The forward rate of binding of surface-tethered reactants: effect of relative motion between two surfaces

The reaction of molecules confined to two dimensions is of interest in cell adhesion, specifically for the reaction between cell surface receptors and substrate-bound ligand. We have developed a model to describe the overall rate of reaction of species that are bound to surfaces under relative motion, such that the Peclet number is order one or greater. The encounter rate between reactive species is calculated from solution of the two-dimensional convection-diffusion equation. The probability that each encounter will lead to binding depends on the intrinsic rate of reaction and the encounter duration. The encounter duration is obtained from the theory of first passage times. We find that the binding rate increases with relative velocity between the two surfaces, then reaches a plateau. This plateau indicates that the increase in the encounter rate is counterbalanced by the decrease in the encounter duration as the relative velocity increases. The binding rate is fully described by two dimensionless parameters, the Peclet number and the Damk?hler number. We use this model to explain data from the cell adhesion literature by incorporating these rate laws into "adhesive dynamics" simulations to model the binding of a cell to a surface under flow. Leukocytes are known to display a "shear threshold effect" when binding selectin-coated surfaces under shear flow, defined as an increase in bind rate with shear; this effect, as calculated here, is due to an increase in collisions between receptor and ligand with increasing shear. The model can be used to explain other published data on the effect of wall shear rate on the binding of cells to surfaces, specifically the mild decrease in binding within a fixed area with increasing shear rate.     

Analysis of cell flux in the parallel plate flow chamber: implications for cell capture studies.

The parallel plate flow chamber provides a controlled environment for determinations of the shear stress at which cells in suspension can bind to endothelial cell monolayers. By decreasing the flow rate of cell-containing media over the monolayer and assessing the number of cells bound at each wall shear stress, the relationship between shear force and binding efficiency can be determined. The rate of binding should depend on the delivery of cells to the surface as well as the intrinsic cell-surface interactions; thus, only if the cell flux to the surface is known can the resulting binding curves be interpreted correctly. We present the development and validation of a mathematical model based on the sedimentation rate and velocity profile in the chamber for the delivery of cells from a flowing suspension to the chamber surface. Our results show that the flux depends on the bulk cell concentration, the distance from the entrance point, and the flow rate of the cell-containing medium. The model was then used in a normalization procedure for experiments in which T cells attach to TNF-alpha-stimulated HUVEC monolayers, showing that a threshold for adhesion occurs at a shear stress of about 3 dyn/cm2.     

Interaction forces between red cells agglutinated by antibody. I. Theoretical.

A general method of calculating forces, torques, and translational and rotational velocities of rigid, neutrally buoyant spheres suspended in viscous liquids undergoing a uniform shear flow has been given by Arp and Mason (1977). The method is based on the matrix formulation of hydrodynamic resistances in creeping flow by Brenner and O'Neill (1972). We describe the solution of the Brenner-O'Neill force-torque vector equation in terms of the particle and external flow field coordinates and derive expressions for the normal force acting along, and the shear force acting perpendicular to, the axis of the doublet of spheres, the latter explicitly given for the first time. The equations consist of a term comprising force and torque coefficients obtained from the matrices of the hydrodynamic resistances (functions of the distance h between sphere surfaces which have been computed), and terms comprising the orientation of the doublet axis relative to the coordinates of the external flow field and the shear stress (which can be experimentally determined). We have applied the theory to a system of doublets of sphered, hardened human red cells of group A or B antigenic type cross-linked by the corresponding antibody at a fixed interparticle distance. Working from studies of the breakup of doublets of red cells in an accelerating Poiseuille flow, given in the succeeding paper, we are able to compute the hydrodynamic force required to separate the two spheres. Previous work has shown that the theory can be applied to doublets in a variable shear, Poiseuille flow, provided the ratio of particle to tube diameter is small. In calculating the force-torque coefficients it was assumed that the cells are crosslinked by antibody with h = 20 nm.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.     

Dynamics of vesicles in a wall-bounded shear flow

We report a detailed study of the behavior (shapes, experienced forces, velocities) of giant lipid vesicles subjected to a shear flow close to a wall. Vesicle buoyancy, size, and reduced volume were separately varied. We show that vesicles are deformed by the flow and exhibit a tank-treading motion with steady orientation. Their shapes are characterized by two nondimensional parameters: the reduced volume and the ratio of the shear stress with the hydrostatic pressure. We confirm the existence of a force, able to lift away nonspherical buoyant vesicles from the substrate. We give the functional variation and the value of this lift force (up to 150 pN in our experimental conditions) as a function of the relevant physical parameters: vesicle-substrate distance, wall shear rate, viscosity of the solution, vesicle size, and reduced volume. Circulating deformable cells disclosing a nonspherical shape also experience this force of viscous origin, which contributes to take them away from the endothelium and should be taken into account in studies on cell adhesion in flow chambers, where cells membrane and the adhesive substrate are in relative motion. Finally, the kinematics of vesicles along the flow direction can be described in a first approximation with a model of rigid spheres.     

Ethanol enhances neutrophil membrane tether growth and slows rolling on P-selectin but reduces capture from flow and firm arrest on IL-1-treated endothelium

The effects of ethanol at physiological concentrations on neutrophil membrane tether pulling, adhesion lifetime, rolling, and firm arrest behavior were studied in parallel-plate flow chamber assays with adherent 1-microm-diameter P-selectin-coated beads, P-selectin-coated surfaces, or IL-1-stimulated human endothelium. Ethanol (0.3% by volume) had no effect on P-selectin glycoprotein ligand-1 (PSGL-1), L-selectin, or CD11b levels but caused PSGL-1 redistribution. Also, ethanol prevented fMLP-induced CD11b up-regulation. During neutrophil collisions with P-selectin-coated beads at venous wall shear rates of 25-100 s(-1), ethanol increased membrane tether length and membrane growth rate by 2- to 3-fold but reduced the adhesion efficiency (detectable bonding per total collisions) by 2- to 3-fold, compared with untreated neutrophils. Without ethanol treatment, adhesion efficiency and adhesion lifetime declined as wall shear rate was increased, whereas ethanol caused the adhesion lifetime over all events to increase from 0.1 s to 0.5 s as wall shear rate was increased, an example of pharmacologically induced hydrodynamic thresholding. Consistent with this increased membrane fluidity and reduced capture, ethanol reduced rolling velocity by 37% and rolling flux by 55% on P-selectin surfaces at 100 s(-1), compared with untreated neutrophils. On IL-1-stimulated endothelium, rolling velocity was unchanged by ethanol treatment, but the fraction of cells converting to firm arrest was reduced from 35% to 24% with ethanol. Overall, ethanol caused competing biophysical and biochemical effects that: 1) reduced capture due to PSGL-1 redistribution, 2) reduced rolling velocity due to increased membrane tether growth, and 3) reduced conversion to firm arrest.     

Tuning the formation and rupture of single ligand-receptor bonds by hyaluronan-induced repulsion

We used a combination of laminar flow chamber and reflection interference microscopy to study the formation and rupture of single bonds formed between Fc-ICAM-1 attached to a substrate and anti-ICAM-1 carried by micrometric beads in the presence of a repulsive hyaluronan (HA) layer adsorbed onto the substrate. The absolute distance between the colloids and the surface was measured under flow with an accuracy of a few nanometers. We could verify the long-term prediction of classical lubrication theory for the movement of a sphere near a wall in a shear flow. The HA polymer layer exerted long-range repulsive steric force on the beads and the hydrodynamics at the boundary remained more or less unchanged. By incubating HA at various concentrations, the thickness of the layer, as estimated by beads most probable height, was tuned in the range 20-200 nm. Frequency of bond formation was decreased by more than one order of magnitude by increasing the thickness of the repulsive layer, while the lifetime of individual bonds was not affected. This study opens the way for further quantitative studies of the effect of molecular environment and separation distance on ligand-receptor association and dissociation.     

Dissecting streptavidin-biotin interaction with a laminar flow chamber

A laminar flow chamber was used to study single molecule interactions between biotinylated surfaces and streptavidin-coated spheres subjected to a hydrodynamic drag lower than a piconewton. Spheres were tracked with 20 ms and 40 nm resolution. They displayed multiple arrests lasting between a few tens of milliseconds and several minutes or more. Analysis of about 500,000 positions revealed that streptavidin-biotin interaction was multiphasic: transient bound states displayed a rupture frequency of 5.3 s(-1) and a rate of transition toward a more stable configuration of 1.3 s(-1). These parameters did not display any significant change when the force exerted on bonds varied between 3.5 and 11 pN. However, the apparent rate of streptavidin-biotin association exhibited about 10-fold decrease when the wall shear rate was increased from 7 to 22 s(-1), which supports the existence of an energy barrier opposing the formation of the transient binding state. It is concluded that a laminar flow chamber can yield new and useful information on the formation of molecular bonds, and especially on the structure of the external part of the energy landscape of ligand-receptor complexes.     

Magnetic resonance microscopy determined velocity and hematocrit distributions in a Couette viscometer

Magnetic resonance microscopy is used to non-invasively measure the radial velocity distribution in Couette flow of erythrocyte suspensions of varying aggregation behavior at a nominal shear rate of 2.20 s(-1) in a 1 mm gap. Suspensions of red blood cells in albumin-saline, plasma and 1.48% Dextran added plasma at average hematocrits near 0.40 are studied, providing a range of aggregation ability. The spatial distribution of the red blood cell volume fraction, hematocrit, is calculated from the velocity distribution. The hematocrit profiles provide direct measure of the thickness of the aggregation and shear rate dependent red blood cell depletion at the Couette surfaces. At the nominal shear rate studied hematocrit distributions for the red blood cells in plasma show a depletion zone near the inner Couette wall but not the outer wall. The red blood cells in plasma with Dextran show cell depletion regions of approximately 100 mum at both the inner and outer Couette surfaces, with greater depletion at the inner wall, but approach the normal blood hematocrit distribution with a doubling of shear rate due to decreased aggregation. The material response of the blood is spatially dependent with the shear rate and the hematocrit distribution non-uniform across the gap.     

The effect of compliance on wall shear in casts of a human aortic bifurcation

Rigid and compliant casts of a human aortic bifurcation were subjected to physiologically realistic pulsatile fluid flows. At a number of sites near the wall in the approximate median plane of the bifurcation of these models, fluid velocity was measured with a laser Doppler velocimeter, and wall motion (in the case of the compliant cast) was determined with a Reticon linescan camera. The velocity and wall motion data were combined to estimate the instantaneous shear rates at the cast wall. Analysis showed that at the outer walls the cast compliance reduced shear rates, while at the walls of the flow divider the shear rate was increased.     

Visualization of flow-dependent concentration polarization of macromolecules at the surface of a cultured endothelial cell monolayer by means of fluorescence microscopy

To substantiate the occurrence of flow-dependent concentration or depletion of atherogenic lipoproteins, which has been theoretically predicted to take place at a blood/endothelium boundary, we have studied the effects of perfusion pressure and wall shear rate on the accumulation and uptake of microspheres by cultured vascular endothelial cells in a monolayer. The study was carried out by flowing a cell culture medium containing fetal calf serum and fluorescent microspheres through a parallel-plate flow chamber having a cultured bovine aortic endothelial cell (BAEC) monolayer on one wall of the chamber. The microspheres had a nominal diameter of 19 nm, approximately the same as that of low-density lipoproteins, and thus served as models and tracers of plasma proteins and lipoproteins. Experiments were carried out in steady flow in the physiological range of wall shear rate and water filtration velocity at the monolayer, while monitoring the intensity of fluorescence of the spheres accumulated at and taken up by the endothelial cells. It was found that in a perfusate containing only fluorescent microspheres, due to increased phagocytic activity of the endothelial cells, the intensity of fluorescence which reflected the number of the microspheres taken up by the endothelial cells, increased almost linearly with time and independently of wall shear rate. However, with perfusates containing fetal calf serum, this abnormal phenomenon did not occur, and the intensity of fluorescence increased with increasing perfusion pressure and decreasing wall shear rate. It was also found that the number of fluorescent microspheres accumulated at and taken up by the BAEC monolayer was shear-dependent only at low wall shear rates, and increased sharply when the flow rate was reduced to zero. These results provided solid experimental evidence that flow-dependent concentration or depletion of macromolecules occurs at the luminal surface of the endothelium at physiological wall shear rates and water filtration velocities, and strongly supports the hypothesis that flow-dependent concentration polarization of lipoproteins plays an important role in the localization of atherosclerosis and intimal hyperplasia in man by facilitating the uptake of atherogenic lipoproteins by endothelial cells.     

Measurement of wall motion and wall shear in a compliant arterial cast

Initial measurements of the time-varying wall shear rate at two sites in a compliant cast of a human aortic bifurcation are presented. The shear rates were derived from flow velocities measured by laser Doppler velocimetry (LDV) near the moving walls of the cast. To derive these shear rate values, the distance from the velocimeter sampling volume to the cast wall must be known. The time variation of this distance was obtained from LDV measurements of the velocity of the wall itself.     

Study of local hydrodynamic environment in cell-substrate adhesion using side-view μPIV technology

Tumor cell adhesion to the endothelium under shear flow conditions is a critical step that results in circulation-mediated tumor metastasis. This study presents experimental and computational techniques for studying the local hydrodynamic environment around adherent cells and how local shear conditions affect cell-cell interactions on the endothelium in tumor cell adhesion. To study the local hydrodynamic profile around heterotypic adherent cells, a side-view flow chamber assay coupled with micro particle imaging velocimetry (μPIV) technique was developed, where interactions between leukocytes and tumor cells in the near-endothelial wall region and the local shear flow environment were characterized. Computational fluid dynamics (CFD) simulations were also used to obtain quantitative flow properties around those adherent cells. Results showed that cell dimension and relative cell-cell positions had strong influence on local shear rates. The velocity profile above leukocytes and tumor cells displayed very different patterns. Larger cell deformations led to less disturbance to the flow. Local shear rates above smaller cells were observed to be more affected by relative positions between two cells.     

Nontraumatic aortic blood flow sensing by use of an ultrasonic esophageal probe.

The measurement of blood velocity fields, volume flow, and arterial wall motion in the descending thoracic aorta provides essential hemodynamic information for both research and clinical diagnosis. The close proximity of the esophagus to the aorta in the dog makes it possible to obtain such data nonsurgically using an ultrasonic esophageal probe; however, the accuracy of such a probe is limited if the angle between the sound beam and the flow axis, known as the Doppler angle, is not precisely known. By use of a pulsed Doppler velocity meter (PUDVM) and a triangulation procedure, accurate empirical measurement of the Doppler angle has been obtained, allowing quantification of blood velocity scans across the aorta. Volume flow is obtained by integration of blood velocity profiles and arterial wall motion is measured with an ultrasonic echo tracking device. Accuracy of the probe was substantiated by comparison with ultrasonic and electromagnetic implanted flow cuff measurements. Use of the probe in measurement of blood velocity, volume flow and arterial wall motion at various locations along the 8- and 10-cm length of the descending thoracic aorta in adult beagle dogs is detailed. The simplicity, accuracy, and nontraumatic aspect of the technique should allow increasing use of such a probe in numerous research and clinical applications.     

Heat transport in laminar flow of erythrocyte suspensions.

Measurements of thermal conductivity were made in laminar flow of dog and turkey erythrocyte suspensions in a stainless stell tube of about 1 mm ID. These measurements were independent of the shear rate, showing that the red cell motion relative to plasma in flowing blood had no effect on the heat transfer. Measurements of thermal conductivity were further made in suspensions of polystyrene spheres of 100 mum and were found to be dependent upon the shear rate. The Graetz solution corresponding to uniform wall temperature was used for determining the value of thermal conductivity in an apparatus calibrated with tap water. The overall accuracy of the results is within 10%. A model based on the particle rotation with the entrained fluid is proposed. It is pointed out that the diffusion of platelets, red cells, and possibly plasma proteins (such as fibrinogen) will be augmented if they happen to be in the hydrodynamic field of rotating erythrocytes.     

Effects of wall shear stress and fluid recirculation on the localization of circulating monocytes in a three-dimensional flow model

There is a correlation between the location of early atherosclerotic lesions and the hemodynamic characteristics at those sites. Circulating monocytes are key cells in the pathogenesis of atherosclerotic plaques and localize at sites of atherogenesis. The hypothesis that the distribution of monocyte adhesion to the vascular wall is determined in part by hemodynamic factors was addressed by studying monocyte adhesion in an in vitro flow model in the absence of any biological activity in the model wall.

Suspensions of U937 cells were perfused (Re = 200) through an axisymmetric silicone flow model with a stenosis followed by a reverse step. The model provided spatially varying wall shear stress, flow separation and reattachment, and a three-dimensional flow pattern. The cell rolling velocity and adhesion rates were determined by analysis of videomicrographs. Wall shear stress was obtained by numerical solution of the equations of fluid motion. Cell adhesion patterns were also studied in the presence of chemotactic peptide gradients.

The cell rolling velocity varied linearly with wall shear stress. The adhesion rate tended to decrease with increasing local wall shear stress, but was also affected by the radial component of velocity and the dynamics of the recirculation region and flow reattachment. Adhesion was increased in the vicinity of chemotactic peptide sources downstream of the expansion site. Results with human monocytes were qualitatively similar to the U937 experiments.

Differences in the adhesion rates of U937 cells occurring solely as a function of the fluid dynamic properties of the flow field were clearly demonstrated in the absence of any biological activity in the model wall.     

Velocity profiles in annular perfusion chamber measured by laser-Doppler velocimetry

p6e fluid flow in the annular perfusion chamber of Baumgartner developed to study platelet vessel wall interaction was examined with laser-Doppler velocimetry. A laminar and stable flow with a Reynolds number of less than or equal to 50 was measured at flow rates up to 3 ml s-1. No turbulence was found. The wall shear rate directly determined from measured velocity profiles agreed well with theory. The experiments underlined the necessity to work with vessels of uniform thickness and a smooth surface.     

Drift and fluctuating motion of artificial platelets during the lateral transport and adhesion process near the wall

Recombinant glycoprotein Ibα latex beads (rGPIbα-LB) are a potential solution to overcoming platelet transfusion problems with artificial platelets. To understand the transport process of artificial platelets and to estimate the particle motion when adhering to the wall surface, we evaluated the lateral motion of rGPIbα-LB in terms of drift and random motion, because the lateral motion is an important factor for transport and adhesion. We observed the lateral motion of rGPIbα-LB flowing with red blood cells toward the immobilized von Willebrand factor (vWf) surface in a model arteriole at wall shear rates of 200–1000 s^?1 and 0–40% Hct. At 40% Hct, wall shear rate dependence was observed for the drift motion, i.e. the lateral velocity of rGPIbα-LB toward the wall. In the near-wall region, the drift motion of contacting particles differed substantially from that of non-contacting particles. Additionally, the trajectories of contacting particles on the vWf surface had specific motion that was not observed on the BSA surface. These results suggest that the adhesion force between rGPIbα and vWf is highly associated with the motion of particles near the wall. These features are desirable for artificial platelets, particularly for the adhesion process.     

Shear‐induced diffusion of red blood cells measured with dynamic light scattering‐optical coherence tomography

Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering‐optical coherence tomography (DLS‐OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution‐constrained three‐dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS‐OCT to measure both RBC velocity and the shear‐induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear‐induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10^?6 mm². These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.