A mathematical model of proximal tubule absorption

A mathematical model previously formulated by us predicts that limit-cycle oscillations (LCO) in nephron flow are mediated by tubuloglomerular feedback (TGF) and that the LCO arise from a bifurcation that depends heavily on the feedback gain magnitude, γ, and on its relationship to a theoretically determined critical value of gain, γc. In this study, we used that model to show how sustained perturbations in proximal tubule flow, a common experimental maneuver, can initiate or terminate LCO by changing the values of γ and γc, thus changing the sign of γ - γc. This result may help explain experiments in which intratubular pressure oscillations were initiated by the sustained introduction or removal of fluid from the proximal tubule (Leyssac PP and Baumbach L. Acta Physiol Scand 117: 415–419, 1983). In addition, our model predicts that, for a range of TGF sensitivities, sustained perturbations that initiate or terminate LCO can yield substantial and abrupt changes in both distal NaCl delivery and NaCl delivery compensation, changes that may play an important role in the response to physiological challenge.

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Flow‐dependent transport in a mathematical model of rat proximal tubule

The FASEB Journal ◽

10.1096/fasebj.21.6.a827-d ◽

2007 ◽

Vol 21 (6) ◽

Author(s):

Alan M. Weinstein ◽

Sheldon Weinbaum ◽

Yi Duan ◽

Zhaopeng Du ◽

QingShang Yan ◽

...

Keyword(s):

Mathematical Model ◽

Proximal Tubule ◽

Dependent Transport ◽

Rat Proximal Tubule

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Mathematical model of megalin trafficking in differentiated proximal tubule cells and its application in Dent disease

The FASEB Journal ◽

10.1096/fasebj.2019.33.1_supplement.751.5 ◽

2019 ◽

Vol 33 (S1) ◽

Author(s):

Katherine Shipman ◽

Kimberly R Long ◽

Youssef Rbaibi ◽

Catherine J Baty ◽

Ora A Weisz

Keyword(s):

Mathematical Model ◽

Proximal Tubule ◽

Dent Disease ◽

Proximal Tubule Cells ◽

Tubule Cells

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Mathematical model of megalin trafficking in differentiated proximal tubule cells

The FASEB Journal ◽

10.1096/fasebj.2018.32.1_supplement.850.4 ◽

2018 ◽

Vol 32 (S1) ◽

Author(s):

Katherine E. Shipman ◽

Kimberly R. Long ◽

Youssef Rbaibi ◽

Catherine J. Baty ◽

Ora A. Weisz

Keyword(s):

Mathematical Model ◽

Proximal Tubule ◽

Proximal Tubule Cells ◽

Tubule Cells

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A mathematical model of the rat kidney: K+-induced natriuresis

AJP Renal Physiology ◽

10.1152/ajprenal.00536.2016 ◽

2017 ◽

Vol 312 (6) ◽

pp. F925-F950 ◽

Cited By ~ 18

Author(s):

Alan M. Weinstein

Keyword(s):

Mathematical Model ◽

Proximal Tubule ◽

Blood Vessels ◽

Collecting Duct ◽

Rat Kidney ◽

Reflection Coefficients ◽

Additional Species ◽

Connecting Tubule ◽

Prior Models ◽

Urine Concentrating Mechanism

A model of the rat nephron (Weinstein. Am J Physiol Renal Physiol 308: F1098–F1118, 2015) has been extended with addition of medullary vasculature. Blood vessels contain solutes from the nephron model, plus additional species from the model of Atherton et al. ( Am J Physiol Renal Fluid Electrolyte Physiol 247: F61–F72, 1984), representing hemoglobin buffering. In contrast to prior models of the urine-concentrating mechanism, reflection coefficients for DVR are near zero. Model unknowns are initial proximal tubule pressures and flows, connecting tubule pressure, and medullary interstitial pressures and concentrations. The model predicts outer medullary (OM) interstitial gradients for Na+, K+, CO2, and [Formula: see text], such that at OM-IM junction, the respective concentrations relative to plasma are 1.2, 3.0, 2.7, and 8.0; within IM, there is high urea and low [Formula: see text], with concentration ratios of 11 and 0.5 near the papillary tip. Quantitative similarities are noted between K+and urea handling (medullary delivery and permeabilities). The model K+gradient is physiologic, and the urea gradient is steeper due to restriction of urea permeability to distal collecting duct. Nevertheless, the predicted urea gradient is less than expected, suggesting reconsideration of proposals of an unrecognized reabsorptive urea flux. When plasma K+is increased from 5.0 to 5.5 mM, Na+and K+excretion increase 2.3- and 1.3-fold, respectively. The natriuresis derives from a 3.3% decrease in proximal Na+reabsorption and occurs despite delivery-driven increases in Na+reabsorption in distal segments; kaliuresis derives from a 30% increase in connecting tubule Na+delivery. Thus this model favors the importance of proximal over distal events in K+-induced diuresis.

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Model of albumin reabsorption in the proximal tubule

AJP Renal Physiology ◽

10.1152/ajprenal.00010.2006 ◽

2007 ◽

Vol 292 (1) ◽

pp. F430-F439 ◽

Cited By ~ 49

Author(s):

Matthew J. Lazzara ◽

William M. Deen

Keyword(s):

Mathematical Model ◽

Proximal Tubule ◽

Flow Rate ◽

Present Model ◽

Albumin Concentration ◽

Glomerular Capillary Wall ◽

Reabsorptive Capacity ◽

And Diffusion ◽

Filtered Load ◽

Tubule Fluid

Normally, the small amount of albumin which passes through the glomerular capillary wall is almost completely reabsorbed in the proximal tubule, via an endocytic mechanism, but the reabsorptive process can be overwhelmed if the filtered load of albumin is too large. To examine the factors that control the fractional reabsorption of albumin ( f), we developed a mathematical model which assumes saturable endocytosis kinetics with a maximum reabsorptive capacity, V max, and which includes the effects of flow and diffusion in the lumen. Limitations in albumin transport from the bulk tubule fluid to the endocytic sites at the bases of the microvilli had only a modest (8%) effect on the value of V max needed to fit micropuncture data on tubule albumin concentrations in rats. For moderate changes in filtered load, there was much greater sensitivity of f to SNGFR than to the albumin concentration of the filtrate ( C0). A 50% increase in SNGFR was predicted to cause four- to fivefold increases in albumin excretion in rats or humans. For large increases in C0, as might result from defects in glomerular sieving, there was a threshold at which the reabsorptive process became saturated and f fell sharply. That threshold corresponded to sieving coefficients of 10−3 to 10−2, the higher values occurring at reduced SNGFR. The predictions of the present model contrast with those of one proposed recently by Smithies ( 32 ), which does not include the effects of tubule flow rate.

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Multiscale Mathematical Model of Drug-Induced Proximal Tubule Injury: Linking Urinary Biomarkers to Epithelial Cell Injury and Renal Dysfunction

Toxicological Sciences ◽

10.1093/toxsci/kfx239 ◽

2017 ◽

Vol 162 (1) ◽

pp. 200-211 ◽

Cited By ~ 11

Author(s):

Yeshitila Gebremichael ◽

James Lu ◽

Harish Shankaran ◽

Gabriel Helmlinger ◽

Jerome Mettetal ◽

...

Keyword(s):

Mathematical Model ◽

Epithelial Cell ◽

Proximal Tubule ◽

Renal Dysfunction ◽

Cell Injury ◽

Urinary Biomarkers ◽

Drug Induced ◽

Multiscale Mathematical Model ◽

Epithelial Cell Injury

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Flow-dependent transport in a mathematical model of rat proximal tubule

AJP Renal Physiology ◽

10.1152/ajprenal.00392.2006 ◽

2007 ◽

Vol 292 (4) ◽

pp. F1164-F1181 ◽

Cited By ~ 44

Author(s):

Alan M. Weinstein ◽

Sheldon Weinbaum ◽

Yi Duan ◽

Zhaopeng Du ◽

QingShang Yan ◽

...

Keyword(s):

Mathematical Model ◽

Proximal Tubule ◽

Low Flow ◽

Diuretic Effect ◽

Model Calculations ◽

Enhanced Sensitivity ◽

Luminal Membrane ◽

Luminal Perfusion ◽

Dependent Transport ◽

Rat Proximal Tubule

The mathematical model of rat proximal tubule has been extended to include calculation of microvillous torque and to incorporate torque-dependent solute transport in a compliant tubule. The torque calculation follows that of Du Z, Yan Q, Duan Y, Weinbaum S, Weinstein AM, and Wang T ( Am J Physiol 290: F289–F296, 2006). In the model calculations, torque-dependent scaling of luminal membrane transporter density [either as an ensemble or just type 3 Na+/H+ exchanger (NHE3) alone] had a relatively small impact on overall Na+ reabsorption and could produce a lethal derangement of cell volume; coordinated regulation of luminal and peritubular transporters was required to represent the overall impact of luminal flow on Na+ reabsorption. When the magnitude of torque-dependent Na+ reabsorption in the model agrees with that observed in mouse proximal tubules, the model tubule shows nearly perfect perfusion-absorption balance at high luminal perfusion rates, but enhanced sensitivity of reabsorption at low flow. With a slightly lower coefficient for torque-sensitive transporter insertion, perfusion-absorption balance in the model tubule is closer to observations in the rat over a broader range of inlet flows. In simulation of hyperglycemia, torque-dependent transport attenuated the diuretic effect and brought the model tubule into closer agreement with experimental observation in the rat. The model was also extended to represent finite rates of hydration and dehydration of CO2 and H2CO3. With carbonic anhydrase inhibition, torque-dependent transport blunted the diuretic effect and enhanced the shift from paracellular to transcellular NaCl reabsorption. The new features of this model tubule are an important step toward simulation of glomerulotubular balance.

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A modular and reusable model of epithelial transport in the proximal convoluted tubule

10.1101/2021.11.11.468301 ◽

2021 ◽

Author(s):

David Phillip Nickerson ◽

Leyla Noroozbabaee ◽

Pablo Javier Blanco ◽

Soroush Safaei

Keyword(s):

Mathematical Model ◽

Open Access ◽

Proximal Tubule ◽

Epithelial Transport ◽

Proximal Convoluted Tubule ◽

Sensitivity Analyses ◽

Transport Models ◽

Modular Model ◽

Solute Fluxes

We review a collection of published renal epithelial transport models, from which we build a consistent and reusable mathematical model able to reproduce many observations and predictions from the literature. The flexible modular model we present here can be adapted to specific configurations of epithelial transport, and in this work we focus on transport in the proximal convoluted tubule of the renal nephron. Our mathematical model of the epithelial proximal convoluted tubule describes the cellular and subcellular mechanisms of the transporters, intracellular buffering, solute fluxes, and other processes. We provide free and open access to the Python implementation to ensure our multiscale proximal tubule model is accessible; enabling the reader to explore the model through setting their own simulations, reproducibility tests, and sensitivity analyses.

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