A computational model for simulating solute transport and oxygen consumption along the nephrons

SGLT2 inhibition in a kidney with reduced nephron number: modeling and analysis of solute transport and metabolism

Sodium-glucose cotransporter 2 (SGLT2) inhibitors enhance urinary glucose, Na+ and fluid excretion, and lower hyperglycemia in diabetes by targeting Na+ and glucose reabsorption along the proximal convoluted tubule. A goal of this study was to predict the effects of SGLT2 inhibitors in diabetic and nondiabetic patients with chronic kidney disease. To that end, we employed computational rat kidney models to explore how SGLT2 inhibition affects renal solute transport and metabolism when nephron populations are normal or reduced. Model simulations suggested that in a nondiabetic rat, acute and chronic SGLT2 inhibition induces glucosuria, diuresis, natriuresis, and kaliuresis. Those effects were stronger with chronic SGLT2 inhibition (due to SGLT1 downregulation) and tempered by nephron loss. In a diabetic rat with normal nephron number, acute SGLT2 inhibition similarly elevated urine fluid, Na+, and K+ excretion, whereas the urinary excretory effects of chronic SGLT2 inhibition were attenuated in proportion to its plasma glucose level lowering effect. Nephron loss in a diabetic kidney was predicted to lower the glucosuric and blood glucose-reducing effect of chronic SGLT2 inhibition, but due to the high luminal glucose delivery in the remaining hyperfiltering nephrons, nephron loss enhanced proximal tubular paracellular Na+ secretion, thereby augmenting the natriuretic, diuretic, and kaliuretic effects. A proposed shift in oxygen-consuming active transport to the outer medulla, which may simulate systemic hypoxia and enhance erythropoiesis, was also preserved with nephron loss. These effects may contribute to the protective effects of SGLT2 inhibitors on blood pressure and heart failure observed in diabetic patients with chronic kidney diseases.

Theoretical assessment of the Ca2+ oscillations in the afferent arteriole smooth muscle cell of the rat kidney

The afferent arteriole (AA) of rat kidney exhibits the myogenic response, in which the vessel constricts in response to an elevation in blood pressure and dilates in response to a pressure reduction. Additionally, the AA exhibits spontaneous oscillations in vascular tone at physiological luminal pressures. These time-periodic oscillations stem from the dynamic exchange of Ca[Formula: see text] between the cytosol and the sarcoplasmic reticulum, coupled to the stimulation of Ca[Formula: see text]-activated potassium and chloride channels, and to the modulation of voltage-gated L-type Ca[Formula: see text] channels. The effects of physiological factors, including blood pressure and vasoactive substances, on AA vasomotion remain to be well characterized. In this paper, we analyze a mathematical model of Ca[Formula: see text] signaling in an AA smooth muscle cell. The model represents detailed transmembrane ionic transport, intracellular Ca[Formula: see text] dynamics as well as kinetics of nitric oxide (NO) and superoxide (O[Formula: see text]) formation, diffusion and reaction. NO is an important factor in the maintenance of blood pressure and O[Formula: see text] has been shown to contribute significantly to the functional alternations of blood vessels in hypertension. We perform a bifurcation analysis of the model equations to assess the effect of luminal pressure, NO and O[Formula: see text] on the behaviors of limit cycle oscillations.

Body mass-specific Na+-K+-ATPase activity in the medullary thick ascending limb: implications for species-dependent urine concentrating mechanisms

In general, the mammalian whole body mass-specific metabolic rate correlates positively with maximal urine concentration (U_max) irrespective of whether or not the species have adapted to arid or mesic habitat. Accordingly, we hypothesized that the thick ascending limb (TAL) of a rodent with markedly higher whole body mass-specific metabolism than rat exhibits a substantially higher TAL metabolic rate as estimated by Na⁺-K⁺-ATPase activity and Na⁺-K⁺-ATPase α1-gene and protein expression. The kangaroo rat inner stripe of the outer medulla exhibits significantly higher mean Na⁺-K⁺-ATPase activity (~70%) compared with two rat strains (Sprague-Dawley and Munich-Wistar), extending prior studies showing rat activity exceeds rabbit. Furthermore, higher expression of Na⁺-K⁺-ATPase α1-protein (~4- to 6-fold) and mRNA (~13-fold) and higher TAL mitochondrial volume density (~20%) occur in the kangaroo rat compared with both rat strains. Rat TAL Na⁺-K⁺-ATPase α1-protein expression is relatively unaffected by body hydration status or, shown previously, by dietary Na⁺, arguing against confounding effects from two unavoidably dissimilar diets: grain-based diet without water (kangaroo rat) or grain-based diet with water (rat). We conclude that higher TAL Na⁺-K⁺-ATPase activity contributes to relationships between whole body mass-specific metabolic rate and high U_max. More vigorous TAL Na⁺-K⁺-ATPase activity in kangaroo rat than rat may contribute to its steeper Na⁺ and urea axial concentration gradients, adding support to a revised model of the urine concentrating mechanism, which hypothesizes a leading role for vigorous active transport of NaCl, rather than countercurrent multiplication, in generating the outer medullary axial osmotic gradient.

Predicted effect of circadian clock modulation of NHE3 of a proximal tubule cell on sodium transport

Major renal functions such as renal blood flow, glomerular filtration rate, and urinary excretion are known to exhibit circadian oscillations. However, the underlying mechanisms that govern these variations have yet to be fully elucidated. To better understand the impact of the circadian clock on renal solute and water transport, we have developed a computational model of the renal circadian clock and coupled that model to an epithelial transport model of the proximal convoluted cell of the rat kidney. The activity of the Na⁺-H⁺ exchanger 3 (NHE3) is assumed to be regulated by changes in transcription of the NHE3 mRNA due to regulation by circadian clock proteins. The model predicts the rhythmic oscillations in NHE3 activity, which gives rise to significant daily fluctuations in Na⁺ and water transport of the proximal tubule cell. Additionally, the model predicts that 1) mutation in period 2 (Per2) or cryptochrome 1 (Cry1) preserves the circadian rhythm and modestly raises Na⁺ reabsorption; 2) mutation in Bmal1 or CLOCK eliminates the circadian rhythm and modestly lowers Na⁺ reabsorption; 3) mutation in Rev-Erb or ROR-related orphan receptor (Ror) has minimal impact on the circadian oscillations. The model represents the first step in building a tool set aimed at increasing our understanding of how the molecular clock affects renal ion transport and renal function, which likely has important implications for kidney disease.

Individualized treatment strategies for hyperuricemia informed by a semi-mechanistic exposure-response model of uric acid dynamics

To provide insight into pharmacological treatment of hyperuricemia we developed a semi-mechanistic, dynamical model of uric acid (UA) disposition in human. Our model represents the hyperuricemic state in terms of production of UA (rate, PUA), its renal filtration (glomerular filtration rate, GFR) and proximal tubular reabsorption (fractional excretion coefficient, FE). Model parameters were estimated using data from 9 Phase I studies of xanthine oxidase inhibitors (XOI) allopurinol and febuxostat and a novel uricosuric, the selective UA reabsorption inhibitor lesinurad, approved for use in combination with a XOI. The model was qualified for prediction of the effect of patients' GFR and FE on concentration of UA in serum (sUA) and UA excretion in urine and their response to drug treatment, using data from 2 Phase I and 4 Phase III studies of lesinurad. Percent reduction in sUA from baseline by a XOI is predicted to be independent of GFR, FE or PUA. Uricosurics are more effective in underexcreters of UA or patients with normal GFR. Co-administration of a XOI and an uricosuric agent should be considered for patients with high sUA first in the treatment algorithm of gout before uptitration of XOI. The XOI dose in combination with a uricosuric can be reduced compared to XOI alone for the same target sUA to the degree dependent on patient's GFR and FE. This exposure-response model of UA can be used to rationally select the best drug treatment option to lower elevated sUA in gout patients under differing pathophysiological situations.

Renal potassium handling in rats with subtotal nephrectomy: modeling and analysis

We sought to decipher the mechanisms underlying the kidney's response to changes in K⁺ load and intake, under physiological and pathophysiological conditions. To accomplish that goal, we applied a published computational model of epithelial transport along rat nephrons in a sham rat, an uninephrectomized (UNX) rat, and a 5/6-nephrectomized (5/6-NX) rat that also considers adaptations in glomerular filtration rate and tubular growth. Model simulations of an acute K⁺ load indicate that elevated expression levels and activities of Na⁺/K⁺-ATPase, epithelial sodium channels, large-conductance Ca²⁺-activated K⁺ channels, and renal outer medullary K⁺ channels, together with downregulation of sodium-chloride cotransporters (NCC), increase K⁺ secretion along the connecting tubule, resulting in a >6-fold increase in urinary K⁺ excretion in sham rats, which substantially exceeds the filtered K⁺ load. In the UNX and 5/6-NX models, the acute K⁺ load is predicted to increase K⁺ excretion, but at significantly reduced levels compared with sham. Acute K⁺ load is accompanied by natriuresis in sham rats. Model simulations suggest that the lesser natriuretic effect observed in the nephrectomized groups may be explained by impaired NCC downregulation in these kidneys. At a single-nephron level, a high K⁺ intake raises K⁺ secretion along the connecting tubule and reabsorption along the collecting duct in sham, and even more in UNX and 5/6-NX. However, the increased K⁺ secretion per tubule fails to sufficiently compensate for the reduction in nephron number, such that nephrectomized rats have an impaired ability to excrete an acute or chronic K⁺ load.

Cell Volume Regulation in the Proximal Tubule of Rat Kidney : Proximal Tubule Cell Volume Regulation

We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K[Formula: see text] and [Formula: see text] channels and [Formula: see text]-[Formula: see text] cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral [Formula: see text]/H[Formula: see text] exchangers. Model predictions were in good agreement with experimental observations in mouse proximal tubule cells assuming that a 10% increase in cell volume induces a fourfold increase in the expression of basolateral K[Formula: see text] and [Formula: see text] channels and [Formula: see text]-[Formula: see text] cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, [Formula: see text]-[Formula: see text] cotransporters are more efficient than basolateral K[Formula: see text] and [Formula: see text] channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular [Formula: see text] reabsorption, that is, to limit the net [Formula: see text] flux decrease during a hyposmotic challenge or the net [Formula: see text] flux increase during a hyperosmotic challenge.

Adaptive changes in GFR, tubular morphology, and transport in subtotal nephrectomized kidneys: modeling and analysis

Removal of renal mass stimulates anatomical and functional adaptations in the surviving nephrons, including elevations in single-nephron glomerular filtration rate (SNGFR) and tubular hypertrophy. A goal of this study is to assess the extent to which the concomitant increases in filtered load and tubular transport capacity preserve homeostasis of water and salt. To accomplish that goal, we developed computational models to simulate solute transport and metabolism along nephron populations in a uninephrectomized (UNX) rat and a 5/6-nephrectomized (5/6-NX) rat. Model simulations indicate that nephrectomy-induced SNGFR increase and tubular hypertrophy go a long way to normalize excretion, but alone are insufficient to fully maintain salt balance. We then identified increases in the protein density of Na⁺-K⁺-ATPase, Na⁺-K⁺-2Cl^- cotransporter, Na⁺-Cl^- cotransporter, and epithelial Na⁺ channel, such that the UNX and 5/6-NX models predict urine flow and urinary Na⁺ and K⁺ excretions that are similar to sham levels. The models predict that, in the UNX and 5/6-NX kidneys, fractional water and salt reabsorption is similar to sham along the initial nephron segments (i.e., from the proximal tubule to the distal convoluted tubule), with a need to further reduce Na⁺ reabsorption and increase K⁺ secretion primarily along the connecting tubules and collecting ducts to achieve balance. Additionally, the models predict that, given the substantially elevated filtered and thus transport load among each of the surviving nephrons, oxygen consumption per nephron segment in a UNX or 5/6-NX kidney increases substantially. But due to the reduced nephron population, whole animal renal oxygen consumption is lower. The efficiency of tubular Na⁺ transport in the UNX and 5/6-NX kidneys is predicted to be similar to sham.

Solute transport and oxygen consumption along the nephrons: effects of Na+ transport inhibitors

Sodium and its associated anions are the major determinant of extracellular fluid volume, and the reabsorption of Na+ by the kidney plays a crucial role in long-term blood pressure control. The goal of this study was to investigate the extent to which inhibitors of transepithelial Na+ transport (TNa) along the nephron alter urinary solute excretion and TNa efficiency and how those effects may vary along different nephron segments. To accomplish that goal, we used the multinephron model developed in the companion study (28). That model represents detailed transcellular and paracellular transport processes along the nephrons of a rat kidney. We simulated the inhibition of the Na+/H+ exchanger (NHE3), the bumetanide-sensitive Na+-K+-2Cl- transporter (NKCC2), the Na+-Cl- cotransporter (NCC), and the amiloride-sensitive Na+ channel (ENaC). Under baseline conditions, NHE3, NKCC2, NCC, and ENaC reabsorb 36, 22, 4, and 7%, respectively, of filtered Na+ The model predicted that inhibition of NHE3 substantially reduced proximal tubule TNa and oxygen consumption (QO2 ). Whole-kidney TNa efficiency, as reflected by the number of moles of Na+ reabsorbed per moles of O2 consumed (denoted by the ratio TNa/QO2 ), decreased by ∼20% with 80% inhibition of NHE3. NKCC2 inhibition simulations predicted a substantial reduction in thick ascending limb TNa and QO2 ; however, the effect on whole-kidney TNa/QO2 was minor. Tubular K+ transport was also substantially impaired, resulting in elevated urinary K+ excretion. The most notable effect of NCC inhibition was to increase the excretion of Na+, K+, and Cl-; its impact on whole-kidney TNa and its efficiency was minor. Inhibition of ENaC was predicted to have opposite effects on the excretion of Na+ (increased) and K+ (decreased) and to have only a minor impact on whole-kidney TNa and TNa/QO2 Overall, model predictions agree well with measured changes in Na+ and K+ excretion in response to diuretics and Na+ transporter mutations.