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4ß1/VCAM-1 Interaction



* Department of Physiology and Biophysics, University of Miami School of Medicine, Miami, Florida, USA;
Wellcome Trust Centre for Cell-Matrix Research, School of Biological Sciences, University of Manchester, Manchester, United Kingdom; and
Celltech Group, Slough, United Kingdom
Correspondence: Address reprint requests to Vincent T. Moy, Dept. of Physiology and Biophysics, University of Miami School of Medicine, 1600 N.W. 10th Ave., Miami, FL 33136. Tel.: 305-243-3201; Fax: 305-243-5931; E-mail: vmoy{at}newssun.med.miami.edu.
| ABSTRACT |
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4ß1 and vascular cell adhesion molecule-1 (VCAM-1) plays a crucial role in both the rolling and firm attachment of leukocytes onto the vascular endothelium. Essential to the
4ß1/VCAM-1 interaction is its mechanical strength that allows the complex to resist the large shear forces imposed by the bloodstream. Herein we employed single-molecule dynamic force spectroscopy to investigate the dynamic strength of the
4ß1/VCAM-1 complex. Our force measurements revealed that the dissociation of the
4ß1/VCAM-1 complex involves overcoming at least two activation potential barriers: a steep inner barrier and a more elevated outer barrier. The inner barrier grants the complex the tensile strength to withstand large pulling forces (>50 pN) and was attributed to the ionic interaction between the chelated Mg2+ ion at the N-terminal A-domain of the ß1 subunit of
4ß1 and the carboxyl group of Asp-40 of VCAM-1 through the use of site-directed mutations. In general, additional mutations within the C-D loop of domain 1 of VCAM-1 suppressed both inner and outer barriers of the
4ß1/VCAM-1 complex, while a mutation at Asp-143 of domain 2 of VCAM-1 resulted in the suppression of the outer barrier, but not the inner barrier. In contrast, the outer barrier of
4ß1/VCAM-1 complex was stabilized by integrin activation. Together, these findings provide a molecular explanation for the functionally relevant kinetic properties of the
4ß1/VCAM-1 interaction. | INTRODUCTION |
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4ß1 (very late antigen-4, VLA-4) and its endothelial ligand vascular cell adhesion molecule-1 (VCAM-1) is essential for the extravasation of many leukocyte subtypes (Kubes, 2002
Integrin
4ß1 is formed by the noncovalent association of the integrin
4 (molecular mass
155 kDa) and ß1 (molecular mass
150 kDa) subunits (Hemler et al., 1987
).
4ß1 is expressed on most leukocytes, including lymphocytes, mast cells, eosinophils, natural killer cells, and monocytes.
4ß1 has two known ligands, VCAM-1 and the extracellular matrix protein, fibronectin. VCAM-1 is expressed on endothelial cells in two alternately spliced forms, a major form consisting of seven Ig-like domains (VCAM-1(7D)) and a minor form, lacking domain 4 (Osborn et al., 1994
). VCAM-1(7D) has two homologous binding sites for
4ß1. One site has been localized to domains 1 and 2 and the second to domains 4 and 5. The binding of
4ß1 to VCAM-1 involves contributions from the N-terminal domains of both
4 and ß1 subunits of
4ß1. The ß1 A-domain contains a metal ion-dependent adhesion site (MIDAS) that has been implicated in VCAM-1 binding (Vonderheide et al., 1994
). In addition, repeats 24 of the N-terminal seven-bladed ß-propeller domain of
4 have also been shown to be important for VCAM-1 binding. The most crucial interaction in the stabilization of the
4ß1/VCAM-1 complex appears to be the electrostatic interaction between Asp-40 of domain 1 (D1) of VCAM-1 and the chelated Mg2+ ion of the ß1 A-domain. Besides Asp-40, other residues that are part of the C-D loop (i.e., T37QIDSPLN) of D1 of VCAM-1 have been shown to be important in
4ß1 binding (Vonderheide et al., 1994
). In addition, recent studies suggested that domain 2 of VCAM-1 is also involved in stabilizing the
4ß1/VCAM-1 complex (Newham et al., 1997
).
The main purpose of this research is to understand the molecular basis by which the
4ß1/VCAM-1 interaction is able to resist a pulling force. Such studies provide important insight into how activated leukocytes are able to remain adherent to the endothelium in the presence of the shear force of the bloodstream. Although the equilibrium binding affinity constant of the
4ß1/VCAM-1 complex has been measured by competitive binding assays (Chigaev et al., 2003
), these measurements cannot be used to extrapolate the unbinding force of the complex (Moy et al., 1994
). To access the mechanical properties of the
4ß1/VCAM-1 complex, we have employed the atomic force microscope (AFM) (Binnig et al., 1986
; Hörber and Miles, 2003
; Radmacher et al., 1992
) to measure the loading rate dependence of complex unbinding (i.e., its dynamic force spectrum (DFS)) (Merkel et al., 1999
) and to characterize the dissociation potential of the complex. Subsequent mutagenesis experiments permitted us to correlate molecular determinants in VCAM-1 to features in the dissociation potential of the complex.
| METHODS |
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4ß1-Fc was generated and purified according to Stephens et al. (2000)
Force apparatus
All single-molecule force measurements were conducted using a home-built AFM that employs a single axis piezoelectric translator equipped with a strain gauge (Physik Instrumente, Waldbronn, Germany) to control the absolute position of the AFM cantilever (Chen and Moy, 2002
). The deflection of the cantilever was monitored optically by using an inverted optical system attached to the AFM. A focused laser spot from a fiber-coupled diode laser (Oz Optics, Nepean, ON, Canada) was reflected off the back of the cantilever onto a two-segment photodiode to monitor the cantilever's deflection. The photodiode signal was preamplified, digitized, and processed by an Apple Power Macintosh computer. The sample holder of the apparatus was designed to accept a standard 35-mm tissue culture dish. The force apparatus was suspended within a refrigerator housing to reduce both mechanical and thermal instabilities.
Attachment of live cells to the AFM cantilever
The human monocytic cell line U937 (ATCC, Manassas, VA) was maintained in RPMI 1640 medium supplemented with 10% fetal bovine serum, 1% glutamine, 50 U/mL penicillin, and 50 µg/mL streptomycin in 5% CO2 at 37°C until needed. Individual U937 cells were attached to the AFM cantilever via concanavalin A (Con A)-mediated linkages (Benoit, 2002
; Zhang et al., 2002
). To prepare the Con A-functionalized cantilever, the cantilevers were soaked in acetone for 5 min, ultraviolet-irradiated for 30 min, and incubated in biotinamidocaproyl-labeled bovine serum albumin (BSA) (biotin-BSA, 0.5 mg/mL in 100 mM NaHCO3, pH 8.6) overnight at 37°C. The cantilevers were then rinsed three times with PBS (10 mM
150 mM NaCl, pH 7.3) and incubated in streptavidin (0.5 mg/mL in phosphate-buffered saline (PBS)) for 10 min at room temperature. After the removal of unbound streptavidin, the cantilevers were incubated in biotinylated Con A (0.5 mg/mL in PBS) and then rinsed with PBS. To attach the cell to the cantilever, the tip of the Con A-functionalized cantilever was positioned above the center of a cell and lowered onto the cell for
1 s. AFM measurements using the U937 functionalized cantilever were carried out in complete culture medium supplemented with 10 mM HEPES.
AFM measurements
The AFM force measurements were performed at room temperature (25°C) in force spectroscopy mode. The AFM force measurements consisted of an approach trace that recorded the force acting on the cantilever while the cantilever was lowered onto the sample, and a retraction trace that recorded the tip/sample interaction while the cantilever was pulled away from the sample. Measurements of unitary unbinding forces were obtained under conditions that minimized contact between the functionalized cantilever and the sample. An adhesion frequency of <30% in the force measurements ensured a >83% probability that the adhesion event was mediated by a single bond (Evans et al., 2001
; Tees et al., 2001
). The concentrations of proteins used in the preparation of the cantilever and substrate were adjusted to achieve adhesion frequencies of 2030%. Measurements were acquired for loading rates between 100 pN/s and 100,000 pN/s. The change of loading rates was achieved by varying the retraction speed of the cantilever from 0.03 to 30 µm/s. Cantilevers were calibrated by equating their thermal vibrational energy to that of a one-dimensional oscillator (Hutter and Bechhoefer, 1993
). The spring constants (
10 mN/m) of the calibrated cantilevers agreed with the values specified by the manufacturer.
The unbinding forces of individual adhesive interactions were derived from the jump in force after the separation of the cantilever from the sample. We acquired 50150 unbinding forces for each histogram. For measurements obtained at fast retraction rates (>1 µm/s), the measured unbinding force was corrected for hydrodynamic drag acting on the cantilever. The determination of hydrodynamic forces was based on a method used by Tees et al. (2001)
. We allowed the cantilever to undergo free movement at different speeds, and the hydrodynamic force for each speed was measured. The damping coefficient of the cantilever in the experimental solution was
2 pN-s/µm.
Dynamic force spectroscopy
Our analysis of the unbinding of the
4ß1/VCAM-1 complex employed the Bell-Evans model (Bell, 1978
; Evans and Ritchie, 1997
), which has been applied to studies of other ligand-receptor systems (Chen and Springer, 2001
; Evans et al., 2001
; Merkel et al., 1999
). In the context of this model, a pulling force f distorts the energy landscape of the ligand-receptor complex, resulting in a lowering of the activation barrier(s), and consequently increases the dissociation rate constant k(f) as follows:
![]() | (1) |
is the width of the potential barrier projected along the direction of the applied force, T is absolute temperature, and kB is Boltzmann's constant. Under conditions of a constant loading rate rf (rf = df/dt), the probability density function for the unbinding of a complex at force f is given by (Evans and Ritchie, 1997
![]() | (2) |
P(f)/
f = 0) is
![]() | (3) |
were obtained from the plot of f* versus ln(rf). | RESULTS |
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4ß1/VCAM-1 complex
4ß1/VCAM-1 interaction. Fig. 1 A illustrates our experimental system, which consisted of an AFM cantilever decorated with recombinant
4ß1-Fc and purified VCAM-1(2D)Fc immobilized on a tissue culture dish.
4ß1-Fc is a soluble form of human
4ß1, produced as a Fc chimera after fusion of the cDNAs encoding the ectodomains of each subunit to genomic DNA encoding the Fc of human
1 IgG (Stephens et al., 2000
4ß1-Fc and native
4ß1 bind VCAM-1 with an apparent Kd of 0.20.3 nM (Stephens et al., 2000
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4ß1-Fc/VCAM-1(2D)Fc interactions, contact between the cantilever tip and substrate was minimized by using a small contact duration (<50 ms) and a small compression force (
100 pN). Fig. 1 B plots a series of eight AFM recordings of the interaction between AFM tip and substrate. Adhesion between the apposing surfaces on contact gave rise to a hysteresis between the approach (shaded) and retraction (black) traces of the measurement, as found in the second, sixth, and eighth traces of Fig. 1 B. The unbinding force
of the
4ß1-Fc/VCAM-1(2D)Fc complex is derived from the force jump that accompanies the unbinding of the complex. Sample force histograms of unbinding force obtained with different loading rates are presented in Fig. 1 C. These histograms show that the unbinding force increases with the loading rate of the measurements. The DFS of the
4ß1-Fc/VCAM-1(2D)Fc interaction was obtained by plotting the mode unbinding force as a function of loading rate as shown in Fig. 2 A. The specificity of the
4ß1-Fc/VCAM-1(2D)Fc interactions was confirmed by a reduction in the frequency of adhesion after the addition of a function-blocking antibody against VCAM-1 (e.g., AF809) or free VCAM-1(2D)Fc molecules (Fig. 2 B). To test whether the adsorbed VCAM-1(2D)Fc was pulled off the substrate rather than separating from the
4ß1-Fc of the AFM tip during our measurements, we covalently coupled VCAM-1(2D)Fc to a glass coverslip (Moy et al., 1999
4ß1-Fc/VCAM-1(2D)Fc complex.
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4ß1-Fc/VCAM-1(2D)Fc force spectra can be divided into two regimes within the range of loading rates accessible by our instrument. Beginning at 150 pN/s, the unbinding force increased exponentially with loading rate up to
20,000 pN/s. Beyond this point, a faster exponential increase is clearly evident. A theoretical framework for understanding how a pulling force affects the dissociation rate of adhesion complex was proposed by Bell (1978)
is the position of the transition state of the complex. Recently, Evans showed that molecular dissociation of a complex that involves overcoming more than one activation barrier may result in a DFS that reveals several exponential domains distinguishable by differences in slopes (Evans and Ritchie, 1997
4ß1-Fc/VCAM-1(2D)Fc interaction is consistent with an intermolecular potential that includes two activation energy barriers. The barriers are characterized by two force-loading regimes in the DFS: slow (15020,000 pN/s) and fast (20,000100,000 pN/s) (Fig. 2 A). Fitting Eq. 3 (see Methods) to the slow and fast regimes gives the Bell model parameters (i.e., k0 and
) for outer and inner barriers, respectively (see Table 1). Based on this analysis, the estimated widths of the inner and outer barriers are
1 and 5.9 Å, respectively.
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5ß1/fibronectin and
Lß2/ICAM-1 complexes (Li et al., 2003
4ß1/VCAM-1 interaction involves a Mg2+ ion that is chelated by the MIDAS site of the ß A-domain and interacts with the Asp-40 residue in domain 1 of VCAM-1 (Wang and Springer, 1998
4ß1/VCAM-1 interaction is largely due to the strong ionic interaction between the chelated Mg2+ and the negatively charged Asp-40 residue. Indeed, the presence of 5 mM EDTA eliminated the inner activation barriers of the
4ß1/VCAM-1 complex (Fig. 3), as previously observed in the
Lß2/ICAM-1 interaction. However, this EDTA effect could be due to a direct or indirect contribution of the divalent cation to the formation of the inner activation barrier since it is conceivable that the ß A-domain is not folded properly in the absence of Mg2+. To further investigate the nature of divalent cation action, we investigated the interaction between
4ß1 and two VCAM-1 mutants that have a single amino acid substitution at the Asp-40 residue. Mutating the Asp-40 residue of VCAM-1 to the neutral residue, alanine (D40A), suppressed the unbinding forces of the
4ß1/VCAM-1 interaction, most noticeably in the high loading regime of the DFS (Fig. 3). However, when Asp-40 is substituted by the negatively charged residue glutamate (D40E), the fast loading regime is still distinguishable from the slow loading regime, indicating that the inner activation barrier is suppressed, but not eliminated.
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4ß1/VCAM-1 (mutants) complexes. Both EDTA treatment and the D40A mutation completely eliminated the inner activation barrier, whereas the D40E mutation widened the inner barrier from 1 Å to 2.7 Å. As discussed below, the consequence of this widening of the inner barrier is that the dissociation rate of the complex becomes more responsive to changes in pulling force in the high force regime. The effects of EDTA treatment and both D40 mutations on the outer activation barrier were similar, resulting in a suppression of the outer barrier as indicated by the 10-fold increase in the dissociation rate for the outer barrier. Taken together, these data demonstrate that the inner barrier of the
4ß1-Fc/VCAM-1(2D)Fc complex requires both the divalent cation Mg2+ and the Asp-40 residue of VCAM-1. The absence of this ionic interaction also destabilized the outer activation barrier.
In addition to Asp-40, we also explored the role of other residues in the C-D loop of the first domain of VCAM-1, including Gln-38 and Leu-43. Fig. 4 A shows that the two C-D loop mutants Q38G and L43K yielded similar DFS. Compared with the wild-type VCAM-1, these mutants have smaller unbinding forces in both the slow and fast loading regimes. The Bell model parameters of these two mutants reveal that the reduced unbinding forces are largely due to a widening in the inner barrier and a suppression in the height of the outer barrier (i.e., larger
). Differences in the dynamic strength of our C-D loop mutants (i.e., D40A, D40E, Q38G, and L43K) appears to be due to a difference in the width of the inner barrier (i.e.,
1).
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4ß1 (Newham et al., 1997
4ß1 binding, though it is not known how these mutations modified
4ß1 binding. It has been proposed that the interaction between D2 of VCAM-1 and
4ß1 is analogous to the interaction between
5ß1 and the synergy site in FNIII9 of fibronectin. We have previously shown that the synergy site of FNIII9 helps stabilize the outer activation barrier of the
5ß1/fibronectin interaction (Li et al., 2003
4ß1 interacting with one of the D2 mutants (i.e., D143A) and found that the mutation suppressed the unbinding force in the slow loading regime, but had no effect on forces in the fast loading regime (Fig. 4 B). A comparison of the Bell model parameters obtained using wild-type VCAM-1 and its D143A mutant reveals that the only difference between the wild-type and mutant interactions is a reduction in the height of the outer activation barrier of mutant complex. These results suggest that D2 of VCAM-1 helps stabilize the activation energy of the outer barrier of the
4ß1/VCAM-1 complex.
Dynamic strength of the native
4ß1/VCAM-1 complex in live cells
An important attribute of integrins is their ability to modulate the adhesive states of cells (Diamond and Springer, 1994
; Dustin and Springer, 1989
; Humphries et al., 2003
; Shimaoka et al., 2002
). In resting leukocytes,
4ß1 is expressed in an inactive, nonadhesive state that binds VCAM-1 with low affinity. Upon activation, the leukocyte expresses an activated form of
4ß1 and becomes adherent to the endothelium. The induction of high-affinity
4ß1 is presumably due to the unclasping and separation of the integrin
and ß cytoplasmic tails, leading to changes in the conformation and/or orientation of the N-terminal domains of both the
and ß subunits (Carman and Springer, 2003
).
To determine if the VCAM-1 binding properties of our recombinant
4ß1-Fc resembles that of native
4ß1, we measured the DFS of
4ß1/VCAM-1(2D) interaction on live U937 cells (Fig. 5 A). U937 is a monocytic cell line that has been used in previous studies of
4ß1 mediated adhesion (Chigaev et al., 2003
). The expression of
4ß1 on U937 cells was confirmed by flow cytometry (data not shown). The high-affinity form of
4ß1 was induced by activation antibody TS2/16, bypassing the requirements of inside-out signal from the cells (Alon et al., 1995
; Chen et al., 1999
; Li et al., 2003
). As shown in Fig. 5 B, the DFS of native
4ß1/VCAM-1 complexes also displayed two loading regimes, similar to the results obtained with recombinant
4ß1-Fc. After activation by TS2/16, the unbinding forces of the native
4ß1/VCAM-1(2D) complex were elevated over the range of loading rates between 100 and 20,000 pN/s, but did not significantly change at loading rates >20,000 pN/s. Fig. 5 B also reveals that the DFS of
4ß1-Fc/VCAM-1(2D)Fc interaction is nearly identical to that of the high-affinity native
4ß1/VCAM-1(2D)Fc interaction. Moreover, the presence of the TS2/16 antibody did not change the DFS of the
4ß1-Fc/VCAM-1(2D)Fc interaction. Hence, we conclude that
4ß1-Fc is locked in a conformational state that resembles the high-affinity conformer of native
4ß1.
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4ß1/VCAM-1(2D) interaction. The dissociation rates of the outer barrier for low- and high-affinity
4ß1/VCAM-1 complexes were 1.4/s and 0.035/s, respectively, reflecting a difference in the energy of the outer barrier. However, no significant difference (P > 0.05) was found in dissociation rates (
100/s) for the inner barrier of both affinity states. Thus, DFS of the native
4ß1/VCAM-1 interaction shows that induction of high-affinity
4ß1 by TS2/16 elevates the energy potential of their outer activation barriers, but has minimal effect on the inner barriers. It should be noted that activation of other integrins including
Lß2 and
5ß1 also manifested in an elevation of the outer activation barrier. Together, these observations suggest that integrin activation, in general, involves changes in height of the outer activation barrier and hence the Kd of the complex.
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| DISCUSSION |
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values from Table 1, we were able to estimate the energy landscape of the
4ß1/VCAM-1 complex. As summarized in Fig. 6 A, the dissociation of the
4ß1/VCAM-1 bond involves overcoming two activation barriers: a steep inner barrier and a more elevated outer barrier. The position of the transition states was estimated by the Bell model parameter
. Estimates of the energy difference between the transition states were calculated as
where
and
are the dissociation rate constants of transition states 1 and 2, respectively. The energy level of the bound complex was arbitrarily chosen. Mutation at the Asp-40 residue of VCAM-1, i.e., D40A, eliminated the inner barrier and lowered the outer barrier by 2.3 kBT. The C-D loop mutant L43K lowered the outer barrier by 3 kBT and widened the inner barrier. However, D143A, a mutation in the D2 of VCAM-1, did not alter the inner barrier, but lowered the outer barrier by 2.3 kBT.
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![]() | (4) |
4ß1/VCAM-1 (mutant) complexes computed using Eq. 4 and the derived Bell model parameters are shown in Fig. 6, B and C. Under pulling forces <
50 pN, the dissociation rate is highly sensitive to pulling forces and is governed principally by the properties of the outer barrier (i.e.,
2 and
). At stronger forces, the dissociation rate is governed by the inner barrier and is less responsive to changes in pulling force. In the absence of the inner barrier, as seen when the Asp-40 residue is mutated to Ala, the dissociation rate of the complex continues to increase exponentially with pulling force. When Asp-40 is mutated to Glu (D40E), the inner barrier remains, though suppressed. As a result, the D40E mutant is expected to show some force resistance above 50 pN. In contrast, mutations that suppress just the outer barrier, as in the D143A mutant, have a greater effect on the dissociation rate of the complex at pulling forces <50 pN.
It is worthwhile to compare the dynamic response of the
4ß1/VCAM-1 complex with other leukocyte adhesion complexes involved in the extravasation and to relate the intrinsic biophysical properties of the adhesion complexes to their function at the cellular level. The process of leukocyte extravasation involves multiple stages: rolling, cell activation, firm adhesion, and, finally, transmigration. Each stage engages a different set of adhesion molecules (Springer, 1994
). Leukocyte rolling is mediated mainly by the selectin family molecules, whereas firm adhesion is mediated by the activated integrins and their adhesive ligands (Kubes, 2002
). Specifically, the L-selectin/ligand and
Lß2/ICAM-1 interactions are known to mediate leukocyte rolling and firm adhesion, respectively (Lawrence and Springer, 1991
), while the
4ß1/VCAM-1 interaction could mediate both leukocyte rolling and firm adhesion (Alon et al., 1995
; Kubes, 2002
). Recently, the mechanical properties of the L-selectin/sLeX complex and the
Lß2/ICAM-1 complex were characterized by single-molecule DFS (Evans et al., 2001
; Zhang et al., 2002
), thus allowing for a comparison of the key molecular components of leukocyte extravasation. An examination of kinetic profiles of the three complexes revealed that the force-dependent dissociation rate of the L-selectin/sLeX complex is faster and more sensitive to a pulling force than the
Lß2/ICAM-1 complex (Fig. 7), suggesting that the L-selectin/sLeX interaction is better suited for cell rolling because, in this capacity the adhesion complex should be transient and need to dissociate readily during cell rolling (Orsello et al., 2001
). Not surprisingly, the more force-resistant
Lß2/ICAM-1 complex is better suited for facilitating firm adhesion. The kinetic profile of the
4ß1/VCAM-1 complex provides a likely explanation of how this complex is able to mediate both cell rolling and firm adhesion. As revealed in Fig. 7, the dissociation kinetics of
4ß1/VCAM-1 bond resembles more the kinetic profile of the L-selectin/sLeX complex at pulling force >
50pN. However, at weak pulling forces, the off rate of the
4ß1/VCAM-1 bond is comparable to that of the
Lß2/ICAM-1 complex. Previous flow-chamber experiments revealed that the shear force exerted on a single selectin bond ranged between 50 and 250 pN (Chen and Springer, 2001
; Smith et al., 1999
). In this force region, the mechanical properties of the
4ß1/VCAM-1 bond resemble the selectin bond and are suitable for rolling. However, when the leukocyte is activated and more integrin complexes are formed, the pulling force shared by individual
4ß1/VCAM-1 complex may be <50 pN. Within this force range, the off rate of the
4ß1/VCAM-1 complex is similar to the
Lß2/ICAM-1 bond and thus capable of facilitating firm adhesion.
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4ß1/VCAM-1 complexes reveal that the dissociation of this complex involves overcoming at least two activation barriers. As a result of the steep inner barrier, the complex is less sensitive to large pulling forces. Using the VCAM-1 mutants, we found that the Asp-40 residue directly forms the inner activation barrier by interacting with the chelated Mg2+ ion, and that the C-D loop participates in the generation of the outer barrier and helps maintain the inner barrier. The kinetic profile of the
4ß1/VCAM-1 complex shows similarity to the L-selectin/sLeX complex in strong pulling forces, but its off rates resemble the
Lß2/ICAM-1 complex in lower pulling forces. This special kinetic profile may reflect a biophysical basis that permits a dual physiological function (i.e., cell rolling and firm adhesion) of the
4ß1/VCAM-1 interaction. | ACKNOWLEDGEMENTS |
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| FOOTNOTES |
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Submitted on May 10, 2004; accepted for publication August 24, 2004.
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