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* Department of Biochemistry and Biophysics, Department of Pharmacology and Physiology, and Department of Biomedical Engineering, University of Rochester, Rochester, New York
Correspondence: Address reprint requests to Richard E. Waugh, Dept. of Biomedical Engineering, University of Rochester, Medical Center Box 639, 601 Elmwood Ave., Rochester, NY 14642. Tel.: 585-275-3768; Fax: 585-273-4746; E-mail: waugh{at}seas.rochester.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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20 to 50%) over the range of forces tested (50–350 pN). In addition, different-sized beads were used to change the force per unit area in the contact zone (contact stress). We conclude that for a given contact stress, the rate of bond formation increases linearly with contact area, but that increasing contact stress results in higher intrinsic rates of bond formation. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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). The importance of fluid shear forces for adhesion between neutrophils and endothelial-cell ligand-presenting surfaces was an important early finding in studies of leukocyte-endothelial interactions (Lawrence et al., 1990; Alon et al., 1996; Finger et al., 1996). Indeed, several studies have shown that cell arrest mediated by integrin bond formation does not generally occur unless the interaction is preceded by cell rolling (Lawrence and Springer, 1991; Rainger et al., 1997; Green et al., 2004). The mechanism for this facilitation of integrin bond formation by cell rolling is not thoroughly understood. It is thought that the rolling interaction (mediated by rapidly binding selectins) increases the time of interaction between regions of the cell and substrate allowing the slower integrin bonds to form (Riha et al., 2003). Cell rolling may also allow time for (or even initiate) signaling events to upregulate integrin affinity for endothelial ligand. In addition to increasing contact time, rolling interactions also have significant effects on the forces of interaction between cells and substrate. Therefore, a complete understanding of the facilitation of integrin bond formation by cell rolling requires more detailed information about how mechanical forces affect the dynamics of integrin bond formation.
On neutrophils, most integrins are members of the family of ß2-integrins, heterodimeric glycoproteins found on leukocytes and having in common the ß2 subunit (CD18). LFA-1 and Mac-1 are the principle members of this group. Both bind to the endothelial ligand intercellular adhesion molecule-1 (ICAM-1), a member of the immunoglobulin superfamily that is widely expressed on the vascular endothelium in response to stimulatory agents (Dustin et al., 1986). Conformational changes in LFA-1 and Mac-1 are necessary for ligand binding (Dransfield et al., 1992; Li et al., 1998). In vivo, these activating conformational changes are brought about by inside-out signaling, i.e., intracellular signaling cascades initiated by chemokines and other stimulatory mechanisms (see review by van Kooyk and Figdor, 2000). Similar conformational changes can be induced using divalent cations. Calcium stabilizes a low affinity form of LFA-1, inhibiting ICAM-1 binding, whereas manganese or magnesium in the presence of the calcium chelator EGTA promotes the LFA-1/ICAM-1 interaction (Dransfield et al., 1992; Tominaga et al., 1998). The effects of divalent ions on the affinity state of Mac-1 are different. Whereas calcium and/or magnesium are essential for integrin affinity changes induced by inflammatory mediators, manganese but not magnesium induces the active form of Mac-1 in the absence of cell activation (Altieri, 1991; Diamond and Springer, 1993). Even though magnesium appears to act only on LFA-1, we have demonstrated previously that Mg2+ increases the likelihood of integrin-mediated homotypic adhesion between neutrophils (Spillmann et al., 2002) and enables adhesion between neutrophils and immobilized ICAM-1 (Lomakina and Waugh, 2004). Thus, suspension of cells in buffers containing Mg2+ and EGTA is an effective way to promote integrin-mediated neutrophil adhesion to ICAM-1 without general activation of the cell.
Prior studies addressing the role of mechanical force and leukocyte deformation during adhesion have focused on adhesion and cell deformation under flow (Firrell and Lipowsky, 1989; Dong et al., 1999; Lei et al., 1999; Dong and Lei, 2000). Neutrophil attachment to a ligand-coated substrate under fluid shear results in cell deformation and a corresponding increase in the contact area between the two surfaces. In these prior studies, investigators have argued that this should facilitate cell recruitment by increasing the area over which adhesive bonds can form and by prolonging the duration of contact, allowing more time for bonds to form. In addition, increasing the size of the contact area between the cell and substrate alters the mechanical forces acting at the adhesive interface and reducing the magnitude of detachment forces at the trailing edge of the cell. An important aspect of the adhesion process that has not been considered in prior studies is the effect that impingement forces between the cell and the substrate may have on the rate of bond formation.
As an approach for assessing the effect of mechanical force on adhesive bonds in the contact zone, flow channel studies have a number of intrinsic disadvantages. The contact area and the duration of contact between the two surfaces are not easily resolved experimentally and vary in a complex way with the magnitude of shear forces on the cells and the formation and breakage of bonds in the contact zone. These difficulties have forced investigators to make approximations and assumptions about the magnitude and distribution of bond forces in the contact zone to extract estimates of coefficients of bond breakage in the contact zone (Chang et al., 2000; Greenberg et al., 2000; Bhatia et al., 2003). In the present study we overcome many of these difficulties by using a micropipette technique that has been applied to study adhesion and two-dimensional bonding kinetics (Spillmann et al., 2002; Lomakina and Waugh, 2004). It provides a direct measure of the adhesion probability while controlling the force, duration, and area of contact between the two interacting surfaces (Chesla et al., 1998; Levin et al., 2001; Spillmann et al., 2002). Using this approach, we have examined the effect of impingement force on bond formation between neutrophils and immobilized ICAM-1. In a companion report we present a mechanical analysis of the increase in contact area with force, and we predict that the contact stress (force per unit area of contact) depends not on the force, but on the curvature of the contacting surfaces. In the present study we find that the rate of bond formation at a given contact stress increases in direct proportion to the contact area, but that increasing contact stress by increasing the curvature of the contacting bead causes an increase in the intrinsic rate of bond formation.
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METHODS |
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Bead preparation
Two types of beads were used in this study. Most experiments were performed with tosyl-activated, paramagnetic Dynabeads (Dynal, Lake Success, NY). The manufacturer supplies these beads in two nominal sizes: 2.8 µm and 4.5 µm. The beads were coated with soluble recombinant forms of two members of the IgG superfamily: either ICAM-1 (R&D Systems, Minneapolis, MN) or neural cell adhesion molecule (NCAM, Chemicon International, Temecula, CA). The molecules were randomly and covalently linked via active tosyl groups to the bead surface. Beads (107) were washed twice in 1.0 ml of 0.1 M phosphate buffer (pH = 7.4) then incubated in 1.0 ml of phosphate buffer plus 1.2 µg of ICAM-1 or 5 µg of NCAM (4.5-µm beads), or 2 µg of ICAM-1 (2.8-µm beads) at room temperature overnight. Unreacted tosyl groups were blocked by a 30-min incubation with 8 mM ethanolamine and then washed twice with 1% bovine serum albumin (BSA, Calbiochem-Novabiochem, La Jolla, CA) in phosphate-buffered saline (PBS, BioWhittaker, Walkersville, MD) and stored in 0.1% BSA in PBS at 4°C.
For some experiments carboxylated beads (Polysciences, Warrington, PA) were used to obtain a wider range of diameters (3.0 µm and 10.0 µm). The beads were first coated with protein-G and then with soluble recombinant forms of human ICAM-1/Fc chimera (R&D Systems) and human NCAM-L1/Fc chimera (R&D Systems). First, protein-G was covalently linked to carboxylated bead surface. Beads were washed twice in 0.1 M carbonate buffer and allowed to mix in 2% carbodiimide solution for 3–4 h. Then beads were washed in 0.02 M phosphate buffer and incubated in 1 ml of 0.2 M borate buffer plus 320 µg of protein-G overnight at room temperature. After unreacted sites were blocked by a 30-min incubation with 4 mM ethanolamine, the beads were resuspended in 1% BSA and incubated for 30 min at room temperature to block any remaining nonspecific protein binding sites.
After beads were coated with protein-G, recombinant forms of ICAM-1/Fc chimera and NCAM-1/Fc chimera were covalently linked to the surface of the beads. For that, 20 µl of the protein-G-coated beads were sonicated for 5 min in 1 ml of BlockAid solution (Molecular Probes, Eugene, OR) to reduce nonspecific binding. Then either 5 µg of ICAM-1/Fc chimera (3-µm beads) or the mixture of 4.5 µg of ICAM-1/Fc and 0.5 µg of NCAM-L1/FC chimeras (10-µm beads) were added to the bead suspension and incubated for 40 min at room temperature on a rotating platform. The beads were washed twice in 0.2 M triethanolamine (Sigma, St. Louis, MO), pH 8.2, and resuspended in 0.5 ml of 0.2 M triethanolamine, containing 20 mM dimethyl pimelimidate (Sigma) to cross-link the chimera to the protein-G. After a 30-min incubation at room temperature, the reaction was stopped by adding 0.5 ml of 50 mM Tris (Sigma), pH = 7.5 with rotational mixing for 15 min. The cross-linked beads were washed twice in 0.1% BSA, 0.05% Tween 20 (Fisher Scientific, Fair Lawn, NJ), and 0.1% sodium azide in PBS and stored in the same washing buffer at 4°C.
The density of ICAM-1 on the beads was measured by flow cytometry (Lomakina and Waugh, 2004). Ligand-coated beads were incubated with FITC-conjugated mouse-anti-human ICAM-1 (clone 15.2, Ancell, Bayport, MN) or an isotype-matched control antibody at 4°C overnight. The antibody 15.2 recognizes the distal domain (D1) of ICAM-1 and inhibits binding to LFA-1 (Staunton et al., 1990). Fluorescence intensity was correlated to the number of bound antibodies on the coated beads using Quantum Simply Cellular Beads (Flow Cytometry Standards, Fishers, IN) as a calibration standard. Beads coated with NCAM served as nonspecific controls for adhesion tests, and the presence of NCAM on the surface was confirmed by incubation with a primary antibody followed by FITC-labeled secondary antibody.
Adhesion tests
The micromanipulation procedure is adapted from one introduced first by Shao and Hochmuth (1996) and Shao et al. (1998) and previously used in our laboratory (Spillmann et al., 2002). A detailed description is provided in a companion report (Lomakina et al., 2004). Diluted blood was placed in a chamber on the stage of an inverted light microscope (Diaphot, Nikon, Garden City, NY). Passive spherical neutrophils were selected from diluted blood suspension on the basis of their multilobular nuclei. (To validate our selection method, cells were selected as if for mechanical measurement, then transferred with a micropipette onto a cover glass and stained. More than 85% of the selected cells were neutrophils as assessed by Wright's stain.)
After selection, neutrophils were transferred into a second chamber using a large micropipette (9–10 µm inside diameter, I.D.) and then allowed to equilibrate for at least 20 min with the suspending solution (or 40 min if an antibody was present). The chamber was open on opposite sides to accommodate opposing micropipettes and contained a dilute suspension of the ICAM-coated beads. Pipettes were filled with Hank's Balanced Salt Solution without Ca2+ or Mg2+, and positioned inside the touch chamber. Before measurement, a negative pressure was applied for 15 min to draw in protein solution and reduce unwanted neutrophil adhesion to the pipette lumen. A neutrophil was aspirated into the large pipette, and a small pipette (2 µm I.D.) was used to position a bead inside the larger pipette (Fig. 1). After the zero pressure was set, a touch sequence was initiated by creating a positive pressure to push the cell into contact with the bead. For each cell bead pair four different impingement pressures in the range of 1.0 to 6.0 pN/µm2 (0.1–0.6 mm H2O) were tested. The equilibrium pressure in the translation pipette was periodically checked, and typical deviations were <0.5 pN/µm2. (In addition, the free velocity of the cell in the pipette was measured, a posteriori, to ensure the pressure remained steady for repeated tests.) After 2 s of contact, the neutrophil was drawn away from the bead by closing a solenoid valve to apply a suction of 2.0 pN/µm2. Contacts were repeated 25 times at each of four different impingement pressures for each cell/bead pair, and three or four cells were tested on a given day of experiment. All measurements were performed at room temperature (22°C). Adhesion tests were recorded on videotape with a time stamp and the withdrawal and impingement pressure overlaid on the image. Distances were calibrated using a stage micrometer.
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Video recordings of the experiments were analyzed to determine what fraction of the contacts resulted in adhesion between the cell and the bead. An adhesive contact was signified by either a small deformation of the neutrophil surface during separation or (in some rare cases) the formation of a thin tube of membrane, a tether, upon withdrawal from the contact zone. The final probability of forming an adhesive contact between a particular neutrophil and bead was calculated as the number of adhesive contacts divided by the total number of touches. The total averaged adhesion probability for ß2-integrin/ICAM-1 binding was corrected to account for nonspecific adhesion according to Chesla et al. (1998),
 | (1) |
In addition to the adhesion probability, the contact area and the force of impingement were determined. The contact area was determined by measuring the contact length (two times the radius of the contact zone), Lcon = 2Rcon, from video recordings (Fig. 1). The macroscopic contact area is given by
 | (2) |
,
 | (3) |
pim is the impingement pressure. The constant C1 is
 | (4) |
= (Rp–Rc)/Rc is the dimensionless film thickness between the cell and the wall of the pipette. The quantities Leq and are obtained from measurements of the free velocity of the cell in the pipette as described in the companion report (Lomakina et al., 2004).
Other quantities
The adhesion probability is related to the average number of bonds formed in the contact zone, 
n
(Chesla et al., 1998),
 | (5) |
). Two groups have shown that the expected number of bonds can be written in terms of a kinetic expression of the form (Chesla et al., 1998; Lomakina and Waugh, 2004)
 | (6) |
c and b are the density of receptors (on the cell surface) and ligands (on the bead surface) in the contact area, Ka is the equilibrium association constant, kr is the reverse rate constant, and t is the interaction time between the two surfaces. Eq. 6 indicates that for a given set of conditions, the expected number of bonds should increase in direct proportion to the contact area. It is important to recognize that Ka and kr are effective kinetic constants that may be affected by a variety of extrinsic factors, such as surface topography and the distribution and mobility of adhesion receptors in the surface. (Note: in the present report we do not distinguish between the area of contact Ac in Eq. 6, and the macroscopic area of contact Amac given in Eq. 2. In fact, the actual area within the contact zone where bonds can form is some (unknown) fraction of the macroscopic contact area because of the irregularity of the cell surface. In our treatment, we lump the ratio of the true contact area to the macroscopic contact area Ac/Amac into the effective equilibrium coefficient Ka.) The dependence of the expected bond number on contact stress is a particular focus of the present study. To evaluate this, the contact stress can be calculated through the relationship
 | (7) |
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RESULTS |
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290 sites/µm2, and the contact duration was 2.0 s. Significant variability in adhesion probability was observed among different cells, but for each cell the adhesion probability increased with increasing force. Three examples are shown in Fig. 2 A. To avoid biasing the data from a possible history-dependence of cell adhesion, the order of application of the impingement pressures was 1.5, 6.0, 3.0, then 4.5 pN/µm2. In Fig. 2 B, the data are grouped according to the impingement pressure, and the horizontal error bars represent the standard deviation of the calculated force at that pressure for the 12 cells. The nearly linear relationship between the mean adhesion probability and the mean force is an accurate reflection of the fact that this is the behavior typically observed for individual cells. The large standard deviation reflects the variability from one cell to another. The range of control values is shown in expanded scale in Fig. 2 C. Introduction of the ß2-blocking antibody IB4, replacement of ICAM-1 with NCAM on the bead surface, or substitution of calcium for Mg2+/EGTA in the suspending buffer all caused similar reductions in adhesion probability. Use of a non-ß2-blocking antibody (anti-CD45, a tyrosine phosphatase found on the neutrophil surface) in the presence of Mg2+/EGTA caused a slight (not statistically significant) increase in cell adhesion.
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n according to Eq. 5. This quantity n is shown in Fig. 3 A as a function of the contact area for all 12 neutrophil-bead pairs. For individual pairs, the expected increase in bond formation with impingement force was consistently observed, but there was considerable variability in the slope of this dependence from cell to cell. A linear regression to the data for each cell is included as a guide for grouping data from individual cells. In Fig. 3 B the data are grouped according to impingement pressure, and the error bars represent the standard deviation of the measured contact area and the calculated bond number for the 12 cell-bead pairs. A weighted (1/variance) linear regression to the data is shown as the solid line, and the dashed line corresponds to a weighted regression to the three highest pressure points, fixed at the origin. Despite the variability from cell to cell, averaged values for the population show a remarkably linear relationship between the expected bond number, n, and contact area (Fig. 3 B).
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To test for contact stress effects, a series of experiments was performed with different-sized beads. Four different bead preparations were tested, two with ICAM-1 bound by tosyl activation (2.8- and 4.5-µm diameter) and two with ICAM-1 chimera bound via protein-G (3.0- and 10-µm diameter); see Methods. As measured by flow cytometry, the number of ICAM-1 binding sites on these beads was found to be 140 sites/µm2 for 2.8-µm beads, 290 sites/µm2for 4.5-µm beads, 640 sites/µm2 for 3.0-µm beads, and 800 sites/µm2 for 10-µm beads. We then compared the intensive bond formation rate, that is, n normalized for contact area and surface density of ICAM-1. The results are shown in Fig. 4. For each case 7–12 cell bead pairs were tested. The impingement force was adjusted such that the mean contact areas were similar for each of the different groups (6.0 µm2). The contact stress was calculated based on a mean value of the cortical tension of 20 pN/µm. For both types of beads tested, a significant increase in the intrinsic rate of bond formation was observed with increasing contact stress. For the protein-G-conjugated beads, a doubling of the contact stress resulted in a twofold increase in bond formation, and for the tosyl-activated beads, a 30% increase in stress resulted in a 35% increase in bond formation.
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DISCUSSION |
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) and the microtopography of the surface itself (Williams et al., 2001). The present findings demonstrate important effects of mechanical force on the specific case of integrin bond formation between neutrophils and immobilized ICAM-1. In the first place, force affects adhesion by the simple, direct mechanism of increasing the contact area between the cell and substrate, causing an increase in adhesion probability that is in direct proportion to the contact area. This is analogous to increasing the reaction volume for a conventional chemical reaction. Naively, one might expect that increasing force would also increase the compressive stress between the surfaces in the contact zone. Yet in our companion report, we demonstrate that the mechanical characterization of the cell as a liquid drop leads to the prediction that the contact stress should not depend on force, but should depend on the curvature of the contacting surfaces. Thus, the linear increase in bond formation rate with contact area is completely consistent with both kinetic expectations (Eq. 6) and the mechanical analysis predicting that any higher order effects due to changing contact stress should not be observed. On the other hand, when the contact stress is increased (by increasing the curvature of the contacting surface), an increase in the intensive rate of bond formation is observed. This is consistent with the expectation that compression of the microvilli on the cell surface should enhance cell adhesion.
It seems likely that the increase in adhesion with increasing contact stress is due to a mechanically induced change in the microtopography of the cell surface. Williams et al. (2001) demonstrated that cell membrane topography can have a substantial influence on the effective association rate between a receptor and ligand. For different cell surfaces (one smooth, one covered with microvilli) they report a 50-fold difference in the binding affinity for the same molecular pair (Williams et al., 2001). Shao et al. (1998) have estimated the compliance of microvilli subjected to pulling forces and estimate a spring constant of 40 pN/µm. For contact stresses of 26–36 pN/µm2, and assuming 5 microvilli/µm2 (Shao et al., 1998), the force supported by each microvillus is 5.0–7.0 pN. If the spring constant in extension is the same as that in compression, this would lead to a decrease in the microvillus length of 125–175 nm, a substantial fraction of the total microvillus length (100–300 nm). These calculations indicate that the effect on surface topography of the contact stresses applied in our study could be substantial.
A direct implication of these findings is that the surface topography of the bead surface could also have a substantial influence on adhesion rates. We have anecdotal evidence that this is indeed the case. Our original experimental design included three different-sized protein-G coupled beads, but the 6.0-µm diameter beads behaved very differently from the 3.0- and 10.0-µm beads. They showed uncharacteristically high levels of ICAM-1 uptake during the coating process, and even when the coating conditions were adjusted to obtain similar surface concentrations of ICAM-1, the intrinsic bond formation rates were substantially higher than expected for these beads. Examination of the bead surfaces by scanning electron microscopy revealed that the 6.0-µm beads had highly irregular surfaces with many protrusions and hole-like structures. In contrast, both the 3.0-µm and the 10.0-µm beads had smooth surfaces with only minor irregularities.
In addition to changing the percentage of membrane area in contact with the substrate within the contact zone, it is also possible that deformation of the cell surface could alter the number and type of molecules in contact with the bead. Several studies have indicated that adhesion molecules are nonuniformly distributed over the neutrophil surface (Erlandsen et al., 1993). If integrins are sequestered away from the tips of microvilli, as ultrastructural evidence indicates, then increasing the proportion of membrane in contact with the bead could result in a disproportionate increase in the concentration of integrin molecules capable of reacting with the ICAM-1 on the bead surface. This possibility is difficult to evaluate given existing information. Ultrastructural studies examining the distribution of adhesion molecules on leukocyte surfaces have used labels against Mac-1 (Erlandsen et al., 1993) or CD-18 (Fernandez-Segura et al., 1996) and have not examined the distribution of LFA-1 specifically. This is critical for our adhesion studies conducted in the presence of Mg2+ because under these conditions it is most likely that LFA-1 is the primary form mediating the adhesion to ICAM-1. That LFA-1 is the active form is supported by experiments conducted previously in our laboratory using blocking antibodies (Lomakina and Waugh, 2004) and is consistent with early reports that there is a significant increase in LFA-1 binding to ICAM-1 in Mg2+ (Dransfield et al., 1992), but that Mac-1 affinity is only slightly increased (Diamond and Springer, 1993). Thus, conclusions about whether the type and concentration of integrins in the contact zone may change with increasing contact stress must await further study.
Individually, and in aggregate, the bond formation rate of neutrophils appears to increase linearly with contact area, and the intrinsic rate of bond formation increases with contact stress. However, the adhesive potential can differ significantly from cell to cell. The reason for this heterogeneity is not apparent. One possibility is that it reflects differences in cell age or in the experience of the cells before removal from the circulation. For all cells tested, there were no visible signs of cell activation; that is, we observed no changes in morphology such as cell ruffling or the formation of pseudopodia. In a previous study, we used flow cytometry to show that magnesium and calcium solutions do not affect the expression of ß2-integrin or selectin molecules on the neutrophil surface, a further indication that, under the conditions of our study, cells remain in an essentially passive state (Spillmann et al., 2002).
Our present findings suggest that increasing impingement forces at the leading edge of the cell may be an important mechanism involved in the transition from rolling to firm, integrin-mediated attachments. This idea is supported by approximate calculations showing that the magnitudes of the contact stresses in our study are comparable to those that a cell is likely to experience in vivo. Similar calculations have been performed by others, but with a focus on the magnitude of peeling forces at the trailing edge of the cell (Alon et al., 1995; Dong et al., 1999). We summarize an approach here to estimate the impingement stress in the contact zone. Fluid forces acting on the cell and tangential force resultants on bonds at the interface create a torque on the cell that must be balanced by a force-couple created by peeling forces at the trailing edge of the cell and impingement stress in the contact region (Fig. 5). We assume that the contact area is circular, with a radius between 2.0 and 4.0 µm (Firrell and Lipowsky, 1989). We apply a hydrodynamic solution (Goldman et al., 1967) to calculate the torque and force on a sphere in contact with a plane wall under shear flow. Dong et al. (1999) has calculated that peeling forces are concentrated in a region that is <8% of the total contact area. Therefore we treat the peeling force as a point load applied at the trailing edge of the cell, and apply a moment balance at the center of the contact zone. For wall shear stresses of 0.1–1.0 pN/µm2 (1.0–10 dyn/cm2) the reaction (peeling) force at the trailing edge of an adherent leukocyte is estimated to be in the range of 100–1500 pN. This vertical component of the peeling stress must be balanced by the reaction (impingement) stress in the remainder of the contact zone. This translates into a contact stress on the order of 5–50 pN/µm2, depending on what assumptions are made about the size of the contact area over which the stress is distributed. This encompasses the range of contact stresses imposed in the present study where there are clear effects of changing contact stress on adhesion probability.
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CONCLUSIONS |
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ACKNOWLEDGEMENTS |
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This work was supported by the US Public Health Service under National Institutes of Health grant PO1 HL 18208.
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FOOTNOTES |
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Submitted on July 20, 2003; accepted for publication September 1, 2004.
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REFERENCES |
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). Addition of an IgG control antibody caused a statistically insignificant increase in the adhesion probability (
). Nonspecific adhesion probability under control conditions (see C) is indicated by the solid line with 95% confidence intervals shown by the dotted lines. (C) Several conditions were used to determine the level of nonspecific binding and demonstrate specificity of ß2-integrin binding to the ICAM-1 beads. The conditions were 5.0 mM Mg2+ plus 10 µg/mL of the ß2-blocking antibody IB4 (
), 5.0 mM Mg2+ with NCAM-coated beads (
), 1.5 mM Ca2+ (•), and 1.5 mM Ca2+ plus 10 µg/mL IB4 (
). Data is reported as the mean ± SD and grouped by the impingement pressure. The lines indicate a variance-weighted linear regression to the mean values, and dashed lines show the 95% confidence interval of the fit. Note the different vertical scale in C.
between the cell and the substrate. The cell radius is Rs and the radius of the contact zone is Rc. The drag and torque on the cell were estimated from the results of Goldman et al. (1967)