Computational study of LDL mass transport in the artery wall

A two-dimensional (2D) numerical simulation of convective–diffusive transport of LDL in the artery wall, coupled with the wall shear stress gradient (WSSG)-dependent LDL consumption of smooth muscle cells (SMCs) is presented. SMCs are modeled as an array of solid cylindrical pillars embedded in a continuous porous media which represents the interstitial proteoglycan and collagen fiber matrix. The internal elastic lamina (IEL), which separates the artery media from the intima, is modeled as an impermeable barrier to both water and LDL except for the fenestral pores that are assumed to be uniformly distributed over the IEL. The predictions demonstrate a range of interesting features of LDL transport and uptake in the media. For cells immediately below the fenestral pores, LDL uptake of SMCs is highly dependent on WSSG. Moreover, the rate of LDL consumption by SMCs is also affected by the diameter of the fenestral pore. This will be helpful in understanding the involvement of transmural transport processes in the initiation and development of atherosclerosis.     

Interstitial flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells

Interstitial flow through the tunica media of an artery wall in the presence of the internal elastic lamina (IEL), which separates it from the subendothelial intima, has been studied numerically. A two-dimensional analysis applying the Brinkman model as the governing equation for the porous media flow field was performed. In the numerical simulation, the IEL was modeled as an impermeable barrier to water flux, except for the fenestral pores, which were uniformly distributed over the IEL. The tunica media was modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells (SMCs) embedded in a fiber matrix simulating the interstitial proteoglycan and collagen fibers. A series of calculations was conducted by varying the physical parameters describing the problem: the area fraction of the fenestral pore (0. 001-0.036), the diameter of the fenestral pore (0.4-4.0 microm), and the distance between the IEL and the nearest SMC (0.2-0.8 microm). The results indicate that the value of the average shear stress around the circumference of the SMC in the immediate vicinity of the fenestral pore could be as much as 100 times greater than that around an SMC in the fully developed interstitial flow region away from the IEL. These high shear stresses can affect SMC physiological function.     

Kinetics of Diffusion and Convection in 3.2-Å Pores: Exact Solution by Computer Simulation

The kinetics of transport in pores the size postulated for cell membranes has been investigated by direct computer simulation (molecular dynamics). The simulated pore is 11 Å long and 3.2 Å in radius, and the water molecules are modeled by hard, smooth spheres, 1 Å in radius. The balls are given an initial set of positions and velocities (with an average temperature of 313° K) and the computer then calculates their exact paths through the pore. Two different conditions were used at the ends of the pore. In one, the ends are closed and the balls are completely isolated. In the other, the ball density in each end region is fixed so that a pressure difference can be established and a net convective flow produced. The following values were directly measured in the simulated experiments: net and diffusive (oneway) flux; pressure, temperature, and diffusion coefficients in the pore; area available for diffusion; probability distribution of ball positions in the pore; and the interaction between diffusion and convection. The density, viscosity, and diffusion coefficients in the bulk fluid were determined from the theory of hard sphere dense gases. From these values, the “equivalent” pore radius (determined by the same procedure that is used for cell membranes) was computed and compared with the physical pore radius of the simulated pore.     

ATP transport through a single mitochondrial channel, VDAC, studied by current fluctuation analysis.

The "molecular Coulter counter" concept has been used to study transport of ATP molecules through the nanometer-scale aqueous pore of the voltage-dependent mitochondrial ion channel, VDAC. We examine the ATP-induced current fluctuations and the change in average current through a single fully open channel reconstituted into a planar lipid bilayer. At high salt concentration (1 M NaCl), the addition of ATP reduces both solution conductivity and channel conductance, but the effect on the channel is several times stronger and shows saturation behavior even at 50 mM ATP concentration. These results and simple steric considerations indicate pronounced attraction of ATP molecules to VDAC's aqueous pore and permit us to evaluate the effect of a single ATP molecule on channel conductance. ATP addition also generates an excess noise in the ionic current through the channel. Analysis of this excess noise shows that its spectrum is flat in the accessible frequency interval up to several kilohertz. ATP exchange between the pore and the bulk is fast enough not to display any dispersion at these frequencies. By relating the low-frequency spectral density of the noise to the equilibrium diffusion of ATP molecules in the aqueous pore, we calculate a diffusion coefficient D = (1.6-3.3)10(-11) m2/s. This is one order of magnitude smaller than the ATP diffusion coefficient in the bulk, but it agrees with recent results on ATP flux measurements in multichannel membranes using the luciferin/luciferase method.     

Random-coil model for glomerular sieving of dextran

Dextran has been the most commonly employed test molecule for probing the selectivity of glomerular filtration to macromolecules of varying size. The usual theories for hindered transport of solid spheres through pores have limited utility in interpreting clearance data for dextran or other linear polymers because such polymers in solution more closely resemble random, solvent-filled coils than solid spheres. To provide a model for glomerular filtration of random-coil macromolecules, the equilibrium partitioning of random coils between cylindrical pores and bulk solution was simulated using Monte Carlo calculations, and those results were combined with a hydrodynamic theory for restricted motion of solvent-filled polymer coils in pores. The rates of transport predicted for either neutral random coils or for solid spheres of the same Stokes-Einstein radius were significantly lower than observed transport rates of dextran through the glomerular capillary wall or across synthetic porous membranes. This facilitation of dextran transport was modeled by postulating weak, attractive interactions between dextran monomers and the pore wall. The random-coil model with attractive interactions, modeled using a short-range, square-well potential, was found to adequately represent dextran sieving data in normal rats. Various limitations of this approach are discussed.     

The effect of the endothelial glycocalyx layer on concentration polarisation of low density lipoprotein in arteries

It has been postulated that a flow-dependent (and hence spatially varying) low density lipoprotein (LDL) concentration polarisation layer forms on the luminal surface of the vascular endothelium. Such a layer has the potential to cause heterogeneity in the distribution of atherosclerotic lesions by spatially modulating the rate of LDL transport into the arterial wall. Theoretical analysis suggests that a transmural water flux which is spatially heterogeneous at the cellular scale can act to enhance LDL concentration polarisation in a shear dependent fashion. However, such an effect is only observed if a relevant Peclet number (i.e. the ratio of LDL convection to LDL diffusion) is of order unity or greater. Based on the diffusivity of LDL in blood plasma, such a Peclet number is found to be far less than unity, implying that the aforementioned enhancement and shear dependence will not occur. However, this conclusion ignores the existence of the endothelial glycocalyx layer (EGL), which may inhibit the diffusion of LDL near the luminal surface of the endothelium, and hence raise any Peclet number associated with the transport of LDL. The present study numerically investigates the effect of the EGL, as well as a heterogeneous transmural water flux, on arterial LDL concentration polarisation. Particular attention is paid to measures of LDL concentration polarisation thought relevant to the rate of transendothelial LDL transport. It is demonstrated that an EGL is unlikely to cause any additional shear dependence of such measures directly, irrespective of whether or not LDL can penetrate into the EGL. However, it is found that such measures depend significantly on the nature of the interaction between LDL and the EGL (parameterised by the height of the EGL, the depth to which LDL penetrates into the EGL, and the diffusivity of LDL in the EGL). Various processes may regulate the interaction of LDL with the EGL, possibly in a flow dependent and hence spatially non-uniform fashion. It is concluded that any such processes may be as important as vascular scale flow features in terms of spatially modulating transendothelial LDL transport via an LDL concentration polarisation mechanism.     

ATP-Induced Shape Change of Nuclear Pores Visualized with the Atomic Force Microscope

Bidirectional transport of molecules between nucleus and cytoplasm through the nuclear pore complexes (NPCs) spanning the nuclear envelope plays a fundamental role in cell function and metabolism. Nuclear import of macromolecules is a two-step process involving initial recognition of targeting signals, docking to the pore and energy-driven translocation. ATP depletion inhibits the translocation step. The mechanism of translocation itself and the conformational changes of the NPC components that occur during macromolecular transport, are still unclear. The present study investigates the effect of ATP on nuclear pore conformation in isolated nuclear envelopes from Xenopus laevis oocytes using the atomic force microscope. All experiments were conducted in a saline solution mimicking the cytosol using unfixed nuclear envelopes. ATP (1 mm) was added during the scanning procedure and the resultant conformational changes of the NPCs were directly monitored. Images of the same nuclear pores recorded before and during ATP exposure revealed dramatic conformational changes of NPCs subsequent to the addition of ATP. The height of the pores protruding from the cytoplasmic surface of the nuclear envelope visibly increased while the diameter of the pore opening decreased. The observed changes occurred within minutes and were transient. The slow-hydrolyzing ATP analogue, ATP-γ-S, in equimolar concentrations did not exert any effects. The ATP-induced shape change could represent a nuclear pore ``contraction.' Received: 10 February 1997/Revised: 10 February 1998     

Permselectivity of the glomerular capillary wall to macromolecules. I. Theoretical considerations.

The transport of macromolecules across the renal glomerular capillary wall has been described theoretically using flux equations based on (a) restricted transport through small pores, and (b) the Kedem-Katchalsky formulation. The various assumptions and limitations inherent in these two approaches are discussed. To examine the coupling between macromolecular solute transport and the determinants of glomerular filtration rate, these flux equations were combined with mass balance relations which allow for variations in the transmembrane driving forces along a glomerular capillary. It was predicted, using both pore theory and the Kedem-Katchalsky equations, that fractional solute clearance should be strongly dependent on the determinants of glomerular filtration rate when convection and diffusion both contribute to solute transport. When convection becomes the sole mechanism for transcapillary solute transport, however, fractional solute clearance is essentially independent of changes in the determinants of glomerular filtration rate. Consequently, unless diffusion is absent, fractional solute clearances alone are insufficient to characterize the permselective properties of the glomerular capillary wall, since these values may be altered by changes in glomerular pressures and flows as well as changes in the properties of the capillary wall per se.     

Heteropore populations of bullfrog alveolar epithelium

Diffusional fluxes of a large number of hydrophilic solutes and water across bullfrog (Rana catesbeiana) alveolar epithelium were measured in the Ussing-type flux chamber. Lungs were isolated from double-pithed animals and studied as flat sheets. Radioactive solutes and water were added to the upstream reservoir, and the rate of change of downstream reservoir radioactivity was monitored. A permeability coefficient was estimated for each substance from a linear relationship between radiotracer concentration in the downstream reservoir and time. These permeability data were used to analyze the equivalent water-filled pore characteristics of the alveolar epithelial barrier. The data reveal that the alveolar epithelium is best characterized by two distinct pore populations rather than by a single homogeneous pore population. The large-pore population consists of pores with a radius of about 5 nm and occupies 4% of the available pore area. The small-pore population consists of pores with a radius of about 0.5 nm and occupies 96% of the available pore area. The number of small pores to large pores is 2.68 X 10(3). After the alveolar surface was damaged by acid, a large-pore population with a radius of about 27 nm was seen, allowing nearly free diffusion of solutes. A major implication of the presence of two populations of pores in the alveolar epithelium is that hydrostatically driven bulk water flow occurs predominantly through the large pores, while osmotically driven bulk water flow takes place predominantly through the small pores. As a result, in general, hydrostatic and osmotic gradients may not be equally effective driving forces for water flow across this tissue.     

Proton transport via the membrane surface

Some proton pumps, such as cytochrome c oxidase (C(c)O), translocate protons across biological membranes at a rate that considerably exceeds the rate of proton transport to the entrance of the proton-conducting channel via bulk diffusion. This effect is usually ascribed to a proton-collecting antenna surrounding the channel entrance. In this paper, we consider a realistic phenomenological model of such an antenna. In our model, a homogeneous membrane surface, which can mediate proton diffusion toward the channel entrance, is populated with protolytic groups that are in dynamic equilibrium with the solution. Equations that describe coupled surface-bulk proton diffusion are derived and analyzed. A general expression for the rate constant of proton transport via such a coupled surface-bulk diffusion mechanism is obtained. A rigorous criterion is formulated of when proton diffusion along the surface enhances the transport. The enhancement factor is found to depend on the ratio of the surface and bulk diffusional constants, pK(a) values of surface protolytic groups, and their concentration. A capture radius for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton can migrate on the membrane surface between a source (such as CcO) and a sink (such as ATP synthase) without fully equilibrating with the bulk. In pure aqueous solutions, protons can travel over long distances (microns). In buffered solutions, the travel distance is much shorter (nanometers); still the enhancement effect of the surface diffusion on the proton flow to a target on the surface can be tens to hundreds at physiological buffer concentrations. These results are discussed in a general context of chemiosmotic theory.     

Concentration polarization of atherogenic lipids in the arterial system

Nomenclature c, Normalized LDL concentration (C*/C0); C0, incoming (bulk) LDL concentration (gr/cm3); Cw, LDL concentration on the luminal surface (gr/cm3); ,wC time average value of LDL concentration on the luminal surface (gr/cm3); D, diffusion coef-ficient of LDL (cm2/s); Q, blood flow rate (mL/s); 0R, average internal radius of the artery (cm); Re, Reynolds number (002/Run); Sc, Schmidt number (/Dn); t, normalized time (00*/tuR); u, normalized axial velocity (0*/uu); 0u, time a…     

Concentration polarization of atherogenic lipids in the arterial system

The transport of atherogenic lipids (LDL) in a straight segment of an artery with a semi-permeable wall was simulated numerically. The numerical analysis predicted that a mass transport phenomenon called ’concentration polarization’ of LDL might occur in the arterial system. Under normal physiological flow conditions, the luminal surface LDL concentration was 5%–14% greater than the bulk concentration in a straight segment of an artery. The luminal surface LDL concentration at the arterial wall was flow-dependent, varying linearly with the filtration rate across the arterial wall and inversely with wall shear rate. At low wall shear rate, the luminal surface LDL concentration was very sensitive to changes in flow conditions, decreasing sharply as wall shear rate increased. In order to verify the numerical analysis, the luminal surface concentration of bovine serum albumin (as a tracer macromolecule) in the canine carotid artery was measured in vitro by directly taking liquid samples from the luminal surface of the artery. The experimental result was in very good agreement with the numerical analysis. The authors believe that the mass transport phenomenon of ‘concentration polarization’ may indeed exist in the human circulation and play an important role in the localization of atherosclerosis.     

The Behaviour of Ions in Narrow Water-Filled Pores

Today, the equilibrium behavior of ions in solution may be predicted with some confidence, essentially because rapid ionic diffusion over small distances ensures homogeneity throughout the solution. Equilibrium concepts such as ionic strength and pH apply. However, when attempting to understand the behavior of ions passing rapidly through narrow pores such as ion channels, no such equilibrium state may be assumed. The passing solution may have been in equilibrium with conditions at the mouth of the pore but will not be in equilibrium with charged molecules on the pore wall. In addition, the water in narrow pores will be partially ordered by contact with the pore walls and will not behave like bulk water.To illustrate this difference, a simple equilibrium calculation of the ion concentrations near a plastic sheet penetrated by narrow pores and containing in its surface partially ionized carboxyl groups is shown to be in good agreement with experiment. However, to predict the non-equilibrium behavior within the narrow pores is much more difficult. To illustrate the difficulty, a Monte Carlo computer model is described which attempts to predict the rapid switching of ion current observed experimentally with these narrow pores.     

Interfacial interactions of glutamate, water and ions with carbon nanopore evaluated by molecular dynamics simulations

Molecular dynamics simulations were used to assess the transport of glutamate, water and ions (Na(+) and Cl(-)) in a single wall carbon nanopore. The spatial profiles of Na(+) and Cl(-) ions are largely determined by the pore wall charges. Co-ions are repelled whereas the counter-ions are attracted by the pore charges, but this 'rule' breaks down when the water concentration is set to a level significantly below that in the physiological bulk solution. In such cases water is less able to counteract the ion-wall interactions (electrostatic or non-electrostatic), co-ions are layered near the counter-ions attracted by the wall charges and are thus layered as counter-ions. Glutamate is concentrated near the pore wall even at physiological water concentration, and irrespective of whether the pore wall is neutral or charged (positively or negatively), and its peak levels are up to 40 times above mean values. The glutamate is thus always layered as a counter-ion. Layering of water near the wall is independent of charges on the pore wall, but its peak levels near the wall are 'only' 6-8 times above the pore mean values. However, if the mean concentration of water is significantly below the level in the physiological bulk solution, its layering is enhanced, whereas its concentration in the pore center diminishes to very low levels. Reasons for such a 'paradoxical' behavior of molecules (glutamate and water) are that the non-electrostatic interactions are (except at very short distances) attractive, and electrostatic interactions (between the charged atoms of the glutamate or water and the pore wall) are also attractive overall. Repulsive interactions (between equally charged atoms) exist, and they order the molecules near the wall, whereas in the pore center the glutamate (and water) angles are largely randomly distributed, except in the presence of an external electric field. Diffusion of molecules and ions is complex. The translational diffusion is in general both inhomogeneous and anisotropic. Non-electrostatic interactions (ion-wall, glutamate-wall or water-wall) powerfully influence diffusion. In the neutral nanopore the effective axial diffusion constants of glutamate, water and Na(+) and Cl(-) ions are all <10% of their values in the bulk, and the electrostatic interactions can reduce them further. Diffusion of molecules and ions is further reduced if the water concentration in the pore is low. Glutamate(-) is slowed more than water, and ions are reduced the most especially co-ions. In conclusion the interfacial interactions influence the spatial distribution of glutamate, water and ions, and regulate powerfully, in a complex manner and over a very wide range their transport through nanosize pores.     

Water Confined in Cylindrical Pores: A Molecular Dynamics Study

Molecular dynamics simulations of water confined in two hydrophilic cylindrical pores—PH and PL—that differ in their silanol surface concentration (7.6 and 3.0 nm⁻², respectively) have been performed at 300 K. A strong interaction of interfacial water molecules with the pore was systematically found and gives rise to a layering effect, a significant distortion of both the hydrogen bond network (HBN) and the tetrahedral structure of these water molecules, and a corresponding subdiffusive mean square displacement along the main axis of the pores. By contrast, water molecules in the inner part of both pores were found to behave similarly to bulk water. The HBN and the tetrahedral configuration of water were more gradually distorted in the PL pore given the larger heterogeneity and rugosity of the surface, and the number of water–pore hydrogen bonds did not scale linearly with the silanol surface concentration of the pores, in part because of the close proximity between silanols in the PH pore. With the PL pore, the dynamic slowing down of water was found consistent with the experiment, suggesting that it provides a better model for the cylindrical MCM-41 mesopores. The structural and dynamical properties of water vary little with the silica force field.     

Interstitial albumin concentration measured during growth of perivascular cuffs in liquid-filled rabbit lung.

The growth rate and albumin concentration of interstitial fluid cuffs were measured in isolated rabbit lungs inflated with albumin solution (3 g/dl) to constant airway (Paw) and vascular pressures for up to 10 h. Cuff size was measured from images of frozen lung sections, and cuff albumin concentration (Cc) was measured from the fluorescence of Evans blue labeled albumin that entered the cuffs from the alveolar space. At 5-cmH2O Paw, cuff size peaked at 1 h and then decreased by 75% in 2 h. The decreased cuff size was consistent with an osmotic absorption into the albumin solution that filled the vascular and alveolar spaces. At 15-cmH2O Paw, cuff size peaked at 0.25 h and then remained constant. Cc rose continuously at both pressures, but was greater at the higher pressure. The increasing Cc with a constant cuff size was modeled as diffusion through epithelial pores. Initial Cc-to-airway albumin concentration ratio was 0.1 at 5-cmH2O Paw and increased to 0.3 at 15 cmH2O, a behavior that indicated an increased permeability with lung inflation. Estimated epithelial reflection coefficient was 0.9 and 0.7, and equivalent epithelial pore radii were 4.5 and 6.1 nm at 5- and 15-cmH2O Paw, respectively. The initial cuff growth occurred against an albumin colloid osmotic pressure gradient because a high interstitial resistance reduced the overall epithelial-interstitial reflection coefficient to the low value of the interstitium.     

The quantitation of ADP diffusion gradients across the outer membrane of heart mitochondria in the presence of macromolecules

We have previously provided evidence that diffusion of metabolites across the porin pores of mitochondrial outer membrane is hindered. A functional consequence of this diffusion limitation is the dynamic compartmentation of ADP in the intermembrane space. These earlier studies were done on isolated mitochondria suspended in isotonic media without macromolecules, in which intermembrane space of mitochondria is enlarged. The present study was undertaken to assess the diffusion limitation of outer membrane in the presence of 10% (w/v) dextran M20, in order to mimic the action of cytosolic macromolecules on mitochondria. Under these conditions, mitochondria have a more native, condensed configuration.Flux-dependent concentration gradients of ADP were estimated by measuring the ADP diffusion fluxes across the porin pores of isolated rat heart mitochondria incubated together with pyruvate kinase (PK), both of which compete for ADP regenerated by mitochondrial creatine kinase (mtCK) within the intermembrane space or by yeast hexokinase (HK) extramitochondrially. From diffusion fluxes and bulk phase concentrations of ADP, its concentrations in the intermembrane space were calculated using Fick's law of diffusion. Flux-dependent gradients up to 23 microM ADP (for a diffusion rate of J(Dif)=1.9 micromol ADP/min/mg mitochondrial protein) were observed. These gradients are about twice those estimated in the absence of dextran and in the same order of magnitude as the cytosolic ADP concentration (30 microM), but they are negligibly low for cytosolic ATP (5 mM). Therefore, it is concluded that the dynamic ADP compartmentation is of biological importance for intact heart cells.If mtCK generates ADP within the intermembrane space, the local ADP concentration can be clearly higher than in the cytosol resulting in higher extramitochondrial phosphorylation potentials. In this way, mtCK contributes to ensure optimal kinetic conditions for ATP-splitting reactions in the extramitochondrial compartment.     

Porin of Paramecium mitochondria isolation, characterization and ion selectivity of the closed state

Porin was isolated and purified from mitochondria of Paramecium tetraurelia. The protein showed a single band of apparent Mr 37,000 on sodium dodecyl sulfate polyacrylamide electrophoretograms. The reconstitution of the protein into artificial lipid bilayer membranes revealed it to be a porin giving pores with an average single-channel conductance of 0.26 nS in 0.1 M KCl. This conductance is about half of that of other eukaryotic porins studied to date. The pore formed by the mitochondrial porin of Paramecium was found to be voltage-dependent and switched to a defined substrate at membrane voltages larger than 20 mV. In the open state the pore exhibited the characteristics of a general diffusion pore because the mobility sequence of the ions inside the pore was similar to that in the bulk aqueous phase. The effective diameter was estimated to be about 1.3 nm. The properties of the low conductance state of the pore were studied in detail. In this state the pore favored the passage of cations, in contrast to the open state which favored anions slightly. The possible role of the low-conductance state in the regulation of transport processes across the outer mitochondrial membrane and in mitochondrial metabolism is discussed.