A mechano-electrochemical model of radial deformation of the capillary glycocalyx

A mechano-electrochemical theory of the surface glycocalyx on capillary endothelial cells is presented that models the structure as a mixture of electrostatically charged macromolecules hydrated in an electrolytic fluid. Disturbances arising from mechanical deformation are introduced as perturbations away from a nearly electroneutral equilibrium environment. Under mechanical compression of the layer, such as might occur on the passing of stiff leukocytes through capillaries, the model predicts that gradients in the electrochemical potential of the compressed layer cause a redistribution of mobile ions within the glycocalyx and a rehydration and restoration of the layer to its equilibrium dimensions. Because of the large deformations of the glycocalyx arising from passing leukocytes, nonlinear kinematics associated with finite deformations of the layer are accounted for in the theory. A pseudo-equilibrium approximation is invoked for the transport of the mobile ions that reduces the system of coupled nonlinear integro-differential equations to a single nonlinear partial differential equation that is solved numerically for the compression and recovery of the glycocalyx using a finite difference method on a fixed grid. A linearized model for small strains is also obtained as verification of the finite difference solution. Results of the asymptotic analysis agree well with the nonlinear solution in the limit of small deformations of the layer. Using existing experimental and theoretical estimates of glycocalyx properties, the glycocalyx fixed-charge density is estimated from the analysis to be approximately 1 mEq/l, i.e., we estimate that there exists approximately one fixed charge on the glycocalyx for every 100 ions in blood. Such a charge density would result in a voltage differential between the undeformed glycocalyx and the capillary lumen of approximately 0.1 mV. In addition to providing insight into the mechano-electrochemical dynamics of the layer under deformation, the model suggests several methods for obtaining improved estimates of the glycocalyx fixed-charge density and permeability in vivo.     

A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle

The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724-H1736, 2000) and Adamson et al. (J Physiol 557: 889-907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281-304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips's original 1-D analysis of the matrix layer (J Physiol 388: 421-435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825-857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.     

Capillary endothelial surface layer selectively reduces plasma solute distribution volume

We previously reported that a 0.4- to 0.5-microm-thick endothelial surface layer confines Dextran 70 (70 kDa) to the central core of hamster cremaster muscle capillaries. In the present study we used a variety of plasma tracers to probe the barrier properties of the endothelial surface layer using combined fluorescence and brightfield intravital microscopy. No permeation of the endothelial surface layer was observed for either neutral or anionic dextrans >/=70 kDa, but a neutral Dextran 40 (40 kDa) and neutral free dye (rhodamine, 0.4 kDa) equilibrated with the endothelial surface layer within 1 min. In contrast, small anionic tracers of similar size (0. 4-40 kDa) permeated the endothelial surface layer relatively slowly with half-times (tau(50)) between 11 and 60 min, depending on tracer size. Furthermore, two plasma proteins, fibrinogen (340 kDa) and albumin (67 kDa), moved slowly into the endothelial surface layer at the same rates, despite greatly differing sizes (tau(50) approximately 40 min). Dextran 70, which did not enter the glycocalyx over the course of these experiments, entered at the same rate as free albumin when it was conjugated to albumin. These findings demonstrate that for anionic molecules size and charge have a profound effect on the penetration rate into the glycocalyx. The equal rates of penetration of the glycocalyx demonstrated by the different protein molecules suggests that multiple factors may influence the penetration of the barrier, including molecular size, charge, and structure.     

Molecular dynamics simulation: A new way to understand the functionality of the endothelial glycocalyx

Endothelial glycocalyx (EG) is a carbohydrate-rich layer which lines the lumen side of blood vessel walls. The EG layer is directly exposed to blood flow. The unique physiological location and its strongly coupled interaction with blood flow allow the EG layer to modulate microvascular mass transport and to sense and transmit mechanical signals from the passing blood. Molecular dynamics (MD) simulation is a computational method which focuses on atomic/molecular behavior at the microscale. The last two decades have witnessed a substantial increase in number and a broadening in scope regarding applications of MD in a wide spectrum of areas, including EG-related research. In this mini-review, MD works which solve EG-related problems and provide new insights into the functionality of EG are considered. Challenges of the MD method in EG research are articulated, and the future of MD in solving EG-related problems is also evaluated.     

Endothelial glycocalyx of blood circulation system. I. Detection,components, and structural organization

The luminal surface of a blood vessel accommodates a complex multicomponent system of mainly carbohydrates and proteins called glycocalyx. According to the concept of the double protective layer, glycocalyx is the first protection barrier of the vascular wall. The structure of glycocalyx is determined by a group of proteoglycans, glycoproteins, and glycosaminoglycans. Two groups of molecules are distinguished within the glycocalyx constituents, that is, membrane proteoglycans (syndecans and glypicans bound to endothelial cell membranes) and soluble proteoglycans (perlecan, biglycan, versican, decorin, and mimecan). There are five types of glycosaminoglycan chains; these are heperan sulfate, chondroitin sulfate, dermatan sulfate, keratan sulfate, and hyaluronan. There is a dynamic equilibrium between the soluble components of glycocalyx and flowing blood, which allows for separation of the endothelial surface layer. Due to its complexity and location at the interface of blood circulation system, glycocalyx is involved in the maintenance of vascular homeostasis. Here, the molecular composition of glycocalyx, properties of its components, biosynthesis, and common structural features are discussed.     

The variance of the distribution of traversal times in a capillary bed

A random walk model of capillary tracer transit times is developed that treats simulataneously: plug flow in the capillary, radial and axial diffusion in the capillary cylinder and tissue annulus, and endothelial barriers to solute transport. The mean transit time is simply the volume of distribution divided by blood flow. Variance of transit times has additive terms for radial, axial, and barrier influences that are reduceable to variances of simpler models of capillary exchange. The dependence of variance on the solute diffusion coefficient is not monotonic, but has a minimum near 0·5 × 10?6 cm²/s for reasonable parameters and no barrier, Small molecules like inert gases are expected to have larger variances with higher diffusion coefficients, while larger molecules and barrier limited solutes will have the reverse dependence. Available literature data indicates that capillary heterogeneity will have a major influence on whole-body variance of transit times.     

Transport of ions across the blood-brain barrier

Capillaries in the brain are formed by a uniquely specialized endothelial cell that regulates the movement of substances between blood and brain. Although they provide an impermeable barrier to some solutes, brain capillary endothelial cells facilitate the transcapillary exchange of others. In addition, they contain specific enzymes that contribute to a metabolic blood-brain barrier by limiting the movement of compounds such as neurotransmitters across the capillary wall. Studies of sodium and potassium transport by brain capillaries indicate that the endothelial cell contains distinct types of ion transport systems on the two sides of the capillary wall, i.e., the luminal and antiluminal membranes of the endothelial cell. As a result, specific solutes can be pumped across the capillary against an electrochemical gradient. These transport systems are likely to play a role in the active secretion of fluid from blood to brain and in maintaining a constant concentration of ions in the brain's interstitial fluid. In this way, the brain capillary endothelium is structurally and functionally related to an epithelium.     

Numerical simulation of oxygen delivery to muscle tissue in the presence of hemoglobin-based oxygen carriers

This work represents a culmination of research on oxygen transport to muscle tissue, which takes into account oxygen transport due to convection, diffusion, and the kinetics of simultaneous reactions between oxygen and hemoglobin and myoglobin. The effect of adding hemoglobin-based oxygen carriers (HBOCs) to the plasma layer of blood in a single capillary surrounded by muscle tissue based on the geometry of the Krogh tissue cylinder is examined for a range of HBOC oxygen affinity, HBOC concentration, capillary inlet oxygen tension (pO(2)), and hematocrit. The full capillary length of the hamster retractor muscle was modeled under resting (V(max) = 1.57 x 10(-4) mLO(2) mL(-1) s(-1), cell velocity (v(c)) = 0.015 cm/s) and working (V(max) = 1.57 x 10(-3) mLO(2) mL(-1) s(-1), v(c) = 0.075 cm/s) conditions. Two spacings between the red blood cell (RBC) and the capillary wall were examined, corresponding to a capillary with and without an endothelial surface layer. Simulations led to the following conclusions, which lend physiological insight into oxygen transport to muscle tissue in the presence of HBOCs: (1) The reaction kinetics between oxygen and myoglobin in the tissue region, oxygen and HBOCs in the plasma, and oxygen and RBCs in the capillary lumen should not be neglected. (2) Simulation results yielded new insight into possible mechanisms of oxygen transport in the presence of HBOCs. (3) HBOCs may act as a source or sink for oxygen in the capillary and may compete with RBCs for oxygen. (4) HBOCs return oxygen delivery to muscle tissue to normal for varying degrees of hypoxia (inlet capillary pO(2) < 30 mmHg) and anemia (hematocrit < 46%) for the hamster model.     

STUDIES ON BLOOD CAPILLARIES : II. Transport of Ferritin Molecules across the Wall of Muscle Capillaries

The pathway by which intravenously injected ferritin molecules move from the blood plasma across the capillary wall has been investigated in the muscle of the rat diaphragm. At 2 min after administration, the ferritin molecules are evenly distributed in high concentration in the blood plasma of capillaries and occur within vesicles along the blood front of the endothelium. At the 10-min time point, a small number of molecules appear in the adventitia, and by 60 min they are relatively numerous in the adventitia and in phagocytic vesicles and vacuoles of adventitial macrophages. Thereafter, the amount of ferritin in the adventitia and pericapillary regions gradually increases so that at 1 day the concentration in the extracellular spaces approaches that in the blood plasma. Macrophages and, to a lesser extent, fibroblasts contain large amounts of ferritin. 4 days after administration, ferritin appears to be cleared from the blood and from the capillary walls, but it still persists in the adventitial macrophages and fibroblasts. At all time points examined, ferritin molecules within the endothelial tunic were restricted to vesicles or to occasional multivesicular or dense bodies; they were not found in intercellular junctions or within the cytoplasmic matrix. Ferritin molecules did not accumulate within or against the basement membranes. Over the time period studied, the concentration of ferritin in the blood decreased, first rapidly, then slowly, in two apparently exponential phases. Liver and spleen removed large amounts of ferritin from the blood. Diaphragms fixed at time points from 10 min to 1 day, stained for iron by the Prussian Blue method, and prepared as cleared whole mounts, showed a progressive and even accumulation of ferritin in adventitial macrophages along the entire capillary network. These findings indicate: (1) that endothelial cell vesicles are the structural equivalent of the large pore system postulated in the pore theory of capillary permeability; (2) that the basement membrane is not a structural restraint in the movement of ferritin molecules across the capillary wall; (3) that transport of ferritin occurs uniformly along the entire length of the capillary; and (4) that the adventitial macrophages monitor the capillary filtrate and partially clear it of the tracer.     

An electrodiffusion model for effects of surface glycocalyx layer on microvessel permeability

To investigate the charge effect of the endothelial surface glycocalyx on microvessel permeability, we extended the three-dimensional model developed by Fu et al. (J Biomech Eng 116: 502-513, 1994) for the interendothelial cleft to include a negatively charged glycocalyx layer at the entrance of the cleft. Both electrostatic and steric exclusions on charged solutes were considered within the glycocalyx layer and at the interfaces. Four charge-density profiles were assumed for the glycocalyx layer. Our model indicates that the overall solute permeability across the microvessel wall including the surface glycocalyx layer and the cleft region is independent of the charge-density profiles as long as they have the same maximum value and the same total charge. On the basis of experimental data, this model predicts that the charge density would be 25-35 meq/l in the glycolcalyx of frog mesenteric capillaries. An intriguing prediction of this model is that when the concentrations of cations and anions are unequal in the lumen due to the presence of negatively charged proteins, the negatively charged glycocalyx would provide more resistance to positively charged solutes than to negatively charged ones.     

Multibreath tracer species dynamics in the lung

By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.     

The blood-brain barrier in a reptile, Anolis carolinensis

An electron microscopic study was made of the ultrastructure and permeability of the capillaries in the cerebral hemispheres of the lizard, Anolis carolinensis. The brain of Anolis is vascularized by a loop-type pattern consisting exclusively of arteriovenous capillary loops. The ultrastructure of the endothelium and the arrangement of the various layers from the capillary lumen to the central nervous tissue is similar to that of mammals. The endothelial cells form a continuous layer around the lumen and are joined by tight interendothelial junctions. The basal lamina of the endothelium is also continuous and encloses pericyte processes. The cells of the nervous tissue rest directly on the basal lamina of the capillary and are separated from each other by a 200 Å space. Intravenously injected horseradish peroxidase (MW 40,000) and ferritin (MW 500,000) were used to study the permeability of the capillaries. The entry of horseradish peroxidase and ferritin into the intercellular spaces of the brain is restricted by the tightness of the interendothelial junctions. No vesicular transport of either tracer occurs; however, ferritin does enter the endothelial cells in vacuoles. No tracer molecules are present in the basal lamina, pericytes, or nervous tissue. The different responses of the endothelial cell to the tracers used in this study suggest that endocytotic activities of endothelial cells involve different processes. Vacuoles formed by marginal folds, vacuoles formed by endothelial surface projections or deep invaginations of the plasma membrane, 600–800 Å vesicles, and coated vesicles all seem to differ in the nature of the substances which they endocytose.     

Calcium dependence of the stimulating action of cadmium on organic acid transport in the frog kidney

The stimulatory effect of cadmium ions on the Na-dependent fluorescein transport into the frog renal proximal tubules ceased with decreasing Ca++ concentration in solution on both the sides of the cell layer down to micromolar level. The decrease in Ca++ concentration per se stimulated fluorescein uptake during short-term incubations. A further diminution of Ca++ concentration in the tubular lumen with the aid of EGTA resulted in a sharp inhibition of the organic acid transport. Amiloride, which prevented the stimulatory effect of cadmium, inhibited the fluorescein transport at both millimolar and micromolar levels of Ca++ concentration, but it failed to affect the transport process after introducing EGTA into the tubular lumen. The results are discussed within the frames of a model regarding extracellular Ca++ as an allosteric inhibitor, and intracellular Ca++ as an allosteric activator of sodium channels in the apical membrane. Cd++ is assumed to compete with Ca++ for binding to centers of the allosteric inhibition, thereby accelerating the sodium ion flux across the cells of the proximal tubules.     

Theory of the electrokinetic behavior of human erythrocytes

We develop a theory of electrophoresis of human erythrocytes that predicts mobilities significantly smaller than those based on the classical Smoluchowski relation. In the classical treatment the charge is assumed to be spread uniformly on the hydrodynamic surface. The present model takes into account that most of the charge, due mainly to sialic acid, is contained in the glycocalyx. The glycocalyx is modeled as a permeable layer of polyelectrolyte molecules anchored to the cell membrane. The charge is assumed to be uniformly distributed throughout this layer. The fluid flow in the layer is treated as being dominated by Stokes friction arising from idealized polymer segments. The Navier-Stokes equations are solved to give the dependence of electroosomotic velocity with distance from the cell surface. An expression for the electrophoretic mobility is obtained which contains two parameters (a) the thickness of the glycocalyx and (b) the mean polymer segment radius. The best fit to experimental data is obtained if these are given the values 75 A and 7 A, respectively. Deviation from experimental data at low ionic strength (less than 0.05 M) occurs. However, this deviation is in the direction one would expect if at low ionic strength the polyelectrolyte layer expands slightly due to decreased charge shielding.     

High glucose causes dysfunction of the human glomerular endothelial glycocalyx

The endothelial glycocalyx is a gel-like layer which covers the luminal side of blood vessels. The glomerular endothelial cell (GEnC) glycocalyx is composed of proteoglycan core proteins, glycosaminoglycan (GAG) chains, and sialoglycoproteins and has been shown to contribute to the selective sieving action of the glomerular capillary wall. Damage to the systemic endothelial glycocalyx has recently been associated with the onset of albuminuria in diabetics. In this study, we analyze the effects of high glucose on the biochemical structure of the GEnC glycocalyx and quantify functional changes in its protein-restrictive action. We used conditionally immortalized human GEnC. Proteoglycans were analyzed by Western blotting and indirect immunofluorescence. Biosynthesis of GAG was analyzed by radiolabeling and quantified by anion exchange chromatography. FITC-albumin was used to analyze macromolecular passage across GEnC monolayers using an established in vitro model. We observed a marked reduction in the biosynthesis of GAG by the GEnC under high-glucose conditions. Further analysis confirmed specific reduction in heparan sulfate GAG. Expression of proteoglycan core proteins remained unchanged. There was also a significant increase in the passage of albumin across GEnC monolayers under high-glucose conditions without affecting interendothelial junctions. These results reproduce changes in GEnC barrier properties caused by enzymatic removal of heparan sulfate from the GEnC glycocalyx. They provide direct evidence of high glucose-induced alterations in the GEnC glycocalyx and demonstrate changes to its function as a protein-restrictive layer, thus implicating glycocalyx damage in the pathogenesis of proteinuria in diabetes.     

A numerical model for studying the effect of plasma layer on the process of blood oxygenation in the pulmonary capillaries

A two layer model for the blood oxygenation in pulmonary capillaries is proposed. The model consists of a core of erythrocytes surrounded by a symmetrically placed plasma layer. The governing equations in the core describe the free molecular diffusion, convection, and facilitated diffusion due to the presence of haemoglobin. The corresponding equations in the plasma layer are based on the free molecular diffusion and the convective effect of the blood. According to the axial train model for the blood flow proposed by Whitmore (1967), the core will move with a uniform velocity whereas flow in the plasma layer will be fully developed. The resulting system of nonlinear partial differential equations is solved numerically. A fixed point iterative technique is used to deal with the nonlinearities. The distance traversed by the blood before getting fully oxygenated is computed. It is shown that the concentration of O2 increases continuously along the length of the capillary for a given ratio of core radius to capillary radius. It is found that the rate of oxygenation increases as the core to capillary ratio decreases. The equilibration length increases with a heterogeneous model in comparison to that in a homogeneous model. The effect of capillary diameters and core radii on the rate of oxygenation has also been examined.     

TNF-alpha increases entry of macromolecules into luminal endothelial cell glycocalyx

The endothelial luminal glycocalyx has been largely ignored as a target in vascular pathophysiology even though it occupies a key location. As a model of the inflammatory response, we tested the hypothesis that tumor necrosis factor-alpha (TNF-alpha) can alter the properties of the endothelial apical glycocalyx. In the intact hamster cremaster microcirculation, fluorescein isothiocyanate (FITC)-labeled Dextrans 70, 580, and 2,000 kDa are excluded from a region extending from the endothelial surface almost 0.5 micrometer into the lumen. This exclusion zone defines the boundaries of the glycocalyx. Red blood cells (RBC) under normal flow conditions are excluded from a region extending even farther into the lumen. The cremaster microcirculation was pretreated with topical or intrascrotal applications of TNF-alpha. After infusion of FITC-dextran, FITC-albumin, or FITC-immunoglubulin G (IgG) via a femoral cannula, microvessels were observed with bright-field and fluorescence microscopy to obtain estimates of the anatomic diameters and the widths of fluorescent tracer columns and of the RBC columns (means +/- SE). After 2 h of intrascrotal TNF-alpha exposure, there was a significant increase in access of FITC-Dextrans 70 and 580 to the space bounded by the apical glycocalyx in arterioles, capillaries, and venules, but no significant change in access of FITC-Dextran 2,000. The effects of TNF-alpha could be observed as early as 20 min after the onset of topical application. TNF-alpha treatment also significantly increased the penetration rate of FITC-Dextran 40, FITC-albumin, and FITC-IgG into the glycocalyx and caused a significant increase in the intraluminal volume occupied by flowing RBC. White blood cell adhesion increased during TNF-alpha application, and we used the selectin antagonist fucoidan to attenuate leukocyte adhesion during TNF-alpha stimulation. This did not inhibit the TNF-alpha-mediated increase in permeation of the glycocalyx. These results show that proinflammatory cytokines can cause disruption of the endothelial apical glycocalyx, leading to an increased macromolecular permeation in the absence of an increase in leukocyte recruitment.     

In vivo Measurement of the Mouse Pulmonary Endothelial Surface Layer

The endothelial glycocalyx is a layer of proteoglycans and associated glycosaminoglycans lining the vascular lumen. In vivo, the glycocalyx is highly hydrated, forming a substantial endothelial surface layer (ESL) that contributes to the maintenance of endothelial function. As the endothelial glycocalyx is often aberrant in vitro and is lost during standard tissue fixation techniques, study of the ESL requires use of intravital microscopy. To best approximate the complex physiology of the alveolar microvasculature, pulmonary intravital imaging is ideally performed on a freely-moving lung. These preparations, however, typically suffer from extensive motion artifact. We demonstrate how closed-chest intravital microscopy of a freely-moving mouse lung can be used to measure glycocalyx integrity via ESL exclusion of fluorescently-labeled high molecular weight dextrans from the endothelial surface. This non-recovery surgical technique, which requires simultaneous brightfield and fluorescent imaging of the mouse lung, allows for longitudinal observation of the subpleural microvasculature without evidence of inducing confounding lung injury.     

Ultracytochemical study of lytic complex insertion in the glycocalyx of red cells during immune hemolysis mediated by complement

Ruthenium red (RR), a cationic dye and an ultrastructural tracer of cell membrane permeability, was used on sheep red blood cells after lysis produced by a specific antibody and guinea pig complement. In addition to the opacification of the glycocalyx, RR stained structures related to lytic complexes, which appeared as rod-like structures with variable dimensions (generally 45 nm in width, 75 nm in height) inserted in the glycocalyx of red cells. They extended across the external layer of the trilaminar plasma membrane without reaching the internal layer or the cytoplasm. RR staining visualized the internal configuration of the lytic complexes and revealed small channels measuring 10 nm in diameter localized within the complexes. These lytic complexes are thought to correspond to membrane attack complex of complement. To the best of our knowledge, this is the first report of ultrastructural positive staining of lytic complexes in thin sections, allowing visualization of their internal configuration and their insertion in the plasma membrane glycocalyx.