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^+ and Cl^− channels and Na^+–HCO₃^− 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 Na^+/H^+ 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+ and Cl− channels and Na+–HCO₃^− cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, Na^+–HCO₃^− cotransporters are more efficient than basolateral K^+ and Cl^− channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular Na^+ reabsorption, that is, to limit the net Na^+ flux decrease during a hyposmotic challenge or the net Na^+ flux increase during a hyperosmotic challenge.This research was supported by the National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases, via grant R01DK106102 to AT Layton. (R01DK106102 - National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases)Accepted manuscrip

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.This research was supported by the Department of Veterans Affairs (to V. Vallon) and by the National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases Grants R01-DK-56248 (to V. Vallon), R01-DK-106102 (A. T. Layton and V. Vallon), and the University of Alabama at Birmingham/ University of California San Diego O'Brien Center for Acute Kidney Injury Research NIH-P30-DK-079337 (to V. Vallon). (Department of Veterans Affairs; R01-DK-56248 - National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases; R01-DK-106102 - National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases; NIH-P30-DK-079337 - University of Alabama at Birmingham/ University of California San Diego O'Brien Center for Acute Kidney Injury Research)Accepted manuscrip

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.This research was supported by the Department of Veterans Affairs (V. Vallon), National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) Grants R01-DK-112042 (V. Vallon) and R01-DK-106102 (A. T. Layton and V. Vallon), and University of Alabama at Birmingham-University of California San Diego O'Brien Center for Acute Kidney Injury Research (NIDDK Grant P30-DK-079337; V. Vallon). (Department of Veterans Affairs; R01-DK-112042 - National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK); R01-DK-106102 - National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK); P30-DK-079337 - University of Alabama at Birmingham-University of California San Diego O'Brien Center for Acute Kidney Injury Research (NIDDK Grant))Accepted manuscrip

Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations

This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations; such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [tn ,tn+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical quadrature. The main purpose of this paper is to present a detailed analysis of the implications of the location of quadrature nodes on the accuracy and stability of the overall method. Comparisons between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau, and uniformly spaced points are presented. Also, for a given set of quadrature nodes, quadrature rules may be formulated that include or exclude function values computed at the left-hand endpoint tn . Quadrature rules that do not depend on the left-hand endpoint (which are referred to as right-hand quadrature rules) are shown to lead to L(α)-stable implicit methods with α≈π/2. The semi-implicit analog of this property is also discussed. Numerical results suggest that the use of uniform quadrature nodes, as opposed to nodes based on Gaussian quadratures, does not significantly affect the stability or accuracy of these methods for orders less than ten. In contrast, a study of the reduction of order for stiff equations shows that when uniform quadrature nodes are used in conjunction with a right-hand quadrature rule, the form and extent of order-reduction changes considerably. Specifically, a reduction of order to $\mathcal{O}(\epsilon^2)$ is observed for uniform nodes as opposed to $\mathcal{O}(\epsilon\Delta{t})$ for non-uniform nodes, where Δt denotes the time step and ε a stiffness parameter such that ε→0 corresponds to the problem becoming increasingly stiff

Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability

Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability. Am J Physiol Renal Physiol 313: F174 –F183, 2017. First published March 29, 2017; doi:10.1152/ajprenal.00482.2016.—The goals of this study were to 1) develop a computational model of solute transport and oxygenation in the kidney of the female spontaneously hypertensive rat (SHR), and 2) apply that model to investigate sex differences in nitric oxide (NO) levels in SHR and their effects on medullary oxygenation and oxidative stress. To accomplish these goals, we first measured NO synthase (NOS) 1 and NOS3 protein expression levels in total renal microvessels of male and female SHR. We found that the expression of both NOS1 and NOS3 is higher in the renal vasculature of females compared with males. To predict the implications of that finding on medullary oxygenation and oxidative stress levels, we developed a detailed computational model of the female SHR kidney. The model was based on a published male kidney model and represents solute transport and the biochemical reactions among O2, NO, and superoxide (O2 ) in the renal medulla. Model simulations conducted using both male and female SHR kidney models predicted significant radial gradients in interstitial fluid oxygen tension (PO2) and NO and O2 concentration in the outer medulla and upper inner medulla. The models also predicted that increases in endothelial NO-generating capacity, even when limited to specific vascular segments, may substantially raise medullary NO and PO2 levels. Other potential sex differences in SHR, including O2 production rate, are predicted to significantly impact oxidative stress levels, but effects on NO concentration and PO2 are limited.This research was supported by the National Institute of Diabetes and Digestive and Kidney Diseases Grant R01-DK-106102 to A. T. Layton, and by American Heart Association Grant 14GRNT20480199 to J. C. Sullivan. (R01-DK-106102 - National Institute of Diabetes and Digestive and Kidney Diseases; 14GRNT20480199 - American Heart Association)Accepted manuscrip

Numerical Methods for Fluid-Structure Interaction - A Review

The interactions between incompressible fluid flows and immersed structures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical-methods based on conforming and non-conforming meshes that are currently available for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interaction

Mechanistic mathematical model of polarity in yeast

The establishment of cell polarity involves positive-feedback mechanisms that concentrate polarity regulators, including the conserved GTPase Cdc42p, at the “front” of the polarized cell. Previous studies in yeast suggested the presence of two parallel positive-feedback loops, one operating as a diffusion-based system, and the other involving actin-directed trafficking of Cdc42p on vesicles. F-actin (and hence directed vesicle traffic) speeds fluorescence recovery of Cdc42p after photobleaching, suggesting that vesicle traffic of Cdc42p contributes to polarization. We present a mathematical modeling framework that combines previously developed mechanistic reaction-diffusion and vesicle-trafficking models. Surprisingly, the combined model recapitulated the observed effect of vesicle traffic on Cdc42p dynamics even when the vesicles did not carry significant amounts of Cdc42p. Vesicle traffic reduced the concentration of Cdc42p at the front, so that fluorescence recovery mediated by Cdc42p flux from the cytoplasm took less time to replenish the bleached pool. Simulations in which Cdc42p was concentrated into vesicles or depleted from vesicles yielded almost identical predictions, because Cdc42p flux from the cytoplasm was dominant. These findings indicate that vesicle-mediated delivery of Cdc42p is not required to explain the observed Cdc42p dynamics, and raise the question of whether such Cdc42p traffic actually contributes to polarity establishment

Sex-specific long-term blood pressure regulation: Modeling and analysis

The final publication is available at Elsevier via https://doi.org/10.1016/j.compbiomed.2018.11.002. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/bync-nd/4.0/Hypertension is a global health challenge: it affects one billion people worldwide and is estimated to account for 60% of all cases or types of cardiovascular disease. In part because sex differences in blood pressure regulation mechanisms are not sufficiently well understood, fewer hypertensive women achieve blood pressure control compared to men, even though compliance and treatment rates are generally higher in women. Thus, the objective of this study is to identify which factors contribute to the sexual dimorphism in response to anti-hypertensive therapies targeting the renin angiotensin system (RAS). To accomplish that goal, we develop sex-specific blood pressure regulation models. Sex differences in the RAS, baseline adosterone level, and the reactivity of renal sympathetic nervous activity (RSNA) are represented. A novel aspect of the model is the representation of sex-specific vasodilatory effect of the bound angiotensin II type two receptor (AT2R-bound Ang II) on renal vascular resistance. Model simulations suggest that sex differences in RSNA are the largest cause of female resistance to developing hypertension due to the direct influence of RSNA on afferent arteriole resistance. Furthermore, the model predicts that the sex-specific vasodilatory effects of AT2R-bound Ang II on renal vascular resistance may explain the higher effectiveness of angiotensin receptor blockers in treating hypertensive women (but not men), compared to angiotensin converting enzyme inhibitors.National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases [grant R01DK106102]National Science Foundation [grant DMS1263995]Canada 150 Research Chair Progra