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

2013 ◽  
Vol 304 (6) ◽  
pp. F634-F652 ◽  
Author(s):  
Aniel Nieves-González ◽  
Chris Clausen ◽  
Mariano Marcano ◽  
Anita T. Layton ◽  
Harold E. Layton ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cell Model ◽  
Cell Volume Regulation ◽  
Mass Conservation ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Transport Efficiency ◽  
Nacl Concentration ◽  
Model Equations ◽  
Static Head

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 O2 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+], [NH4+], 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.

scholarly journals Transport efficiency and workload distribution in a mathematical model of the thick ascending limb

2013 ◽  
Vol 304 (6) ◽  
pp. F653-F664 ◽  
Author(s):  
Aniel Nieves-González ◽  
Chris Clausen ◽  
Anita T. Layton ◽  
Harold E. Layton ◽  
Leon C. Moore
Keyword(s):  
Mathematical Model ◽  
Concentration Gradient ◽  
Transport Model ◽  
Cell Volume Regulation ◽  
Mass Conservation ◽  
Ph Control ◽  
Tubuloglomerular Feedback ◽  
Thick Ascending Limb ◽  
Transport Pathways ◽  
Transport Efficiency

The thick ascending limb (TAL) is a major NaCl reabsorbing site in the nephron. Efficient reabsorption along that segment is thought to be a consequence of the establishment of a strong transepithelial potential that drives paracellular Na+ uptake. We used a multicell mathematical model of the TAL to estimate the efficiency of Na+ transport along the TAL and to examine factors that determine transport efficiency, given the condition that TAL outflow must be adequately dilute. The TAL model consists of a series of epithelial cell models that represent all major solutes and transport pathways. Model equations describe luminal flows, based on mass conservation and electroneutrality constraints. Empirical descriptions of cell volume regulation (CVR) and pH control were implemented, together with the tubuloglomerular feedback (TGF) system. Transport efficiency was calculated as the ratio of total net Na+ transport (i.e., paracellular and transcellular transport) to transcellular Na+ transport. Model predictions suggest that 1) the transepithelial Na+ concentration gradient is a major determinant of transport efficiency; 2) CVR in individual cells influences the distribution of net Na+ transport along the TAL; 3) CVR responses in conjunction with TGF maintain luminal Na+ concentration well above static head levels in the cortical TAL, thereby preventing large decreases in transport efficiency; and 4) under the condition that the distribution of Na+ transport along the TAL is quasi-uniform, the tubular fluid axial Cl− concentration gradient near the macula densa is sufficiently steep to yield a TGF gain consistent with experimental data.

scholarly journals NKCC2A and NFAT5 regulate renal TNF production induced by hypertonic NaCl intake

2013 ◽  
Vol 304 (5) ◽  
pp. F533-F542 ◽  
Author(s):  
Shoujin Hao ◽  
Lars Bellner ◽  
Nicholas R. Ferreri
Keyword(s):  
Tap Water ◽  
Primary Cultures ◽  
Fold Increase ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Activated T Cells ◽  
Mrna Accumulation ◽  
Nacl Concentration ◽  
Promoter Construct ◽  
Mrna And Protein Expression

Pathways that contribute to TNF production by the kidney are not well defined. Mice given 1% NaCl in the drinking water for 3 days exhibited a 2.5-fold increase in urinary, but not plasma, TNF levels compared with mice given tap water. Since furosemide attenuated the increase in TNF levels, we hypothesized that hypertonic NaCl intake increases renal TNF production by a pathway involving the Na+-K+-2Cl− cotransporter (NKCC2). A 2.5-fold increase in NKCC2A mRNA accumulation was observed in medullary thick ascending limb (mTAL) tubules from mice given 1% NaCl; a concomitant 2-fold increase in nuclear factor of activated T cells 5 (NFAT5) mRNA and protein expression was observed in the outer medulla. Urinary TNF levels were reduced in mice given 1% NaCl after an intrarenal injection of a lentivirus construct designed to specifically knockdown NKCC2A (EGFP-N2A-ex4); plasma levels of TNF did not change after injection of EGFP-N2A-ex4. Intrarenal injection of EGFP-N2A-ex4 also inhibited the increase of NFAT5 mRNA abundance in the outer medulla of mice given 1% NaCl. TNF production by primary cultures of mTAL cells increased approximately sixfold in response to an increase in osmolality to 400 mosmol/kgH2O produced with NaCl and was inhibited in cells transiently transfected with a dnNFAT5 construct. Transduction of cells with EGFP-N2A-ex4 also prevented increases in TNF mRNA and protein production in response to high NaCl concentration and reduced transcriptional activity of a NFAT5 promoter construct. Since NKCC2A expression is restricted to the TAL, NKCC2A-dependent activation of NFAT5 is part of a pathway by which the TAL produces TNF in response to hypertonic NaCl intake.

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity

2005 ◽  
Vol 289 (6) ◽  
pp. F1367-F1381 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Rat Kidney ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Model Calculations ◽  
Concentrating Mechanism ◽  
Vasa Recta ◽  
Urine Concentrating Mechanism

In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1346–F1366, 2005), a region-based mathematical model was formulated for the urine concentrating mechanism (UCM) in the outer medulla (OM) of the rat kidney. In the present study, we quantified the sensitivity of that model to several structural assumptions, including the degree of regionalization and the degree of inclusion of short descending limbs (SDLs) in the vascular bundles of the inner stripe (IS). Also, we quantified model sensitivity to several parameters that have not been well characterized in the experimental literature, including boundary conditions, short vasa recta distribution, and ascending vasa recta (AVR) solute permeabilities. These studies indicate that regionalization elevates the osmolality of the fluid delivered into the inner medulla via the collecting ducts; that model predictions are not significantly sensitive to boundary conditions; and that short vasa recta distribution and AVR permeabilities significantly impact concentrating capability. Moreover, we investigated, in the context of the UCM, the functional significance of several aspects of tubular segmentation and heterogeneity: SDL segments in the IS that are likely to be impermeable to water but highly permeable to urea; a prebend segment of SDLs that may be functionally like thick ascending limb (TAL); differing IS and outer stripe Na+ active transport rates in TAL; and potential active urea secretion into the proximal straight tubules. Model calculations predict that these aspects of tubular of segmentation and heterogeneity generally enhance solute cycling or promote effective UCM function.

scholarly journals A mathematical model of O2 transport in the rat outer medulla. I. Model formulation and baseline results

2009 ◽  
Vol 297 (2) ◽  
pp. F517-F536 ◽  
Author(s):  
Jing Chen ◽  
Anita T. Layton ◽  
Aurélie Edwards
Keyword(s):  
Mathematical Model ◽  
Structural Organization ◽  
Capillary Flow ◽  
Renal Medulla ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Vasa Recta ◽  
Complex Structural ◽  
The Impact

The mammalian kidney is particularly vulnerable to hypoperfusion, because the O2 supply to the renal medulla barely exceeds its O2 requirements. In this study, we examined the impact of the complex structural organization of the rat outer medulla (OM) on O2 distribution. We extended the region-based mathematical model of the rat OM developed by Layton and Layton ( Am J Physiol Renal Physiol 289: F1346–F1366, 2005) to incorporate the transport of RBCs, Hb, and O2. We considered basal cellular O2 consumption and O2 consumption for active transport of NaCl across medullary thick ascending limb epithelia. Our model predicts that the structural organization of the OM results in significant Po2 gradients in the axial and radial directions. The segregation of descending vasa recta, the main supply of O2, at the center and immediate periphery of the vascular bundles gives rise to large radial differences in Po2 between regions, limits O2 reabsorption from long descending vasa recta, and helps preserve O2 delivery to the inner medulla. Under baseline conditions, significantly more O2 is transferred radially between regions by capillary flow, i.e., advection, than by diffusion. In agreement with experimental observations, our results suggest that 79% of the O2 supplied to the medulla is consumed in the OM and that medullary thick ascending limbs operate on the brink of hypoxia.

Nonlinear filter properties of the thick ascending limb

1997 ◽  
Vol 273 (4) ◽  
pp. F625-F634 ◽  
Author(s):  
H. E. Layton ◽  
E. Bruce Pitman ◽  
Leon C. Moore
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Transit Time ◽  
Concentration Profile ◽  
Tubuloglomerular Feedback ◽  
Thick Ascending Limb ◽  
Transport Parameters ◽  
Nodal Structure ◽  
Nacl Concentration ◽  
Fluid Transit Time

A mathematical model was used to investigate the filter properties of the thick ascending limb (TAL), that is, the response of TAL luminal NaCl concentration to oscillations in tubular fluid flow. For the special case of no transtubular NaCl backleak and for spatially homogeneous transport parameters, the model predicts that NaCl concentration in intratubular fluid at each location along the TAL depends only on the fluid transit time up the TAL to that location. This exact mathematical result has four important consequences: 1) when a sinusoidal component is added to steady-state TAL flow, the NaCl concentration at the macula densa (MD) undergoes oscillations that are bounded by a range interval envelope with magnitude that decreases as a function of oscillatory frequency; 2) the frequency response within the range envelope exhibits nodes at those frequencies where the oscillatory flow has a transit time to the MD that equals the steady-state fluid transit time (this nodal structure arises from the establishment of standing waves in luminal concentration, relative to the steady-state concentration profile, along the length of the TAL); 3) for any dynamically changing but positive TAL flow rate, the luminal TAL NaCl concentration profile along the TAL decreases monotonically as a function of TAL length; and 4) sinusoidal oscillations in TAL flow, except at nodal frequencies, result in nonsinusoidal oscillations in NaCl concentration at the MD. Numerical calculations that include NaCl backleak exhibit solutions with these same four properties. For parameters in the physiological range, the first few nodes in the frequency response curve are separated by antinodes of significant amplitude, and the nodes arise at frequencies well below the frequency of respiration in rat. Therefore, the nodal structure and nonsinusoidal oscillations should be detectable in experiments, and they may influence the dynamic behavior of the tubuloglomerular feedback system.

scholarly journals Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide

2011 ◽  
Vol 301 (5) ◽  
pp. F979-F996 ◽  
Author(s):  
Aurélie Edwards ◽  
Anita T. Layton
Keyword(s):  
Nitric Oxide ◽  
Active Transport ◽  
Collecting Duct ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Nacl Transport ◽  
Complex Interactions ◽  
Medullary Thick Ascending Limb ◽  
The Impact ◽  
Stimulation Of

We expanded our region-based model of water and solute exchanges in the rat outer medulla to incorporate the transport of nitric oxide (NO) and superoxide (O2−) and to examine the impact of NO-O2− interactions on medullary thick ascending limb (mTAL) NaCl reabsorption and oxygen (O2) consumption, under both physiological and pathological conditions. Our results suggest that NaCl transport and the concentrating capacity of the outer medulla are substantially modulated by basal levels of NO and O2−. Moreover, the effect of each solute on NaCl reabsorption cannot be considered in isolation, given the feedback loops resulting from three-way interactions between O2, NO, and O2−. Notwithstanding vasoactive effects, our model predicts that in the absence of O2−-mediated stimulation of NaCl active transport, the outer medullary concentrating capacity (evaluated as the collecting duct fluid osmolality at the outer-inner medullary junction) would be ∼40% lower. Conversely, without NO-induced inhibition of NaCl active transport, the outer medullary concentrating capacity would increase by ∼70%, but only if that anaerobic metabolism can provide up to half the maximal energy requirements of the outer medulla. The model suggests that in addition to scavenging NO, O2− modulates NO levels indirectly via its stimulation of mTAL metabolism, leading to reduction of O2 as a substrate for NO. When O2− levels are raised 10-fold, as in hypertensive animals, mTAL NaCl reabsorption is significantly enhanced, even as the inefficient use of O2 exacerbates hypoxia in the outer medulla. Conversely, an increase in tubular and vascular flows is predicted to substantially reduce mTAL NaCl reabsorption. In conclusion, our model suggests that the complex interactions between NO, O2−, and O2 significantly impact the O2 balance and NaCl reabsorption in the outer medulla.

Depolarization of the macula densa induces superoxide production via NAD(P)H oxidase

2007 ◽  
Vol 292 (6) ◽  
pp. F1867-F1872 ◽  
Author(s):  
Ruisheng Liu ◽  
Jeffrey L. Garvin ◽  
YiLin Ren ◽  
Patrick J. Pagano ◽  
Oscar A. Carretero
Keyword(s):  
Nitric Oxide ◽  
Superoxide Dismutase ◽  
Oxidase Inhibitor ◽  
Fluorescent Dye ◽  
Macula Densa ◽  
Superoxide Production ◽  
Tubuloglomerular Feedback ◽  
Thick Ascending Limb ◽  
Loop Of Henle ◽  
Nacl Concentration

Superoxide (O2−) enhances tubuloglomerular feedback by scavenging nitric oxide at the macula densa. However, the singling pathway of O2− production in the macula densa is not known. We hypothesized that the increase in tubular NaCl concentration that initiates tubuloglomerular feedback induces O2− production by the macula densa via NAD(P)H oxidase, which is activated by macula densa depolarization. We isolated and microperfused the thick ascending limb of the loop of Henle and attached macula densa in rabbits. A fluorescent dye, dihydroethidium, was used to detect O2− production at the macula densa. When luminal NaCl was switched from 10 to 80 mM, a situation of initiating maximum tubuloglomerular feedback response, O2− production significantly increased. To make sure that the shifts in the oxyethidium/dihydroethidium ratio were due to changes in O2−, we used tempol (10−4 M), a stable membrane-permeant superoxide dismutase mimetic. With tempol present, when we switched from 10 to 80 mM NaCl, the increase in oxyethidium/dihydroethidium ratio was blocked. To determine the source of O2−, we used the NAD(P)H oxidase inhibitor apocynin. When luminal NaCl was switched from 10 to 80 mM in the presence of apocynin, O2− production was inhibited by 80%. To see whether the effect of increasing luminal NaCl involves Na-K-2Cl cotransporters, we inhibited them with furosemide. When luminal NaCl was switched from 10 to 80 mM in the presence of furosemide, O2− production was blocked. To test whether depolarization of the macula densa induces O2− production, we artificially induced depolarization by adding valinomycin (10−6 M) and 25 mM KCl to the luminal perfusate. Depolarization alone significantly increases O2− production. We conclude that increasing luminal NaCl induces O2− production during tubuloglomerular feedback. O2− generated by the macula densa is primarily derived from NAD(P)H oxidase and is induced by depolarization.

Potential in microroughness domain of metal surface employed in cathodic protection mode

2021 ◽  
Vol 2021 (3) ◽  
pp. 48-54
Author(s):  
V. Lukovich ◽  
◽  
V. Kartuzov ◽  
Keyword(s):  
Mathematical Model ◽  
Metal Surface ◽  
Cathodic Protection ◽  
Computational Experiment ◽  
Computational Domain ◽  
Protective Potential ◽  
Long Time ◽  
Protection Mode ◽  
Model Equations ◽  
Iterative Procedures

This effort presents the results of investigation of cathodic protection process of a section of the main pipeline, which has been operating in cathodic protection mode for a long time and which insulation has completely exfoliated from metal surface, and a cavity between is filled with water and salt impurities. In this case, a decisive factor is a fact that a metal surface is covered with microroughnesses in the form of protrusions with almost conical shape. The surface is immersed in electrolyte. At the electrolyte-metal interface, a potential difference is formed - a corrosion potential, which creates an unstable equilibrium among the potentials of metal and electrolyte. A mathematical model is designed and implemented into a numerical algorithm and computer program. A computational experiment has been carried out to calculate the potential around microroughness. The model describes a change in potential in this area at incomplete and complete cathodic protection of metal surface. The basis of computational model is a selection of one of metal protrusions of material microheterogeneity and placing it in a cylinder, which diameter coincides with that one of the lower base of this protrusion, and its upper part passes through the apex of the protrusion. Mathematical model equations with corresponding boundary conditions and their discrete implementation are presented. The solution of problems is obtained by iterative procedures based on reference values of protective potential taken from practice. The results of computational experiment are presented in the form of graphs: 1) potential distribution in the field of electrolytes; 2) changes in electrolyte potential at the border with protrusion at different values of polarization potential; 3) changes in polarization resistance in the area (calculated). The geometry of computational domain was also varied, and the values of protective potential were determined to ensure the absence of corrosion. Keywords: corrosion, microroughness, protective potential, plastic current density, electrolyte

Localization and regulation of the rat renal Na(+)-K(+)-2Cl- cotransporter, BSC-1

1996 ◽  
Vol 271 (3) ◽  
pp. F619-F628 ◽  
Author(s):  
C. A. Ecelbarger ◽  
J. Terris ◽  
J. R. Hoyer ◽  
S. Nielsen ◽  
J. B. Wade ◽  
...  
Keyword(s):  
Rat Kidney ◽  
Rat Colon ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Water Excretion ◽  
Saline Loading ◽  
Cloned Cdna ◽  
Urinary Concentrating Ability

To investigate the role of the thick ascending limb (TAL) Na(+)-K(+)-2Cl- cotransporter in regulation of water excretion, we have prepared a peptide-derived polyclonal antibody based on the cloned cDNA sequence of the rat type 1 bumetanide-sensitive cotransporter, BSC-1 (also termed "NKCC-2"). Immunoblots revealed a single broad 161-kDa band in membrane fractions of rat renal outer medulla and cortex but not from rat colon or parotid gland. A similar protein was labeled in mouse kidney. Immunoperoxidase immunohistochemistry in rat kidney revealed labeling restricted to the medullary and cortical TAL segments. Because long-term regulation of urinary concentrating ability may depend on regulation of Na(+)-K(+)-2Cl- cotransporter abundance, we used immunoblotting to evaluate the effects of several in vivo factors on expression levels of BSC-1 protein in rat kidney outer medulla. Chronic oral saline loading with 0.16 M NaCl markedly increased BSC-1 abundance. However, long-term vasopressin infusion or thirsting of rats did not affect BSC-1 abundance. Chronic furosemide infusion caused a 9-kDa upward shift in apparent molecular mass and an apparent increase in expression level. These results support the previous identification of BSC-1 as the TAL Na(+)-K(+)-2Cl- transporter and demonstrate that the expression of this transporter is regulated.

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