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Force Required to Break α5β1Integrin-Fibronectin Bonds in Intact Adherent Cells Is Sensitive to Integrin Activation State*

Binding of integrin receptors to extracellular ligands is a complex process involving receptor-ligand interactions at the cell-substrate interface, signals activating the receptors, and assembly of cytoskeletal and adhesion plaque proteins at the cytoplasmic face. To analyze the contribution of these elements to overall cell adhesion, we have developed a model system that characterizes the functional binding characteristic for adhesion receptors as the force required to separate the integrin-ligand bond. A spinning disk device was used to apply a range of controlled hydrodynamic forces to adherent cells. The adhesion of K562 erythroleukemia cells, a cell line expressing a single fibronectin receptor, integrin α5β1, which was uniformly activated with the monoclonal antibody TS2/16, to defined fibronectin surface densities was examined. Cell adhesion strength increased linearly with receptor and ligand densities. Based on chemical equilibrium principles, it is shown that adhesion strength is directly proportional to the number of receptor-ligand bonds. This analysis provides for the definition of a new physical parameter, the adhesion constant ψ, which is related to the bond strength and binding equilibrium constant and has units of force-length2. This parameter can be measured by the experimental system presented and is governed by the activation state of integrin receptors. This simplified model isolates the integrin receptor-ligand binding parameters and provides a basis for analysis of the functions of signaling and cytoskeletal elements in the adhesion process.

Specific receptor-mediated adhesion to surface ligands is a fundamental property of most cell types. This adhesion is essential to the formation of multicellular organisms and is tightly regulated during development (1). Many pathological conditions, such as blood clotting defects and tumor invasion and metastasis, involve abnormal adhesion processes (2). Understanding of cell adhesion is also critical to biotechnological applications and to the development of devices for medical implantation (3)(4)(5)(6). Early experiments focused on cell adhesion as a structural element required for the organization of cells in multicellular organisms, but recent breakthroughs have shown that adhesion is directly involved in the transmission of signals essential for cell proliferation and differentiation (7)(8)(9).
The integrin family of heterodimeric receptors provides the dominant adhesion mechanism for most cells which adhere to extracellular matrix components, including fibronectin (Fn) 1 and laminin (10,11). Many of these receptors have been cloned and sequenced, and their ligands have been identified (11). Biochemical and functional assays have indicated that integrin-mediated adhesion is regulated through several mechanisms, including matrix deposition (12,13), protease activity (14), expression of multiple integrins (10), modulation of receptor-ligand binding affinity (15), and cytoskeletal reorganization (16,17). For example, most adherent cells grown in culture use ␣ 5 ␤ 1 integrin as the dominant receptor binding to Fn synthesized by the cells or exogenously supplied. ␣ 5 ␤ 1 integrin binds to the RGD region in the 10th type III repeat and to the synergy site in the 9th type III repeat of Fn (18). This receptor is generally expressed in an inactive or low binding form on cells that are in suspension or that have been recently trypsinized (15). Receptor interaction with Fn results in an energy-dependent binding that may involve a conformational change in the integrin (15). This binding also causes rapid association of the receptor-ligand complex with the actin cytoskeleton (17). Receptor clustering is followed by the association of a complex of cytoplasmic proteins that include structural proteins, such as vinculin and talin, and signaling molecules like ras, FAK, and MAPK (19,20). Although these changes in conformation and clustering contribute to the overall adhesion, a mechanistic understanding of the specific contributions of these factors to receptor-mediated cell adhesion is still incomplete.
The adhesive properties of adhesion receptors can be defined in terms of the force required to break the bonds between the receptor and its extracellular ligand. This is implicit in all adhesion assays. The most common assay consists of seeding cells onto substrates, washing "non-adherent" cells off, and counting the remaining cells. Although these wash assays have contributed to our understanding of cell adhesion, they are limited in their ability to provide well defined, sensitive physical measurements. Given the complexity of the adhesion process, analysis of the biomechanical and biochemical interactions involved requires the development of both a new experimental system for measurement and a new approach to the analysis of these adhesion interactions.
Quantitative adhesion assays have been developed to apply controlled detachment forces through centrifugation (21), hydrodynamic fluid flow (22)(23)(24)(25)(26)(27)(28)(29)(30), or micromanipulation (31)(32)(33). Although these methods have provided measurements of adhesion strength, the functional dependence of adhesion strength on receptor-ligand parameters remains unknown. Here we present an experimental framework for the analysis of receptor-ligand interactions involved in cell adhesion. Using a device that applies a well-defined range of hydrodynamic forces to adherent cells expressing a single Fn receptor, ␣ 5 ␤ 1 integrin, we obtained specific force measurements of adhesion mediated by ␣ 5 ␤ 1 integrin-Fn bonds. Furthermore, we demonstrate that cell adhesion strength increases linearly with the number of receptor-ligand complexes and is described by a simple receptor-ligand model. The receptor-ligand interaction is characterized by a novel experimental parameter, which represents the fundamental adhesion properties of the specific receptor-ligand pair under controlled experimental conditions and is governed by the activation state of the integrin receptor.

EXPERIMENTAL PROCEDURES
Cells and Reagents-K562 cells (ATCC number CCL-243) were obtained from A. Gerwitz (University of Pennsylvania) and grown in Dulbecco's modified Eagle's medium supplemented with 10% calf serum and penicillin-streptomycin. TS2/16 and HFN7.1 hybridomas were obtained from ATCC (Rockville, MD). AIIB2 and BIIG2 hybridomas were a gift from C. Damsky. mAbs were affinity purified from supernatants on protein G-Sepharose columns. Human plasma Fn and cell culture reagents were purchased from Life Technologies Inc. Ethidium homodimer was obtained from Molecular Probes (Eugene, OR). Glass coverslips were purchased from Bellco (Vineland, NJ). Sulfo-BSOCOES cross-linker was purchased from Pierce. All other reagents were obtained from Sigma.
Quantitative Adhesion Assay-Cell adhesion to adsorbed Fn was measured using a spinning disk device (30). This apparatus consists of a disk spinning in large fluid volume ( Fig. 1) and applies a linear range of forces to adherent cells. K562 cells were washed and resuspended in DPBS ϩ 2 mM glucose. Cells (400 cells/mm 2 ) were uniformly seeded onto Fn-coated glass coverslips (25 mm diameter) mounted on the device and allowed to attach for 15 min in the presence or absence of mAbs. The chamber of the device was filled with buffer, and disks were spun for 10 min at constant speed with controlled acceleration rates. Adherent cells were fixed in 3.7% formaldehyde, permeabilized with 1% Triton X-100, and stained with ethidium homodimer. Disks were analyzed by counting the number of nuclei per microscope field (0.5 mm 2 ) using a motorized stage and image analysis software (Phase 3 Imaging, Version 3.0, Glen Mills, PA). Sixty-one fields were analyzed per disk and normalized to the nuclei count at the disk center for which the applied force is zero. Using a non-linear computer algorithm, the fraction of adherent cells (f) was fitted to a sigmoidal curve (f ϭ 1.0/(1.0 ϩ exp [b ( Ϫ 50 )]) where is the surface shear stress, b is the inflection slope, and 50 is the inflection point.
For integrin cross-linking experiments, cells were seeded onto Fncoated coverslips for 10 min, incubated in 1 mM sulfo-BSOCOES for 5 min, and then spun and analyzed as before.
Receptor Binding to Soluble Fn-Measurements of receptor binding to soluble Fn were performed (15). Briefly, K562 cells were washed and resuspended in DPBS ϩ 2 mM glucose ϩ 1 mg/ml BSA. Binding experiments were conducted in 200-l volumes, consisting of 100 l of cell suspension (1.3 ϫ 10 6 cells), 50 l of 125 I-Fn, and 50 l of TS2/16 mAb, buffer, or inhibitor (EDTA ϩ NaN 3 ). After incubating for 30 min at 22°C under gentle agitation, 50-l aliquots were layered in triplicate onto 300 l of 20% sucrose. Bound Fn was separated from unbound by centrifugation at 12,000 ϫ g for 3 min and quantified. For nonspecific binding, cells were incubated in 5 mM EDTA ϩ 0.01% NaN 3 . Binding data was analyzed for absolute number of receptors per cell and equilibrium binding constant using a non-linear computer algorithm for monovalent receptor-ligand binding.
Overexpression of ␣ 5 ␤ 1 Integrin-K562 cells were transfected with pRSVneo ␣ 5 (34) by electroporation at 300 V/500 microfarad (Gene-Pulser II, Bio-Rad, Hercules, CA). Colonies were selected for G418 antibiotic resistance and analyzed by flow cytometry using the anti-␣ 5 rat mAb BIIG2 or anti-␤ 1 rat mAb AIIB2. Briefly, cells were resuspended in DPBS ϩ 0.1% BSA ϩ 0.01% NaN 3 . Cells were incubated in primary mAb, washed, incubated in fluorescein isothiocyanate-conjugated anti-rat IgG, and analyzed in a FACScan (Becton Dickinson, San Jose, CA). Receptor values for the transfected cells were converted to absolute numbers by combining cytometry data with soluble Fn binding measurements for untransfected cells.

Analytic Approach to Measure the Force Required to Detach
Cells-The objective of this analysis was to develop an experimental framework to reduce the number of variables associated with adhesion measurements and provide measurements of the force required to disrupt specific receptor-ligand interactions. We used a spinning disk device to apply a range of hydrodynamic forces to adherent cells (30). For this configuration, the applied force varies linearly along the surface of the disk allowing the application of a wide range of forces in a single experiment under uniform chemical conditions. The flow patterns in this device were validated using an electrochemical method over the full range of speeds used in the adhesion experiments. As shown in Equation 1, the applied shear stress (force/area) at any point on the surface of the disk varies linearly with radial position and is given, where r is radial position from the disk center, and are fluid density and viscosity, respectively, and is angular speed.
Cells were seeded on a coverslip mounted on the device and spun at a constant speed. Fluid flow over the cells on the disk produces a detachment force that is proportional to the hydrodynamic shear force in Equation 1. Cells at the center experience negligible force, and cell numbers decrease toward the outside of the disk as the applied force increases. Thus, for a single disk, a linear range of forces is applied to a large cell population producing a cell detachment profile that allows the calculation of a mean detachment force. We define this mean detachment force as the adhesion strength.
The applied hydrodynamic force is dependent on cell shape; for spherical cells, exact solutions have been derived (35,36). K562 cells were chosen because they remain spherical even when plated on Fn-coated surfaces. From a biochemical perspective, this cell line is an ideal model because it allows the examination of a single receptor-ligand interaction. These cells express a single Fn receptor, integrin ␣ 5 ␤ 1 , and no other ␣ chains that associate with ␤ 1 (37). The ␣ 5 ␤ 1 receptor on K562 cells is expressed in a low binding state based on its reduced ability to bind Fn in solution and weak cell adhesion to Fn. To increase Fn binding, ␣ 5 ␤ 1 integrin was activated by addition of mAb TS2/16 (38). TS2/16 was added at saturating levels to provide for uniform activation of all ␣ 5 ␤ 1 .
Cell densities for individual fields exhibited a Poisson distribution prior to spinning, and it is expected that the ability of individual cells to withstand a specific detachment force will be a normally distributed property over the population. The combination of these distributions predicts a sigmoidal adhesion curve with a mean adhesion strength given by the shear stress for 50% detachment ( 50 ). As expected, the fraction of adherent cells (f) decreased non-linearly with shear stress (), and the data was fitted to a sigmoidal curve (Fig. 2). The sigmoidal model accurately described the experimental data (mean R 2 ϭ 0.90 Ϯ 0.10). Since all scored fields were used to calculate 50 , this value represents the measurement of the effect of the force field on Ͼ12,000 cells. The values determined by this assay have been reproducible within 10% over a 10-month period.
The Detachment Model Is Specific for the ␣ 5 ␤ 1 Integrin-Fn Bond-Experiments at different rotational speeds for the same Fn concentration demonstrated that the observed sigmoidal decrease in cell numbers was a function of applied force. By varying the rotational speed, the detachment profile shifted along the disk surface; however, the shear stress for 50% detachment remained the same for all speeds (data not shown). Experiments using different cell seeding densities revealed that, for the cell densities examined (200 -800 cells/mm 2 ), the detachment profile and attachment strength were independent of cell density (data not shown).
Experiments were conducted for different seeding times to determine whether TS2/16-activated K562 cells exhibit adhesion strengthening upon receptor binding. There were no differences in adhesion strength between 5 and 15 min or at 15 min in the presence of NaN 3 to inhibit energy-dependent processes (data not shown), demonstrating no evident strengthening response at these initial times and validating this cell model for analyzing the initial integrin receptor-Fn interaction.
The mechanism of detachment was examined using the membrane-impermeable, homobifunctional NHS-ester sulfo-BSOCOES to cross-link integrins bound to Fn. Cross-linking bound integrins in TS2/16-activated cells resulted in Ͼ2-fold increase in adhesion strength compared with uncross-linked controls, shown as a right shift in the detachment profile (Fig.  3). Cross-linking cells without activated receptors yielded background levels of adhesion (data not shown), indicating that the adhesive force is specifically provided by the bound receptors. The significant increase in adhesion strength as a result of cross-linking bound receptors demonstrates that detachment occurs at the integrin-Fn junction, and the assay, therefore, measures the strength of this interaction.
Disruption of the actin cytoskeleton with cytochalasin D (CD, 1 M) altered the failure mechanism by compromising cellular integrity. CD treatment of cells cross-linked to the substrate reduced adhesion to the same levels as uncross-linked cells (Fig. 3), suggesting that failure occurs somewhere other than at the integrin-Fn junction. Moreover, CD-treated cells ruptured and left behind considerable cellular debris after detachment; this was not observed in untreated cells. These findings suggest that treatment with CD is not appropriate for examining the role of actin cytoskeleton in cell adhesion because it is not specific to the actin-adhesion complex interaction and introduces a mechanical artifact.
To examine the relationship between adhesion strength and ligand density, disks coated with different levels of Fn were analyzed. Fig. 4 shows a family of detachment profiles for different Fn densities. As expected, increasing the Fn coating concentration generates a family of sigmoids that shift to the right with increasing concentration, indicating a direct relationship between ligand density and adhesion strength. To further analyze the specificity of the interaction, the mAbs HFN7.1 that interacts with the cell binding domain of Fn (39) and BIIG2 which reacts with the ␣ 5 chain and inhibits its binding to Fn (40) were examined. In the presence of TS2/16, each of these mAbs reduced K562 adhesion to levels similar to those in the absence of TS2/16 or surface Fn (Fig. 5). The low level of adhesion in the presence of these inhibitory mAbs or in the absence of TS2/16 represents nonspecific adhesion due primarily to electrostatic interactions.
Receptor-Ligand Adhesion Model-Our analysis is based on the theoretical work of Bell (41) as later refined by Hammer and Lauffenburger (36). The adhesion model considers a spherical cell with a single class of receptors attaching to a surface through uniformly distributed receptor-ligand complexes. The force per unit area or shear stress for detachment, d , is given by the following.
This equation consists of five elements: (i) a geometric parameter (G) related to the total force exerted by the bonds in the contact area to resist the hydrodynamic force applied to the cell. (ii) The adhesion constant is a novel experimental parameter specific to the receptor-ligand interaction. is related to the bond strength and receptor-ligand affinity and has units of force-length 2 . This parameter is analogous to the equilibrium binding constant used for describing receptor-ligand interactions in solution. (iii) N R represents the receptor density.
(iv) N L is adsorbed ligand density. (v) represents the nonspecific adhesion between the cell and the surface, arising largely from electrostatic interactions. This model predicts that adhesion strength is determined directly by the number of receptorligand complexes in the contact area and that the constant is a measure of bond strength. For this model, is independent of geometry and ligand and receptor densities but is dependent on integrin activation state. If valid, this experimental approach could be used to provide a direct measurement of the activation state of integrin receptors. The ability to perform this analysis on whole cells ensures proper presentation of the receptors on the surface and provides a system that is amenable to genetic manipulation and Dependence on Ligand Density N L -125 I-Fn was adsorbed to glass surfaces at different coating concentrations, and adsorbed ligand was quantified (Fig. 6). Fn surface density is relatively linear up to about 10 g/ml coating concentration, after which it saturates. These values are in general agreement with previous measurements (42)(43)(44). The saturation density represents the approximate amount of Fn required for a monolayer coating based on estimates of the dimensions of the Fn molecule (45).
Combining measurements for adsorbed Fn density with adhesion profiles for different ligand densities, mean adhesion strength ( 50 ) was plotted as a function of Fn surface density (N L ) (Fig. 7). Mean adhesion strength increased linearly with Fn surface density in the presence of activating mAb TS2/16. In the absence of TS2/16, adhesion strength was independent of Fn surface density and was indistinguishable from nonspecific binding measured in EDTA ϩ NaN 3 . This linear relationship is consistent with the model and the difference in the two conditions results from differences in bond strength and affinity for the integrin-Fn bond arising from binding of activating mAb. Differences in slope demonstrate differences in the activation state of integrin ␣ 5 ␤ 1 that are reflected by differences in since all other parameters are held constant.
Dependence on Receptor Density N R -The absolute number of receptors per cell was determined from binding curves of 125 I-Fn to K562 cells in suspension in presence of TS2/16 (Fig.  8). This analysis revealed 1.0 Ϯ 0.08 ϫ 10 5 receptors per cell and K D equal to 98 Ϯ 16 nM (R 2 ϭ 0.94). In the absence of activating mAb, binding of soluble Fn was indistinguishable from cells treated with EDTA ϩ NaN 3 (nonspecific binding). Thus, as for cell detachment, solution binding of Fn to the untreated ␣ 5 ␤ 1 receptor expressed on K562 cells was below the detection limits of this method. The receptor number and binding constant values obtained for these cells are in good agreement with previous measurements (15,46).
To vary receptor density, K562 cells were transfected with the pRSVneo ␣ 5 vector and screened for increased levels of surface expressed ␣ 5 ␤ 1 . The adhesion strength for stable transfectants expressing ␣ 5 ␤ 1 integrin at 1.9, 2.3, and 5.6 times the levels on parental cells was measured for a fixed Fn surface density (110 ng/cm 2 ). Adhesion strength increased linearly with receptor density (Fig. 9), as predicted by the model. The linear increases in adhesion strength with both ligand and receptor densities suggest that adhesion strength is a function of the number of bonds formed in the contact area. For a monovalent receptor-ligand interaction, the number of bonds formed per unit area (N B ) is as follows, where K is an equilibrium affinity constant and N R and N L are the receptor and ligand densities. Fig. 10 shows that cell adhesion strength increased linearly with the product of receptor  and ligand densities as predicted by Equation 2. Therefore, adhesion strength varies linearly with the number of receptorligand complexes.

DISCUSSION
In this research, we have integrated engineering and cell biology principles in order to analyze cell adhesion. From the engineering perspective, we have applied the concept that, under well-defined mechanical conditions, the force required to detach a cell could be used to evaluate the strength of the receptor-ligand bond. This principle was implemented using a spinning disk device to apply a range of forces to adherent cells in order to determine the mean adhesion strength. From the cell biology perspective, it was necessary to isolate the parameters so that adhesion due to a specific receptor-ligand pair would dominate the analysis. The majority of the published adhesion data does not provide ligand or receptor dependence relationships that can be interpreted in terms of a single receptor-ligand pair, suggesting that additional factors related to the physical configuration of the assay (e.g. a poorly defined mechanical environment) and/or parameters related to cell handling or expression of multiple elements contribute to the adhesion. The K562 cell system represents a cell with a single Fn receptor, ␣ 5 ␤ 1 integrin, which is expressed in an inactive state but which can be activated by specific mAbs (15). The ability to use this passive activation system provides cell surface receptors that are uniformly activated. Adhesion strength increased linearly with both ligand and receptor densities over the full range of adsorbed Fn densities, consistent with a theoretical model based on a monovalent receptor-ligand interaction. Blocking experiments with mAbs directed against both ligand and receptor demonstrated that the assay measured the ␣ 5 ␤ 1 integrin-Fn interaction. Furthermore, adhesion strength increased linearly with the product of receptor and ligand den-sities, indicating that adhesion strength is directly proportional to the number of ␣ 5 ␤ 1 -Fn bonds, as predicted by chemical equilibrium principles. This result is in agreement with Palecek et al. who observed increases in adhesion strength with the product of receptor-ligand densities (47).
A critical assumption of the adhesion model is uniformly stressed bonds within the contact area (36). In reality, the applied force results in bond loading that is position-dependent with maximum stressing at the upstream edge of the contact area and decreasing toward the downstream edge. Several complex models incorporating nonuniform bond loading predict a non-linear dependence of adhesion strength on the product of receptor-ligand densities (48 -50). Our experimental findings do not support these predictions. A simple explanation for this difference is that the portion of the contact area in which the bonds are maximally stressed constitutes an effective contact area for this experimental system. Once the bonds in this effective contact area are broken, the remaining bonds are insufficient to restrain the cell from detaching. At this point, we have no independent means of determining the proportion of the theoretical contact area that contributes to the effective contact area.
Validation of the proposed conceptual framework for cell adhesion through parametric analysis of the effects of ligand and receptor densities on adhesion strength demonstrates that the strength of the specific receptor-ligand interaction can be described by a new parameter, the adhesion constant . In the Hammer-Lauffenburger model, the geometric parameter G is equal to 0.03(a/R) 3 , where R is the cell radius and a is the radius of the contact area. In the present analysis, for a contact radius of 1 m, for TS2/16-activated ␣ 5 ␤ 1 integrin has a value of 2.8 ϫ 10 Ϫ18 dyne-cm 2 (2.8 ϫ 10 Ϫ27 N-m 2 ). This experimental parameter is the fundamental descriptor for the specific receptor-ligand interaction and is independent of receptor and ligand densities. The adhesion constant is analogous to the chemical dissociation constant K D except that in the later case the dissociation is measured under conditions of free diffusion and in the former under mechanical loading. While it is likely that there is some relationship between these parameters, the exact relationship is not yet clear. One report suggests a logarithmic relationship based on the analysis of the binding of protein A to Fc regions of IgG from different species (50). This analysis is limited to a single interaction type and may not, for example, apply when comparing IgGs and integrins.
These data address a fundamental property of integrin adhesion receptors, the relationship between receptor-ligand bonds and adhesion strength. Following the initial encounter of a cell expressing integrin receptors with a substrate containing an appropriate ligand, there is an activation of the receptor which is thought to involve cell signaling and a change in the conformation of the receptor resulting in initial binding (15,51). Over time, there is the accumulation of structural proteins, including vinculin, talin and ␣-actinin, and signaling molecules, including FAK, src, paxillin, to the sites of adhesion (19,20,52). Actin stress fibers connect, and the complex assembles into an adhesion plaque. This is thought to involve a redistribution of integrin receptors to concentrate at these sites (53). It has been proposed that this assembly contributes to the total adhesion strength (54). Since these complexes are fully within the cytoplasmic domain, they can do so only indirectly through the transmembrane receptors either by increasing their affinity for ligand or inducing some form of cooperative binding through receptor aggregation. In the former case, changes in receptor binding would be reflected in increases in or the slope of the cell strength-Fn density plot. In the latter case, cooperative binding would change the shape of the binding plot from linear or first order to higher order. In fact, mathematical models considering receptor clustering and adhesion plaque development predict this non-linear behavior (55,56). In the model system used here, addition of TS2/16 provides a uniform passive activation of ␣ 5 ␤ 1 integrin resulting in a change in the slope of the cell strength-Fn density plot due to a switch to a new value for the receptor-ligand interaction itself. The absence of cooperative binding effects in this simple model is expected since K562 cells do not assemble focal contacts and do not spread. It is possible that cooperative binding will be observed in more complex systems; however, the simple model is necessary to establish a baseline from which deviations can be measured.
The experimental analysis presented provides a direct means for measuring the adhesion constant characteristic for the interaction of a specific receptor conformation with a ligand of specific conformation. This is important because integrin receptors can exist in different conformations (10) that represent different activation states and different ligand binding properties (57). This approach provides a direct method of accessing these interactions in intact cells under conditions of adhesion. In other experiments (42, 44, 58 -60), it has been shown that the conformation of adsorbed Fn is dependent on the physicochemical characteristics of the surface. These differences in Fn conformation lead to differences in the strength of the Fn-integrin bond (58). The analytic approach presented here provides the basis for analysis of biochemical factors and signaling events that contribute to the receptor-mediated adhesion of cells.