A dynamic numerical method for models of renal tubules

We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow direction. To obtain second-order convergence in space and time, we employ the recently developed ENO (Essentially Non-Oscillatory) methodology. We present examples of computed flows and concentration profiles in representative model contexts. Finally, we indicate briefly how model tubules may be coupled to construct large-scale simulations of the renal counterflow system.     

A sparse matrix method for renal models

A sparse matrix method for the numerical solution of nonlinear differential equations arising in modeling of the renal concentrating mechanism is given. The method involves a renumbering of the variables and equations such that the resulting Jacobian matrix has a block tridiagonal structure and the blocks above and below the main diagonal have a known set of complementary nonzero columns. The computer storage for the method is O(n). Results of some numerical experiments showing the stability of the method are given.     

Ultrastructural changes of renal tubules in the riboflavin deficient mouse

Ultrastructural changes of the tubular epithelium in the mouse kidney produced by dietary riboflavin deficiency were studied by electron microscopy and cytochemistry. In riboflavin deficient mouse kidney, the ultrastructural changes are localized to the pars recta of the proximal tubule. They comprise so called vacuolar degeneration on light microscopy, which consists of the formation of giant mitochondria and vacuoles. During the development of riboflavin deficiency, mitochondria decrease in number and enlarge in size through fusion. Sometimes they are larger than nuclei in size. The vacuoles observed in tubular epithelia are divided into two different groups according to their morphological characteristics and origins. One is derived from proliferated peroxisomes, and another from increased cytoplasmic bodies termed cytosomes and cytosegresomes. These increased vacuoles occupy almost all of cytoplasm. Cytochemical studies also reveal that these vacuoles are peroxisomes and lysosomes. These changes are reversible on supplementation with riboflavin.     

Modulation of cell membrane area in renal collecting tubules by corticosteroid hormones

Isolated renal cortical collecting tubules obtained from rabbits treated chronically with desoxycorticosterone acetate (DOCA) have been found to possess elevated transepithelial potential differences and a greatly increased capacity for ion transport. Structural exmination of tubules from rabbits exposed to either DOCA or dexamethasone for 11--18 d reveals a marked increase in basolateral cell membrane area in these tubules. Morphometric analysis shows that this effect is specifically on the basolateral membrane area of only one of the two cell types found in this nephron segment. Increases of greater than 140% and 90% are found for the basolateral membrane area of the principal cells for DOCA and dexamethasone, respectively, but no change could be detected in the basolateral membrane area of the intercalated cells found in this nephron segment. No siginificant changes were found in luminal membrane area, cell number, or cell volume for either cell type. These observations demonstrate that significant changes in membrane area can occur in differentiated epithelia and suggest that this may be an important mechanism for modulating epithelial transport capacity.     

Phosphate transport after acute changes in total NAD content in renal proximal tubules

Suspensions of proximal tubules were obtained by collagenase digestion of rat renal cortex followed by centrifugation on a percoll gradient. NAD content in tubules incubated at 37 degrees C was decreased by 40-60% compared with tubules incubated at 4 degrees C. This change occurred within 30 min and was maintained for up to 2 hr. Inhibitors of NAD hydrolysing enzymes prevented the depletion of cellular NAD at 37 degrees C. Acute changes in proximal tubule NAD content at 37 degrees C were not accompanied by changes in phosphate uptake by brush border membrane vesicles subsequently prepared from the same tubules. In contrast, incubation of tubules with parathyroid hormone (10(-6) M) produced the expected inhibition (20%) of brush border membrane transport of phosphate. One implication of these findings is that acute changes in total NAD content of proximal tubules at 37 degrees C may not influence the phosphate transport system in the renal brush border membrane. Other interpretations are discussed.     

A hydrodynamical study of the flow in renal tubules

The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q ₀ can be expressed as a Fourier integral (whereQ ₀ is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.     

Evidence for a decreased membrane recycling in the cells of renal proximal tubules exposed to high concentrations of ferritin

Summary The present study was performed to investigate whether membrane recycling via the dense apical tubules in cells of renal proximal tubules could be modified after exposure to large amounts of cationized ferritin. Proximal tubules in the rat kidney were microinfused in vivo with cationized ferritin for 10 or 30 min and then fixed with glutaraldehyde by microinfusion, or proximal tubules were microinfused with ferritin for 30 min and then fixed 2 h thereafter. The tubules were processed for electron microscopy, and the surface density and the volume density of the different cell organelles involved in endocytosis were determined by morphometry. The morphometric analyses showed that after loading of the endocytic vesicles with ferritin the surface density of dense apical tubules decreased to about 50% of the original value. However, 2 h later when ferritin had accumulated in the lysosomes the surface density of dense apical tubules had returned to control values. Furthermore, cationized ferritin was virtually absent from the Golgi region, indicating that the Golgi apparatus in these cells does not participate in membrane recycling. In conclusion, the present study shows that membrane recycling in renal proximal tubule cells can in part be inhibited by loading the endocytic vacuoles with ferritin.     

Acute sodium-dependent changes in membrane dynamic properties.

Na+ ions, which can play a pathogenic role in the development of high blood pressure, have been reported to regulate membrane enzymatic activities, receptor-ligand interaction and coupling of G-protein receptors to their effectors. This study was designed to investigate the in vitro effects of Na+ ions on membrane dynamic properties. The fluorescence anisotropy values of TMA-DPH (trimethylamino-diphenylhexatriene, probe selectively incorporated into the outer leaflet of the plasma membrane) was evaluated in platelets and erythrocytes of sodium-dependent hypertension-prone and -resistant rats of the Sabra Strain. Whereas no difference was observed between the 2 strains, TMA-DPH anisotropy was found to be strongly influenced in platelets by external Na+ ions. In the absence of external Na+, TMA-DPH anisotropy increased in human and rat platelets. In contrast, Na+ ions did not affect the anisotropy when the probe was inserted into erythrocyte ghosts. This indicates that Na+ ions can acutely regulate order parameter and microviscosity of platelet plasma membrane in the regions explored by the probe.     

DESI-MSI and METASPACE indicates lipid abnormalities and altered mitochondrial membrane components in diabetic renal proximal tubules

Metabolomics - Food and dietary ingredients have significant effects on metabolism and health. To evaluate whether and how different diets affected the serum lipidomic profile of dogs. Sixteen...     

Insulin absorption in renal proximal tubules: A quantitative immunocytochemical study

The purposes of the present study are mainly biological concerning proximal tubular handling of insulin: we will study the intracellular transport to subcellular compartments involved in insulin degradation, the specificity and saturability of the luminal endocytic absorption of insulin, the visualization of transtubular transport, and finally, if possible, the evaluation of the relative distribution (accumulation) of insulin in endocytic vacuoles and lysosomes. The second part is methodological: application of quantitative immunocytochemistry to endocytosis, quantitation of the effect of particle size and antigen density on labeling density on tissue sections, labeling at very low antigen densities, and effect of fish gelatin on background. Isolated renal proximal tubules were perfused with native insulin, ¹²⁵I-insulin, or [leucine^B-25]-insulin (2% receptor-binding ability and full immunoreactivity) or exposed to native insulin from the basolateral membranes. In conclusion, the luminal uptake of insulin is of low specificity, as native and [leucine^B-25]-insulin were accumulated to the same extent. Endocytic uptake is of high capacity and the mechanism is saturable. Insulin accumulated in endocytic vacuoles and lysosomes, thus following the classical degradation pathway. No other subcellular compartment is associated with insulin degradation. It was not possible to detect the basolateral uptake, indicating loss of immunoreactivity after binding to its receptor. Absolute quantitative immunocytochemistry is applicable in studying endocytosis. The labeling density increases nonproportionally with antigen density probably caused by steric hindrances. Reduction of the particle size (16 to 6 nm) increased the labeling density 17.6 times.     

A reference dataset for verifying numerical electrophysiological heart models

Background  

The evaluation, verification and comparison of different numerical heart models are difficult without a commonly available database that could be utilized as a reference. Our aim was to compile an exemplary dataset.     

An efficient numerical method for distributed-loop models of the urine concentrating mechanism

In this study we describe an efficient numerical method, based on the semi-Lagrangian (SL) semi-implicit (SI) method and Newton's method, for obtaining steady-state (SS) solutions of equations arising in distributed-loop models of the urine concentrating mechanism. Dynamic formulations of these models contain large systems of coupled hyperbolic partial differential equations (PDEs). The SL method advances the solutions of these PDEs in time by integrating backward along flow trajectories, thus allowing large time steps while maintaining stability. The SI approach controls stiffness arising from transtubular transport terms by averaging these terms in time along flow trajectories. An approximate SS solution of a dynamic formulation obtained via the SLSI method can be used as an initial guess for a Newton-type solver, which rapidly converges to a highly accurate numerical approximation to the solution of the ordinary differential equations that arise in the corresponding SS model formulation. In general, it is difficult to specify a priori for a Newton-type solver an initial guess that falls within the radius of convergence; however, the initial guess generated by solving the dynamic formulation via the SLSI method can be made sufficiently close to the SS solution to avoid numerical instability. The combination of the SLSI method and the Newton-type solver generates stable and accurate solutions with substantially reduced computation times, when compared to previously applied dynamic methods.     

Towards accurate numerical method for monodomain models using a realistic heart geometry

The simulation of cardiac electrophysiological waves are known to require extremely fine meshes, limiting the applicability of current numerical models to simplified geometries and ionic models. In this work, an accurate numerical method based on a time-dependent anisotropic remeshing strategy is presented for simulating three-dimensional cardiac electrophysiological waves. The proposed numerical method greatly reduces the number of elements and enhances the accuracy of the prediction of the electrical wave fronts. Illustrations of the performance and the accuracy of the proposed method are presented using a realistic heart geometry. Qualitative and quantitative results show that the proposed methodology is far superior to the uniform mesh methods commonly used in cardiac electrophysiology.     

General method for the derivation and numerical solution of epithelial transport models

Summary A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.     

A fluorimetric method based on changes in membrane potential for screening paralytic shellfish toxins in mussels

To prevent the consumption of bivalves contaminated with paralytic shellfish poisoning (PSP), toxin levels in seafood products are estimated by using the official mouse bioassay. Because of the limitations of this bioassay other methods of monitoring toxins are clearly needed. We have developed a test to screen for PSP toxins based on its functional activity; the toxins bind to the voltage-gated Na+ channels and block their activity. The method is a fluorimetric assay that allows quantitation of the toxins by detecting changes in the membrane potential of human excitable cells. This assay gives an estimate of toxicity, since each toxin present in the sample binds to sodium channels with an affinity which is proportional to its intrinsic toxic potency. The detection limits for paralytic shellfish toxins were found to be 1 ng saxitoxin equivalents/ml compared to the regulatory limit threshold of 400 ng/ml (equivalent to 80 microg/100 g) used in most countries. Our results indicate that this fluorescent assay is a specific, very sensitive, rapid, and reliable method of monitoring PSP toxin levels in samples from seafood products and toxic algae.