described as a Na⁺-independent and ouabain-insensitive ion carrier that could be stimulated by cell swelling and N-ethylmaleimide (NEM), a thiol-reacting agent. Twenty years later, this system was found to be dispensed by four different isoforms in animal cells. The first one was identified in the expressed sequence tag (EST) database by Gillen et al. based on the assumption that it would be homologous to the Na⁺-dependent K⁺-Cl^- cotransport system for which the molecular identity had already been uncovered. Not long after, the three other isoforms were once again identified in the EST databank. Among those, KCC4 has generated much interest a few years ago when it was shown to sustain distal renal acidification and hearing development in mouse. As will be seen in this review, many additional roles were ascribed to this isoform, in keeping with its wide distribution in animal species. However, some of them have still not been confirmed through animal models of gene inactivation or overexpression. Along the same line, considerable knowledge has been acquired on the mechanisms by which KCC4 is regulated and the environmental cues to which it is sensitive. Yet, it is inferred to some extent from historical views and extrapolations.

Mathematical model reveals role of nucleotide signaling in airway surface liquid homeostasis and its dysregulation in cystic fibrosis

Mucociliary clearance is composed of three components (i.e., mucin secretion, airway surface hydration, and ciliary-activity) which function coordinately to clear inhaled microbes and other foreign particles from airway surfaces. Airway surface hydration is maintained by water fluxes driven predominantly by active chloride and sodium ion transport. The ion channels that mediate electrogenic ion transport are regulated by extracellular purinergic signals that signal through G protein-coupled receptors. These purinoreceptors and the signaling pathways they activate have been identified as possible therapeutic targets for treating lung disease. A systems-level description of airway surface liquid (ASL) homeostasis could accelerate development of such therapies. Accordingly, we developed a mathematical model to describe the dynamic coupling of ion and water transport to extracellular purinergic signaling. We trained our model from steady-state and time-dependent experimental measurements made using normal and cystic fibrosis (CF) cultured human airway epithelium. To reproduce CF conditions, reduced chloride secretion, increased potassium secretion, and increased sodium absorption were required. The model accurately predicted ASL height under basal normal and CF conditions and the collapse of surface hydration due to the accelerated nucleotide metabolism associated with CF exacerbations. Finally, the model predicted a therapeutic strategy to deliver nucleotide receptor agonists to effectively rehydrate the ASL of CF airways.

The renal cortical collecting duct: a secreting epithelium?

KEY POINTS

The cortical collecting duct (CCD) plays an essential role in sodium homeostasis by fine-tuning the amount of sodium that is excreted in the urine. Ex vivo, the microperfused CCD reabsorbs sodium in the absence of lumen-to-bath concentration gradients. In the present study, we show that, in the presence of physiological lumen-to-bath concentration gradients, and in the absence of endocrine, paracrine and neural regulation, the mouse CCD secretes sodium, which represents a paradigm shift. This secretion occurs via the paracellular route, as well as a transcellular pathway that is energized by apical H+ /K+ -ATPase type 2 pumps operating as Na+ /K+ exchangers. The newly identified transcellular secretory pathway represents a physiological target for the regulation of sodium handling and for anti-hypertensive therapeutic agents.

ABSTRACT

In vitro microperfusion experiments have demonstrated that cortical collecting ducts (CCDs) reabsorb sodium via principal and type B intercalated cells under sodium-depleted conditions and thereby contribute to sodium and blood pressure homeostasis. However, these experiments were performed in the absence of the transepithelial ion concentration gradients that prevail in vivo and determine paracellular transport. The present study aimed to characterize Na+ , K+ and Cl- fluxes in the mouse CCD in the presence of physiological transepithelial concentration gradients. For this purpose, we combined in vitro measurements of ion fluxes across microperfused CCDs of sodium-depleted mice with the predictions of a mathematical model. When NaCl transport was inhibited in all cells, CCDs secreted Na+ and reabsorbed K+ ; Cl- transport was negligible. Removing inhibitors of type A and B intercalated cells increased Na+ secretion in wild-type (WT) mice but not in H+ /K+ -ATPase type 2 (HKA2) knockout mice. Further inhibition of basolateral NaCl entry via the Na+ -K+ -2Cl- cotransporter in type A intercalated cells reduced Na+ secretion in WT mice to the levels observed in HKA2-/- mice. With no inhibitors, WT mouse CCDs still secreted Na+ and reabsorbed K+ . In vivo, HKA2-/- mice excreted less Na+ than WT mice after switching to a high-salt diet. Taken together, our results indicate that type A intercalated cells secrete Na+ via basolateral Na+ -K+ -2Cl- cotransporters in tandem with apical HKA2 pumps. They also suggest that the CCD can mediate overall Na+ secretion, and that its ability to reabsorb NaCl in vivo depends on the presence of acute regulatory factors.

Physiological role of SLC12 family members in the kidney

The solute carrier family 12, as numbered according to Human Genome Organisation (HUGO) nomenclature, encodes the electroneutral cation-coupled chloride cotransporters that are expressed in many cells and tissues; they play key roles in important physiological events, such as cell volume regulation, modulation of the intracellular chloride concentration, and transepithelial ion transport. Most of these family members are expressed in specific regions of the nephron. The Na-K-2Cl cotransporter NKCC2, which is located in the thick ascending limb, and the Na-Cl cotransporter, which is located in the distal convoluted tubule, play important roles in salt reabsorption and serve as the receptors for loop and thiazide diuretics, respectively (Thiazide diuretics are among the most commonly prescribed drugs in the world.). The activity of these transporters correlates with blood pressure levels; thus, their regulation has been a subject of intense research for more than a decade. The K-Cl cotransporters KCC1, KCC3, and KCC4 are expressed in several nephron segments, and their role in renal physiology is less understood but nevertheless important. Evidence suggests that they are involved in modulating proximal tubule glucose reabsorption, thick ascending limb salt reabsorption and collecting duct proton secretion. In this work, we present an overview of the physiological roles of these transporters in the kidney, with particular emphasis on the knowledge gained in the past few years.

Mechanisms of astrocytic K(+) clearance and swelling under high extracellular K(+) concentrations

In response to the elevation of extracellular K(+) concentration ([K(+)]out), astrocytes clear excessive K(+) to maintain conditions necessary for neural activity. K(+) clearance in astrocytes occurs via two processes: K(+) uptake and K(+) spatial buffering. High [K(+)]out also induces swelling in astrocytes, leading to edema and cell death in the brain. Despite the importance of astrocytic K(+) clearance and swelling, the underlying mechanisms remain unclear. Here, we report results from a simulation analysis of astrocytic K(+) clearance and swelling. Astrocyte models were constructed by incorporating various mechanisms such as intra/extracellular ion concentrations of Na(+), K(+), and Cl(-), cell volume, and models of Na,K-ATPase, Na-K-Cl cotransporter (NKCC), K-Cl cotransporter, inwardly-rectifying K(+) (KIR) channel, passive Cl(-) current, and aquaporin channel. The simulated response of astrocyte models under the uniform distribution of high [K(+)]out revealed significant contributions of NKCC and Na,K-ATPase to increases of intracellular K(+) and Cl(-) concentrations, and swelling. Moreover, we found that, under the non-uniform distribution of high [K(+)]out, KIR channels localized at synaptic clefts absorbed excess K(+) by depolarizing the equivalent potential of K(+) (E K) above membrane potential, while K(+) released through perivascular KIR channels was enhanced by hyperpolarizing E K and depolarizing membrane potential. Further analysis of simulated drug effects revealed that astrocyte swelling was modulated by blocking each of the ion channels and transporters. Our simulation analysis revealed controversial mechanisms of astrocytic K(+) clearance and swelling resulting from complex interactions among ion channels and transporters.

Simulation of Cl(-) Secretion in Epithelial Tissues: New Methodology Estimating Activity of Electro-Neutral Cl(-) Transporter

Transcellular Cl⁻ secretion is, in general, mediated by two steps; (1) the entry step of Cl⁻ into the cytosolic space from the basolateral space across the basolateral membrane by Cl⁻ transporters, such as Na⁺-K⁺-2Cl⁻ cotransporter (NKCC1, an isoform of NKCC), and (2) the releasing step of Cl⁻ from the cytosolic space into the luminal (air) space across the apical membrane via Cl⁻ channels, such as cystic fibrosis transmembrane conductance regulator (CFTR) Cl⁻ channel. Transcellular Cl⁻ secretion has been characterized by using various experimental techniques. For example, measurements of short-circuit currents in the Ussing chamber and patch clamp techniques provide us information on transepithelial ion movements via transcellular pathway, transepithelial conductance, activity (open probability) of single channel, and whole cell currents. Although many investigators have tried to clarify roles of Cl⁻ channels and transporters located at the apical and basolateral membranes in transcellular Cl⁻ secretion, it is still unclear how Cl⁻ channels/transporters contribute to transcellular Cl⁻ secretion and are regulated by various stimuli such as Ca²⁺ and cAMP. In the present study, we simulate transcellular Cl⁻ secretion using mathematical models combined with electrophysiological measurements, providing information on contribution of Cl⁻ channels/transporters to transcellular Cl⁻ secretion, activity of electro-neutral ion transporters and how Cl⁻ channels/transporters are regulated.

Parameter estimation for mathematical models of a nongastric H+(Na+)-K(+)(NH4+)-ATPase

The role of nongastric H(+)-K(+)-ATPase (HKA) in ion homeostasis of macula densa (MD) cells is an open question. To begin to explore this issue, we developed two mathematical models that describe ion fluxes through a nongastric HKA. One model assumes a 1H(+):1K(+)-per-ATP stoichiometry; the other assumes a 2H(+):2K(+)-per-ATP stoichiometry. Both models include Na+ and NH4+ competitive binding with H+ and K+, respectively, a characteristic observed in vitro and in situ. Model rate constants were obtained by minimizing the distance between model and experimental outcomes. Both 1H(+)(1Na(+)):1K(+)(1NH4 (+))-per-ATP and 2H(+)(2Na(+)):2K(+)(2NH4 (+))-per-ATP models fit the experimental data well. Using both models, we simulated ion net fluxes as a function of cytosolic or luminal ion concentrations typical for the cortical thick ascending limb and MD region. We observed that (1) K+ and NH4+ flowed in the lumen-to-cytosol direction, (2) there was competitive behavior between luminal K+ and NH4+ and between cytosolic Na+ and H+, 3) ion fluxes were highly sensitive to changes in cytosolic Na+ or H+ concentrations, and 4) the transporter does mostly Na+ / K+ exchange under physiological conditions. These results support the concept that nongastric HKA may contribute to Na+ and pH homeostasis in MD cells. Furthermore, in both models, H+ flux reversed at a luminal pH that was <5.6. Such reversal led to Na+ / H+ exchange for a luminal pH of <2 and 4 in the 1:1-per-ATP and 2:2-per-ATP models, respectively. This suggests a novel role of nongastric HKA in cell Na+ homeostasis in the more acidic regions of the renal tubules.

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.

Functional consequences of NKCC2 splice isoforms: insights from a Xenopus oocyte model

The Na(+)-K(+)-2Cl(-) cotransporter NKCC2 is exclusively expressed in the renal thick ascending limb (TAL), where it exists as three main splice isoforms, NKCC2B, NKCC2A, and NKCC2F, with the latter two predominating. NKCC2A is expressed in both medullary and cortical TAL, but NKCC2F localizes to the medullary TAL. The biochemical characteristics of the isoforms have been extensively studied by ion uptake studies in Xenopus oocytes, but the functional consequences of alternative splicing remain unclear. We developed a charge-difference model of an NKCC2-transfected oocyte. The model closely recapitulated existing data from ion-uptake experiments. This allowed the reconciliation of different apparent Km values reported by various groups, which have hitherto either been attributed to species differences or remained unexplained. Instead, simulations showed that apparent Na(+) and Cl(-) dependencies are influenced by the ambient K(+) or Rb(+) bath concentrations, which differed between experimental protocols. At steady state, under bath conditions similar to the outer medulla, NKCC2F mediated greater Na(+) reabsorption than NKCC2A. Furthermore, Na(+) reabsorption by the NKCC2F-transfected oocyte was more energy efficient, as quantified by J NKCC/J Pump. Both the increased Na(+) reabsorption and the increased efficiency were eroded as osmolarity decreased toward levels observed in the cortical TAL. This supports the hypothesis that the NKCC2F is a medullary specialization of NKCC2 and demonstrates the utility of modeling in analyzing the functional implications of ion uptake data at physiologically relevant steady states.

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.

Mathematical modeling of kidney transport

In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.

Calcium reabsorption in the distal tubule: regulation by sodium, pH, and flow

We developed a mathematical model of Ca(2+) transport along the late distal convoluted tubule (DCT2) and the connecting tubule (CNT) to investigate the mechanisms that regulate Ca(2+) reabsorption in the DCT2-CNT. The model accounts for apical Ca(2+) influx across transient receptor potential vanilloid 5 (TRPV5) channels and basolateral Ca(2+) efflux via plasma membrane Ca(2+)-ATPase pumps and type 1 Na(+)/Ca(2+) exchangers (NCX1). Model simulations reproduce experimentally observed variations in Ca(2+) uptake as a function of extracellular pH, Na(+), and Mg(2+) concentration. Our results indicate that amiloride enhances Ca(2+) reabsorption in the DCT2-CNT predominantly by increasing the driving force across NCX1, thereby stimulating Ca(2+) efflux. They also suggest that because aldosterone upregulates both apical and basolateral Na(+) transport pathways, it has a lesser impact on Ca(2+) reabsorption than amiloride. Conversely, the model predicts that full NCX1 inhibition and parathyroidectomy each augment the Ca(2+) load delivered to the collecting duct severalfold. In addition, our results suggest that regulation of TRPV5 activity by luminal pH has a small impact, per se, on transepithelial Ca(2+) fluxes; the reduction in Ca(2+) reabsorption induced by metabolic acidosis likely stems from decreases in TRPV5 expression. In contrast, elevations in luminal Ca(2+) are predicted to significantly decrease TRPV5 activity via the Ca(2+)-sensing receptor. Nevertheless, following the administration of furosemide, the calcium-sensing receptor-mediated increase in Ca(2+) reabsorption in the DCT2-CNT is calculated to be insufficient to prevent hypercalciuria. Altogether, our model predicts complex interactions between calcium and sodium reabsorption in the DCT2-CNT.

Fluid dilution and efficiency of Na(+) transport in a mathematical model of a thick ascending limb cell

Thick ascending limb (TAL) cells are capable of reducing tubular fluid Na(+) concentration to as low as ~25 mM, and yet they are thought to transport Na(+) efficiently owing to passive paracellular Na(+) absorption. Transport efficiency in the TAL is of particular importance in the outer medulla where O(2) availability is limited by low blood flow. We used a mathematical model of a TAL cell to estimate the efficiency of Na(+) transport and to examine how tubular dilution and cell volume regulation influence transport efficiency. The TAL cell model represents 13 major solutes and the associated transporters and channels; model equations are based on mass conservation and electroneutrality constraints. We analyzed TAL transport in cells with conditions relevant to the inner stripe of the outer medulla, the cortico-medullary junction, and the distal cortical TAL. At each location Na(+) transport efficiency was computed as functions of changes in luminal NaCl concentration ([NaCl]), [K(+)], [NH(4)(+)], junctional Na(+) permeability, and apical K(+) permeability. Na(+) transport efficiency was calculated as the ratio of total net Na(+) transport to transcellular Na(+) transport. Transport efficiency is predicted to be highest at the cortico-medullary boundary where the transepithelial Na(+) gradient is the smallest. Transport efficiency is lowest in the cortex where luminal [NaCl] approaches static head.

Kinetics of hyperosmotically stimulated Na-K-2Cl cotransporter in Xenopus laevis oocytes

A detailed study of hypertonically stimulated Na-K-2Cl cotransport (NKCC1) in Xenopus laevis oocytes was carried out to better understand the 1 K(+):1 Cl(-) stoichiometry of transport that was previously observed. In this study, we derived the velocity equations for K(+) influx under both rapid equilibrium assumptions and combined equilibrium and steady-state assumptions and demonstrate that the behavior of the equations and curves in Lineweaver-Burke plots are consistent with a model where Cl(-) binds first, followed by Na(+), a second Cl(-), and then K(+). We further demonstrate that stimulation of K(+) movement by K(+) on the trans side is an intrinsic property of a carrier that transports multiple substrates. We also demonstrate that K(+) movement through NKCC1 is strictly dependent upon the presence of external Na(+), even though only a fraction of Na(+) is in fact transported. Finally, we propose that the larger transport of K(+), as compared with Na(+), is a result of the return of partially unloaded carriers, which masks the net 1Na(+):1K(+):2Cl(-) stoichiometry of NKCC1. These data have profound implications for the physiology of Na-K-2Cl cotransport, since transport of K-Cl in some conditions seems to be uncoupled from the transport of Na-Cl.

A tool for multi-scale modelling of the renal nephron

We present the development of a tool, which provides users with the ability to visualize and interact with a comprehensive description of a multi-scale model of the renal nephron. A one-dimensional anatomical model of the nephron has been created and is used for visualization and modelling of tubule transport in various nephron anatomical segments. Mathematical models of nephron segments are embedded in the one-dimensional model. At the cellular level, these segment models use models encoded in CellML to describe cellular and subcellular transport kinetics. A web-based presentation environment has been developed that allows the user to visualize and navigate through the multi-scale nephron model, including simulation results, at the different spatial scales encompassed by the model description. The Zinc extension to Firefox is used to provide an interactive three-dimensional view of the tubule model and the native Firefox rendering of scalable vector graphics is used to present schematic diagrams for cellular and subcellular scale models. The model viewer is embedded in a web page that dynamically presents content based on user input. For example, when viewing the whole nephron model, the user might be presented with information on the various embedded segment models as they select them in the three-dimensional model view. Alternatively, the user chooses to focus the model viewer on a cellular model located in a particular nephron segment in order to view the various membrane transport proteins. Selecting a specific protein may then present the user with a description of the mathematical model governing the behaviour of that protein-including the mathematical model itself and various simulation experiments used to validate the model against the literature.

Regulation of pendrin by pH: dependence on glycosylation

Mutations in the anion exchanger pendrin are responsible for Pendred syndrome, an autosomal recessive disease characterized by deafness and goitre. Pendrin is highly expressed in kidney collecting ducts, where it acts as a chloride/bicarbonate exchanger and thereby contributes to the regulation of acid–base homoeostasis and blood pressure. The present study aimed to characterize the intrinsic properties of pendrin. Mouse pendrin was transfected in HEK (human embryonic kidney) 293 and OKP (opossum kidney proximal tubule) cells and its activity was determined by monitoring changes in the intracellular pH induced by variations of transmembrane anion gradients. Combining measurements of pendrin activity with mathematical modelling we found that its affinity for Cl−, HCO3− and OH− varies with intracellular pH, with increased activity at low intracellular pH. Maximal pendrin activity was also stimulated at low extracellular pH, suggesting the presence of both intracellular and extracellular proton regulatory sites. We identified five putative pendrin glycosylation sites, only two of which are used. Mutagenesis-induced disruption of pendrin glycosylation did not alter its cell-surface expression or polarized targeting to the apical membrane and basal activity, but fully abrogated its sensitivity to extracellular pH. The hither to unknown regulation of pendrin by external pH may constitute a key mechanism in controlling ionic exchanges across the collecting duct and inner ear.

Large-scale phosphoproteomic analysis of membrane proteins in renal proximal and distal tubule

Recent advances in mass spectrometry (MS) have provided means for large-scale phosphoproteomic profiling of specific tissues. Here, we report results from large-scale tandem MS [liquid chromatography (LC)-MS/MS]-based phosphoproteomic profiling of biochemically isolated membranes from the renal cortex, with focus on transporters and regulatory proteins. Data sets were filtered (by target-decoy analysis) to limit false-positive identifications to <2%. A total of 7,125 unique nonphosphorylated and 743 unique phosphorylated peptides were identified. Among the phosphopeptides identified were sites on transporter proteins, i.e., solute carrier (Slc, n = 63), ATP-binding cassette (Abc, n = 4), and aquaporin (Aqp, n = 3) family proteins. Database searches reveal that a majority of the phosphorylation sites identified in transporter proteins were previously unreported. Most of the Slc family proteins are apical or basolateral transporters expressed in proximal tubule cells, including proteins known to mediate transport of glucose, amino acids, organic ions, and inorganic ions. In addition, we identified potentially important phosphorylation sites for transport proteins from distal nephron segments, including the bumetanide-sensitive Na-K-2Cl cotransporter (Slc12a1 or NKCC2) at Ser(87), Thr(101), and Ser(126) and the thiazide-sensitive Na-Cl cotransporter (Slc12a3 or NCC) at Ser(71) and Ser(124). A subset of phosphorylation sites in regulatory proteins coincided with known functional motifs, suggesting specific regulatory roles. An online database from this study (http://dir.nhlbi.nih.gov/papers/lkem/rcmpd/) provides a resource for future studies of transporter regulation.

A mathematical model of rat ascending Henle limb. III. Tubular function

K+ plays a catalytic role in AHL Na+ reabsorption via Na+-K+-2Cl- cotransporter (NKCC2), recycling across luminal K+ channels, so that luminal K+ is not depleted. Based on models of the ascending Henle limb (AHL) epithelium, it has been hypothesized that NH4+ may also catalyze luminal Na+ uptake. This hypothesis requires that luminal NH4+ not be depleted, implying replenishment via either direct secretion of NH4+, or NH3 in parallel with a proton. In the present work, epithelial models of rat medullary and cortical AHL (Weinstein AM, Krahn TA. Am J Physiol Renal Physiol 298: F000-F000, 2009) are configured as tubules and examined in simulations of function in vitro and in vivo to assess the feasibility of a catalytic role for NH4+ in Na+ reabsorption. Modulation of Na+ transport is also examined by peritubular K+ concentration and by Bartter-type transport defects in NKCC2 (type 1), in luminal membrane K+ channels (type 2), and in peritubular Cl- channels (type 3). It is found that a catalytic role for NH4+, which is significant in magnitude (relative to K+), is quantitatively realistic, in terms of uptake via NKCC2, and in terms of luminal membrane ammonia backflux. Simulation of a 90% NKCC2 defect is predicted to double distal Na+ delivery; it is also predicted to increase distal acid delivery (principally as NH4+). With doubling of medullary K+, the model predicts a 30% increase in distal Na+ delivery, but in this case there is a decrease in AHL acidification. This effect of peritubular K+ on proton secretion appears to be akin to type 3 Bartter's pathophysiology, in which there is decreased peritubular HCO3- exit, cytosolic alkalinization, and a consequent decrease in luminal proton secretion by NHE3. One consequence of overlapping and redundant roles for K+ and NH4+, is a blunted impact of luminal membrane K+ permeability on overall Na+ reabsorption, so that type 2 Bartter pathophysiology is not well captured by the model.

A mathematical model of rat ascending Henle limb. II. Epithelial function

A mathematical model of ascending Henle limb (AHL) epithelium has been fashioned using kinetic representations of Na+-K+-2Cl- cotransporter (NKCC2), KCC4, and type 3 Na+/H+ exchanger (NHE3), with transporter densities selected to yield the reabsorptive Na+ flux expected for rat tubules in vivo. Of necessity, this model predicts fluxes that are higher than those measured in vitro. The kinetics of the NKCC and KCC are such that Na+ reabsorption by the model tubule is responsive to variation in luminal NaCl concentration over the range of 30 to 130 mM, with only minor changes in cell volume. Peritubular KCC accounts for about half the reabsorptive Cl- flux, with the remainder via peritubular Cl- channels. Transcellular Na+ flux is turned off by increasing peritubular KCl, which produces increased cytosolic Cl- and thus inhibits NKCC2 transport. In the presence of physiological concentrations of ammonia, there is a large acid challenge to the cell, due primarily to NH4+ entry via NKCC2, with diffusive NH3 exit to both lumen and peritubular solutions. When NHE3 density is adjusted to compensate this acid challenge, the model predicts luminal membrane proton secretion that is greater than the HCO3(-)-reabsorptive fluxes measured in vitro. The model also predicts luminal membrane ammonia cycling, with uptake via NKCC2 or K+ channel, and secretion either as NH4+ by NHE3 or as diffusive NH3 flux in parallel with a secreted proton. If such luminal ammonia cycling occurs in vivo, it could act in concert with luminal K+ cycling to facilitate AHL Na+ reabsorption via NKCC2. With physiological ammonia, peritubular KCl also blunts NHE3 activity by inhibiting NH4+ uptake on the Na-K-ATPase, and alkalinizing the cell.