The reaction-limited kinetics of membrane-to-surface adhesion and detachment

A probabilistic model for ligand-cytoskeleton transmembrane adhesion: predicting the behavior of microspheres on the surface of migrating cells

A theoretical model describing the attachment and cytoskeletal coupling of microspheres to the dorsal surface of motile cells was developed. Integral membrane receptors beneath a ligand-coated microsphere are allowed to be either free, attached to the microsphere, bound to the rearward moving actin network, or linked to both the bead and the cytoskeleton, and to switch between these four states. The binding transitions being modeled as chemical reactions governed by rate constants taken from literature, the chance for a receptor to be in each binding state over time is obtained by solving mass-balance equations for the probability functions. The population of n such receptors beneath the microsphere is accounted for by a binomial distribution for each state. Adhesion and transmembrane coupling (resulting in microsphere transport) being defined by a minimal number of ligand-receptor and receptor-cytoskeleton bonds, respectively, the probabilities of attachment and transport of the microsphere over time are expressed in terms of state probability distributions. It is found that increasing the ligand density raises the attachment and transport probabilities, in good quantitative agreement with recent experiments using optical tweezers and accurate position tracking. Increasing the bead size does not affect attachment, but raises the transport probability with a marked transition for bead diameter around 100 nm, as for experimental data. Increasing the restraining force decreases the transport probability, probably by inducing a rupture of receptor-cytoskeleton bonds. This study thus provides a framework that helps understand the process of cortical flow associated with cell locomotion.

Structural basis of collagen recognition by integrin alpha2beta1

We have determined the crystal structure of a complex between the I domain of integrin alpha2beta1 and a triple helical collagen peptide containing a critical GFOGER motif. Three loops on the upper surface of the I domain that coordinate a metal ion also engage the collagen, with a collagen glutamate completing the coordination sphere of the metal. Comparison with the unliganded I domain reveals a change in metal coordination linked to a reorganization of the upper surface that together create a complementary surface for binding collagen. Conformational changes propagate from the upper surface to the opposite pole of the domain, suggesting both a basis for affinity regulation and a pathway for signal transduction. The structural features observed here may represent a general mechanism for integrin-ligand recognition.

Rupture of multiple parallel molecular bonds under dynamic loading

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root, or logarithmic.

Time and force dependence of the rupture of glycoprotein IIb-IIIa-fibrinogen bonds between latex spheres

We studied the shear-induced breakup of doublets of aldehyde/sulfate (A/S) latex spheres covalently linked with purified platelet GPIIb-IIIa receptor, and cross-linked by fibrinogen. Flow cytometry with fluorescein isothiocyanate-fibrinogen showed than an average of 22,500 molecules of active GPIIb-IIIa were captured per sphere, with a mean K(d) = 56 nM for fibrinogen binding. The spheres, suspended in buffered 19% Ficoll 400 containing 120 or 240 pM fibrinogen, were subjected to Couette flow in a counter-rotating cone-plate rheoscope. Doublets, formed by two-body collisions at low shear rate (G = 8 s(-1)) for < or =15 min, were subjected to shear stress from 0.6 to 2.9 Nm(-2), their rotations recorded until they broke up or were lost to view. Although breakup was time dependent, occurring mostly in the first 2 rotations after the onset of shear, the percentage of doublets broken up after 10 rotations were almost independent of normal hydrodynamic force, F(n): at 240 pN, 15.6, 16.0, and 17.0% broke up in the force range 70-150 pN, 150-230 pN, and 230-310 pN. Unexpectedly, at both [fibrinogen], the initial rate of breakup was highest in the lowest force range, and computer simulation using a stochastic model of breakup was unable to simulate the time course of breakup. When pre-sheared at low G for >15 min, no doublets broke up within 10 rotations at 70 < F(n) < 310 pN; it required >3 min shear (>1110 rotations) at F(n) = 210 pN for significant breakup to occur. Other published work has shown that binding of fibrinogen to GPIIb-IIIa immobilized on plane surfaces exhibits an initial fast reversible process with relative low affinity succeeded by transformation of GPIIb-IIIa to a stable high-affinity complex. We postulate that most doublet breakups observed within 10 rotations were from a population of young doublets having low numbers of bonds, by dissociation of the initial receptor complex relatively unresponsive to force. The remaining, older doublets with GPIIb-IIIa in the high-affinity complex were not broken up in the time or range of forces studied.

Force probe measurements of antibody-antigen interactions

The surface force apparatus has been used to quantify directly the forces that govern the interactions between proteins and ligands. In this work, we describe the measured interactions between the antigen fluorescein and the Fab' fragment of the monoclonal 4-4-20 anti-fluorescyl IgG antibody. Here we first describe the use of the surface force apparatus to demonstrate directly the impact of the charge composition in the region of the antibody binding site on the antibody interactions. Several approaches are described for immobilizing antigens, antibodies, and proteins in general for direct force measurements. The measured force profiles presented are accompanied by an extensive discussion of protocols used to analyze the force-distance curves and to interpret them in terms of the antibody structure. In addition to long-range electrostatic forces, we also consider short-range forces that can affect the strength of adhesion between the Fab' and immobilized fluorescein. The latter investigations demonstrate the influence of interfacial properties on the recognition of surface-bound antigens.

Mapping the collagen-binding site in the I domain of the glycoprotein Ia/IIa (integrin alpha(2)beta(1))

The I domain present within the alpha2 chain of the integrin alpha(2)beta(1) (GPIa/IIa) contains the principal collagen-binding site. Based on the crystal structure of the alpha2-I domain, a hypothetical model was proposed in which collagen binds to a groove on the upper surface of the I domain (Emsley, J., King, S. L., Bergelson, J. M., and Liddington, R. C. (1997) J. Biol. Chem. 272, 28512-28517). We have introduced point mutations into 13 residues on the upper surface of the domain. Recombinant mutant proteins were assayed for binding to monoclonal antibodies 6F1 and 12F1, to collagen under static conditions, and for the ability to retain adhesive activity under flow conditions. The mutations to residues surrounding the metal ion-dependent adhesion site that caused the greatest loss of collagen binding under both static and flow conditions are N154S in the betaA-alpha1 turn, N190D in the betaB-betaC turn, D219R in the alpha3-alpha4 turn, and E256V and H258V in the betaD-alpha5 turn. Mutation in one of the residues that coordinate the metal binding, S155A, completely lost the adhesive activity under flow but bound normally under static conditions, whereas the mutation Y285F had the converse effect. We conclude that the upper surface of the domain, including the metal ion-dependent adhesion site motif, defines the collagen recognition site.

Kinetics and mechanics of cell adhesion

Cell adhesion is mediated by specific interaction between receptors and ligands. Such interaction provides not only physical linkage but also communication between the cell and its environment. The kinetics and mechanics of cell adhesion are coupled, because force can influence the formation and dissociation of receptor-ligand bonds. The kinetic rates and their force dependence determine how likely, how rapidly and how strongly cells bind as well as how long they remain bound. Since adhesion molecules are linked to apposing cellular membranes, their interaction is governed by two-dimensional (2D) kinetics. This is in contrast to the three-dimensional (3D) binding of soluble ligands to cell surface receptors. Unlike the 3D case in which many methods are available for measuring kinetic rates, not until recently have the 2D kinetic rates become experimentally measurable. In this review, I will discuss the recent progress in the experimental methods that enable quantification of the relevant kinetic and mechanical parameters, the fundamental concepts that underlie the physics of the biological phenomena, and the mathematical models that relate functions to the intrinsic properties of the adhesion molecules.

Biomechanics of cell rolling: shear flow, cell-surface adhesion, and cell deformability

The mechanics of leukocyte (white blood cell; WBC) deformation and adhesion to endothelial cells (EC) has been investigated using a novel in vitro side-view flow assay. HL-60 cell rolling adhesion to surface-immobilized P-selectin was used to model the WBC-EC adhesion process. Changes in flow shear stress, cell deformability, or substrate ligand strength resulted in significant changes in the characteristic adhesion binding time, cell-surface contact and cell rolling velocity. A 2-D model indicated that cell-substrate contact area under a high wall shear stress (20 dyn/cm2) could be nearly twice of that under a low stress (0.5 dyn/cm2) due to shear flow-induced cell deformation. An increase in contact area resulted in more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy that inputs to a cell decreased due to a flattened cell shape. The model also predicted a plateau of WBC rolling velocity as flow shear stresses further increased. Both experimental and computational studies have described how WBC deformation influences the WBC-EC adhesion process in shear flow.

Direct force measurements of the streptavidin-biotin interaction

The interaction between streptavidin and its ligand, biotin, were studied by direct force measurements. The complimentary approaches of surface force apparatus (SFA) and atomic force microscopy (AFM) were used to elucidate both long-range and short-range adhesive interactions of the streptavidin biotin interaction. The high spatial resolution of the SFA provided a detailed profile of the intersurface forces of apposing surfaces functionalized with streptavidin and biotin. Measurements obtained by the SFA corresponded to long and intermediate-range forces that are important in determining ligand receptor association. AFM was used to measure the unbinding force of individual streptavidin biotin complexes. These measurements revealed the short-range interactions (i.e. hydrophobic and hydrogen bonding forces) that stabilize the intermolecular bond.

Role of endothelial cell-substrate contact area and fibronectin-receptor affinity in cell adhesion to HEMA/EMA copolymers

The objective of this study was to examine the effect of substrate hydrophobicity on cell-substrate contact area and the affinity between adsorbed fibronectin (Fn) and its receptor. Homo- and copolymer films of hydrophobic ethyl methacrylate (EMA) and hydrophilic hydroxyethyl methacrylate (HEMA) were spun-cast onto glass slides. Bovine aortic endothelial cells (BAEC) were plated for 2 h in serum-free medium onto polymers preadsorbed with Fn. Cells were fixed, labeled, and examined by total internal reflection fluorescence microscopy (TIRFM) to determine the topography of the basal surface as a function of distance from the substrate. Phase contrast microscopy was used to examine the total projected area of adherent cells. The cumulative contact area was greatest on cells attached to surfaces prepared from 0% HEMA and lowest on surfaces with the highest HEMA content. An equilibrium adhesion model used these data together with the critical force for detachment and the Fn density (Burmeister et al., J Biomed Mater Res 1996;30:13-22) to determine the affinity between Fn and its receptor and the bond strength. The affinity and force per bond decreased with increasing HEMA content. These results indicate that differences in the strength of endothelial cell adhesion to polymers are influenced by the conformation of the adsorbed adhesion proteins.

Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.

Selectin-carbohydrate interactions in shear flow

Hydrodynamic shear creates mechanical stresses on selectin bonds, modulating affinity and kinetic parameters. Chemical modification of sialyl Lewis(x) increases the strength of L-selectin bonds without altering recognition, suggesting that mechanical and biorecognition characteristics are separable. L-selectin bond formation rates may be strongly influenced by sulfate orientation in sulfo sialyl Lewis(x).

A direct comparison of selectin-mediated transient, adhesive events using high temporal resolution

Leukocyte capture and rolling on the vascular endothelium is mediated principally by the selectin family of cell adhesion receptors. In a parallel plate flow chamber, neutrophil rolling on purified selectins or a selectin-ligand substrate was resolved by high speed videomicroscopy as a series of ratchet-like steps with a characteristic time constant (Kaplanski, G., C. Farnarier, O. Tissot, A. Pierres, A.-M. Benoliel, M. C. Alessi, S. Kaplanski, and P. Bongrand. 1993. Biophys. J. 64:1922-1933; Alon, R., D. A. Hammer, and T. A. Springer. 1995. Nature (Lond.). 374:539-542). Under shear, neutrophil arrests due to bond formation events were as brief as 4 ms. Pause time distributions for neutrophils tethering on P-, E-, L-selectin, or peripheral node addressin (PNAd) were compared at estimated single bond forces ranging from 37 to 250 pN. Distributions of selectin mediated pause times were fit to a first order exponential, resulting in a molecular dissociation constant (k(off)) for the respective selectin as a function of force. At estimated single bond forces of 125 pN and below, all three selectin dissociation constants fit the Bell and Hookean spring models of force-driven bond breakage equivalently. Unstressed k(off) values based on the Bell model were 2.4, 2.6, 2.8, 3.8 s(-1) for P-selectin, E-selectin, L-selectin, and PNAd, respectively. Bond separation distances (reactive compliance) were 0.39, 0.18, 1.11, 0.59 A for P-selectin, E-selectin, L-selectin, and PNAd, respectively. Dissociation constants for L-selectin and P-selectin at single bond forces above 125 pN were considerably lower than either Bell or Hookean spring model predictions, suggesting the existence of two regimes of reactive compliance. Additionally, interactions between L-selectin and its leukocyte ligand(s) were more labile in the presence of flow than the L-selectin endothelial ligand, PNAd, suggesting that L-selectin ligands may have different molecular and mechanical properties. Both types of L-selectin bonds had a higher reactive compliance than P-selectin or E-selectin bonds.

Numerical analysis of the deformation of an adherent drop under shear flow

The adhesion of leukocytes to substrates is an important biomedical problem and has drawn extensive research. In this study, employing both single and compound drop models, we investigate how hydrodynamics interacts with an adherent liquid drop in a shear flow. These liquid drop models have recently been used to describe the rheological behavior of leukocytes. Numerical simulation confirms that the drop becomes more elongated when either capillary number or initial contact angle increases. Our results show that there exists a thin region between the drop and the wall as the drop undergoes large stretching, which allows high pressure to build up and provides a lift force. In the literature, existing models regard the leukocyte as a rigid body to calculate the force and torque acting on the drop in order to characterize the binding between cell receptors and endothelial ligands. The present study indicates that such a rigid body model is inadequate and the force magnitude obtained from it is less than half of that obtained using the deformable drop models. Furthermore, because of its much higher viscosity, the cell nucleus introduces a hydrodynamic time scale orders of magnitude slower than the cytoplasm. Hence the single and compound drops experience different dynamics during stretching, but exhibit very comparable steady-state shapes. The present work offers a framework to facilitate the development of a comprehensive dynamic model for blood cells.

Adhesion energy of receptor-mediated interaction measured by elastic deformation

We investigated the role of receptor binding affinity in surface adhesion. A sensitive technique was developed to measure the surface energy of receptor-mediated adhesion. The experimental system involved a functionalized elastic agarose bead resting on a functionalized glass coverslip. Attractive intersurface forces pulled the two surfaces together, deforming the bead to produce an enlarged contact area. The Johnson-Kendall-Roberts (JKR) model was used to relate the surface energy of the interaction to the elasticity of the bead and the area of contact. The surface energies for different combinations of modified surfaces in solution were obtained from reflection interference contrast microscopy (RICM) measurements of the contact area formed by the bead and the coverslip. Studies with surfaces functionalized with ligand-receptor pairs showed that the relationship between surface energy and the association constant of the ligand binding has two regimes. At low binding affinity, surface energy increased linearly with the association constant, while surface energy increased logarithmically with the association constant in the high affinity regime.

Probabilistic modeling of shear-induced formation and breakage of doublets cross-linked by receptor-ligand bonds

A model was constructed to describe previously published experiments of shear-induced formation and breakage of doublets of red cells and of latexes cross-linked by receptor-ligand bonds (. Biophys. J. 65:1318-1334; Tees and Goldsmith. 1996. Biophys. J. 71:1102-1114;. Biophys. J. 71:1115-1122). The model, based on McQuarrie's master equations (1963. J. Phys. Chem. 38:433-436), provides unifying treatments for three distinctive time periods in the experiments of particles in a Couette flow in which a doublet undergoes 1) formation upon two-body collision between singlets; 2) evolution of bonds at low shear rate; and 3) break-up at high shear rate. Neglecting the applied force at low shear rate, the probability of forming a doublet per collision as well as the evolution of probability distribution of bonds in a preformed doublet were solved analytically and found to be in quite good agreement with measurements. At high shear rate with significant force acting to accelerate bond dissociation, the predictions for break-up of doublets were obtained numerically and compared well with data in both individual and population studies. These comparisons enabled bond kinetic parameters for three types of particles cross-linked by two receptor-ligand systems to be calculated, which agreed well with those computed from Monte Carlo simulations. This work can be extended to analyze kinetics of receptor-ligand binding in cell aggregates, such as those of neutrophils and platelets in the circulation.

An automatic braking system that stabilizes leukocyte rolling by an increase in selectin bond number with shear

Wall shear stress in postcapillary venules varies widely within and between tissues and in response to inflammation and exercise. However, the speed at which leukocytes roll in vivo has been shown to be almost constant within a wide range of wall shear stress, i.e., force on the cell. Similarly, rolling velocities on purified selectins and their ligands in vitro tend to plateau. This may be important to enable rolling leukocytes to be exposed uniformly to activating stimuli on endothelium, independent of local hemodynamic conditions. Wall shear stress increases the rate of dissociation of individual selectin-ligand tether bonds exponentially (, ) thereby destabilizing rolling. We find that this is compensated by a shear-dependent increase in the number of bonds per rolling step. We also find an increase in the number of microvillous tethers to the substrate. This explains (a) the lack of firm adhesion through selectins at low shear stress or high ligand density, and (b) the stability of rolling on selectins to wide variation in wall shear stress and ligand density, in contrast to rolling on antibodies (). Furthermore, our data successfully predict the threshold wall shear stress below which rolling does not occur. This is a special case of the more general regulation by shear of the number of bonds, in which the number of bonds falls below one.

Mechanisms that regulate the function of the selectins and their ligands

Selectins are a family of three cell adhesion molecules (L-, E-, and P-selectin) specialized in capturing leukocytes from the bloodstream to the blood vessel wall. This initial cell contact is followed by the selectin-mediated rolling of leukocytes on the endothelial cell surface. This represents the first step in a cascade of molecular interactions that lead to leukocyte extravasation, enabling the processes of lymphocyte recirculation and leukocyte migration into inflamed tissue. The central importance of the selectins in these processes has been well documented in vivo by the use of adhesion-blocking antibodies as well as by studies on selectin gene-deficient mice. This review focuses on the molecular mechanisms that regulate expression and function(s) of the selectins and their ligands. Cell-surface expression of the selectins is regulated by a variety of different mechanisms. The selectins bind to carbohydrate structures on glycoproteins, glycolipids, and proteoglycans. Glycoproteins are the most likely candidates for physiologically relevant ligands. Only a few glycoproteins are appropriately glycosylated to allow strong binding to the selectins. Recently, more knowledge about the structure and the regulated expression of some of the carbohydrates on these ligands necessary for selectin binding has been accumulated. For at least one of these ligands, the physiological function is now well established. A novel and exciting aspect is the signaling function of the selectins and their ligands. Especially in the last two years, convincing data have been published supporting the idea that selectins and glycoprotein ligands of the selectins participate in the activation of leukocyte integrins.

Two-stage activation for alpha5beta1 integrin binding to surface-adsorbed fibronectin

By analyzing the functional binding of alpha5beta1 integrin to adsorbed fibronectin in intact cells, we demonstrate that integrin activation results in linear increases in adhesion strength as a function of ligand density, suggesting that modulation of the receptor-ligand interaction is the dominant mechanism for adhesion during the initial stages of adhesion and that cooperative binding contributes little to initial adhesion strength. Using this experimental framework, we show the existence of three distinct activation states for alpha5beta1 integrin binding to adsorbed fibronectin for both passive, antibody-induced and active, cell-controlled activation. During the initial phase of adhesion, alpha5beta1 integrin is activated in an energy-dependent process from the nonbinding ground state to an intermediate state in which the receptor binds fibronectin and provides significant mechanical coupling. In later stages of adhesion maturation, alpha5beta1 integrin is activated to a higher binding state, which provides significant increases in adhesion strength compared with the intermediate state. These multiple binding states most likely result from different integrin conformations and reflect distinct interactions between alpha5beta1 and sites on adsorbed fibronectin. Multiple activation states for alpha5beta1 suggest the existence of distinct stages in adhesion signaling and strengthening and can provide a versatile mechanism for the regulation of adhesive interactions.

Kinetics of beta2-integrin and L-selectin bonding during neutrophil aggregation in shear flow

Activated neutrophils aggregate in a shear field via bonding of L-selectin to P-selectin glycoprotein ligand-1 (PSGL-1) followed by a more stable bonding of LFA-1 (CD11a/CD18) to intercellular adhesion molecule 3 (ICAM-3) and Mac-1 (CD11b/CD18) to an unknown counter receptor. Assuming that the Mac-1 counter receptor is ICAM-3-like in strength and number, rate processes were deconvoluted from neutrophil homoaggregation data for shear rates (G) of 100-3000 s-1 with a two-body hydrodynamic collision model (. Biophys. J. 73:2819-2835). For integrin-mediated aggregation (characteristic bond strength of 5 microdynes) in the absence of L-selectin contributions, an average forward rate of kf = 1.57 x 10(-12) cm2/s predicted the measured efficiencies for G = 100-800 s-1. For a selectin bond formation rate constant equal to the integrin bond formation rate constant, the colloidal stability of unactivated neutrophils was satisfied for a reverse rate of the L-selectin-PGSL bond corresponding to an average bond half-life of 10 ms at a characteristic bond strength of 1 microdyne. Colliding neutrophils initially bridged by at least one L-selectin-PSGL-1 bond were calculated to rotate from 8 to 50 times at G = 400 to 3000 s-1, respectively, before obtaining mechanical stability in sheared fluid of either 0.75 or 1.75 cP viscosity. Thus for G > 400 s-1, the interaction time needed for the rotating aggregates to become stable was relatively constant at 52.5 +/- 8.5 ms, largely independent of shear rate or shear stress. Aggregation data and the colloidal stability criterion can provide a consistent set of forward and reverse rate constants and characteristic bond strengths for a known time-dependent stoichiometry of receptors on cells interacting in a shear flow field.

The kinetics and shear threshold of transient and rolling interactions of L-selectin with its ligand on leukocytes

The kinetics of rolling and transient adhesions through selectins may depend on the kinetics and mechanical properties of the selectin:ligand bond, as well as on cellular properties including receptor-anchoring to the cell membrane and cytoskeleton. Kinetics are known to depend on the selectin and may also be ligand dependent. Here, we study the kinetics of transient and rolling interactions of leukocytes with L-selectin immobilized on a substrate. Remarkably, all properties examined are similar to those seen when the sidedness is opposite, i.e., when the L-selectin ligand is on the substrate and when the ligand is isolated from HEV rather than present on leukocytes. The similar properties include rolling velocity, a threshold shear stress above 0.4 dyn/cm2 required to support rolling, a k degreesoff of 7.0 to 6.8 s-1 for the L-selectin tether bond, and a mechanical bond length of 0.24 to 0.20 A. Our results argue against a model in which L-selectin shedding mediates rolling. Furthermore, the fast and force-resistant kinetic properties suggest that L-selectin is specialized dynamically for tethering leukocytes to vessel walls and adherent leukocytes.

Studying receptor-mediated cell adhesion at the single molecule level

Cell adhesion is essentially mediated by specific interactions between membrane receptors and ligands. It is now apparent that the mere knowledge of the on- and off-rate of association of soluble forms of these receptors and ligands is not sufficient to yield accurate prediction of cell adhesive behavior. During the last few years, a variety of complementary techniques relying on the use of hydrodynamic flow, atomic force microscopy, surface forces apparatus or soft vesicles yielded accurate information on i) the dependence of the lifetime of individual bonds on applied forces and ii) the distance dependence of the association rate of bound receptors and ligands. The purpose of this review is, first to recall the physical significance of these parameters, and second to describe newly obtained results. It is emphasized that molecular size and flexibility may be a major determinant of the efficiency of receptor mediated adhesion, and this cannot be studied by conventional methods dealing with soluble molecules.

Static and dynamic lengths of neutrophil microvilli

Containing most of the L-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) on their tips, microvilli are believed to promote the initial arrest of neutrophils on endothelium. At the rolling stage following arrest, the lifetimes of the involved molecular bonds depend on the pulling force imposed by the shear stress of blood flow. With two different methods, electron microscopy and micropipette manipulation, we have obtained two comparable neutrophil microvillus lengths, both approximately 0.3 microm in average. We have found also that, under a pulling force, a microvillus can be extended (microvillus extension) or a long thin membrane cylinder (a tether) can be formed from it (tether formation). If the force is </=34 pN (+/- 3 pN), the length of the microvillus will be extended; if the force is >61 pN (+/- 5 pN), a tether will be formed from the microvillus at a constant velocity, which depends linearly on the force. When the force is between 34 pN and 61 pN (transition zone), the degree of association between membrane and cytoskeleton in individual microvilli will dictate whether microvillus extension or tether formation occurs. When a microvillus is extended, it acts like a spring with a spring constant of approximately 43 pN/microm. In contrast to a rigid or nonextendible microvillus, both microvillus extension and tether formation can decrease the pulling force imposed on the adhesive bonds, and thus prolonging the persistence of the bonds at high physiological shear stresses.

Force required to break alpha5beta1 integrin-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 alpha5beta1, 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 psi, 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.

Modifying the mechanical property and shear threshold of L-selectin adhesion independently of equilibrium properties

Interactions between adhesion molecules on two different cells differ from interactions between receptors and soluble ligands in that the adhesion molecule interaction (bond) is often subjected to force. It is widely assumed by cell biologists that the 'strength' of a bond is a simple function of the affinity of one adhesion molecule for the other, whereas biophysicists suggest that bonds have 'mechanical properties' that affect their strength. Mechanical properties are a function of the shape of the energy landscape related to bond formation and dissociation, whereas affinity is related only to the net energy change. Mechanical properties determine the amount by which the kinetics and affinity of bonds are altered by applied force. To date there has been no experimental manipulation of an adhesion molecule that has been shown to affect mechanical properties. L-selectin is an adhesion molecule that mediates lymphocyte binding to, and rolling on, high endothelial venules; these are prerequisites for the emigration of lymphocytes from the bloodstream into lymph nodes. Here we report a selective and reversible chemical modification of a mucin-like ligand that alters the mechanical properties of its bond with L-selectin. The effect of force on the rate of bond dissociation, that is, on a mechanical property, is altered, whereas there is little or no effect of the modification on the rate of bond dissociation in the absence of force. Moreover, the puzzling requirement for hydrodynamic shear flow above a threshold level for L-selectin interactions is dramatically altered.

Determining force dependence of two-dimensional receptor-ligand binding affinity by centrifugation

Analyses of receptor-ligand interactions are important to the understanding of cellular adhesion. Traditional methods of measuring the three-dimensional (3D) dissociation constant (Kd) require at least one of the molecular species in solution and hence cannot be directly applied to the case of cell adhesion. We describe a novel method of measuring 2D binding characteristics of receptors and ligands that are attached to surfaces and whose bonds are subjected to forces. The method utilizes a common centrifugation assay to quantify adhesion. A model for the experiment has been formulated, solved exactly, and tested carefully. The model is stochastically based and couples the bond force to the binding affinity. The method was applied to examine tumor cell adherence to recombinant E-selectin. Satisfactory agreement was found between predictions and data. The estimated zero-force 2D Kd for E-selectin/carbohydrate ligand binding was approximately 5 x 10(3) microm(-2), and the bond interaction range was subangstrom. Our results also suggest that the number of bonds mediating adhesion was small (<5).

The kinetics of L-selectin tethers and the mechanics of selectin-mediated rolling

Two mechanisms have been proposed for regulating rolling velocities on selectins. These are (a) the intrinsic kinetics of bond dissociation, and (b) the reactive compliance, i.e., the susceptibility of the bond dissociation reaction to applied force. To determine which of these mechanisms explains the 7.5-11.5-fold faster rolling of leukocytes on L-selectin than on E- and P-selectins, we have compared the three selectins by examining the dissociation of transient tethers. We find that the intrinsic kinetics for tether bond dissociation are 7-10-fold more rapid for L-selectin than for E- and P-selectins, and are proportional to the rolling velocities through these selectins. The durations of pauses during rolling correspond to the duration of transient tethers on low density substrates. Moreover, applied force increases dissociation kinetics less for L-selectin than for E- and P-selectins, demonstrating that reactive compliance is not responsible for the faster rolling through L-selectin. Further measurements provide a biochemical and biophysical framework for understanding the molecular basis of rolling. Displacements of tethered cells during flow reversal, and measurements of the distance between successive pauses during rolling provide estimates of the length of a tether and the length of the adhesive contact zone, and suggest that rolling occurs with as few as two tethers per contact zone. Tether bond lifetime is an exponential function of the force on the bond, and the upper limit for the tether bond spring constant is of the same order of magnitude as the estimated elastic spring constant of the lectin-EGF unit. Shear uniquely enhances the rate of L-selectin transient tether formation, and conversion of tethers to rolling adhesions, providing further understanding of the shear threshold requirement for rolling through L-selectin.

Simulation of detachment of specifically bound particles from surfaces by shear flow

The receptor-mediated adhesion of cells to ligand-coated surfaces is important in many physiological and biotechnological processes. Previously, we measured the detachment of antibody-coated spheres from counter-antibody- and protein A-coated substrates using a radial-flow detachment assay and were able to relate mechanical adhesion strength to chemical binding affinity (Kuo and Lauffenburger, Biophys. J. 65:2191-2200 (1993)). In this paper, we use "adhesive dynamics" to simulate the detachment of antibody-coated hard spheres from a ligand-coated substrate. We modeled the antibody-ligand (either counter-antibody or protein A) bonds as adhesive springs. In the simulation as in the experiments, beads attach to the substrate under static conditions. Flow is then initiated, and detachment is measured by the significant displacement of previously bound particles. The model can simulate the effects of many parameters on cell detachment, including hydrodynamic stresses, receptor number, ligand density, reaction rates between receptor and ligand, and stiffness and reactive compliance of the adhesive springs. The simulations are compared with experimental detachment data, thus relating measured bead adhesion strength to molecular properties of the adhesion molecules. The simulations accurately recreated the logarithmic dependence of adhesion strength on affinity of receptor-ligand recognition, which was seen in experiments and predicted by analytic theory. In addition, we find the value of the reactive compliance, the parameter which relates the strain of a bond to its rate of breakage, that gives the best match between theory and experiment to be 0.01. Finally, we analyzed the effect of varying either the forward or reverse rate constants as different ways to achieve the same affinity, and showed that adhesion strength depends uniquely on the equilibrium affinity, not on the kinetics of binding. Given that attachment is independent of affinity, detachment and attachment are distinct adhesive phenomena.

Image enhancement of the in vivo leukocyte-endothelium contact zone using optical sectioning microscopy

A major determinant of the strength of leukocyte [white blood cell (WBC)] to endothelium [endothelial cell (EC)] adhesion is the contact area formed between the two cells, which is often obscured by out-of-focus information inherent to intravital microscopy. To improve visualization of the WBC-EC contact zone, techniques of optical sectioning microscopy were developed to enhance brightfield images of WBC-EC adhesion in postcapillary venules of the mesentery of the rat. A 50x/1.0 NA objective was held in a piezoelectric mount that was computer-driven, and video images were obtained by digitizing images from a CCD camera while focusing through the vertical direction in 1 micron steps over a depth of 16 microns. Using measurements of the microscope's optical transfer function, deconvolution of the central image was performed in the Fourier domain using the technique of singular value decomposition with Tikhonov-Miller regulation to remove out-of-focus information. Measurement of the length of the WBC-EC contact zone (LC) in the original images yielded values on the order of 4.32 +/- 1.08 microns (mean +/- SD). The enhanced images showed a significantly 35% smaller LC equal to 2.78 +/- 0.70 micron. Topical application of the chemoattractant f-met-leu-phe resulted in a 26% increase in LC to 3.49 +/- 0.72 micron, thus suggesting that upregulation of adhesion molecules on the WBC membrane results in the recruitment of additional membrane area from surface ruffles into the zone of adhesion. Other advantages of the deconvolution were to visualize structural characteristics of the microvascular wall and parenchymal tissue in greater detail. Thus, brightfield optical sectioning microscopy may provide a valuable tool for in vivo studies of the microvasculature, and serves as a useful alternative to fluorescence microscopy without the undesirable effects of exogenous fluorophores and exposure to ultraviolet radiation.

Rolling and transient tethering of leukocytes on antibodies reveal specializations of selectins

Antibodies immobilized on the wall of a flow chamber can support leukocyte rolling in shear flow. IgM mAb to Lewis(x) (CD15) and sialyl Lewis(x) (CD15s), which are carbohydrate antigens related to selectin ligands, plus mAb to CD48 and CD59, could mediate rolling. IgM and IgG mAb to L-selectin (CD62L), lymphocyte function-associated antigen 1 (CD11a), CD43, intercellular adhesion molecule 3 (CD50), and CD45 mediated only firm adhesion. In contrast to selectins, antibodies supported rolling only within a restricted range of site densities and wall shear stresses, outside of which firm adhesion or detachment occurred. When wall shear stress was increased, rolling velocity increased rapidly for antibodies but not for selectins. The kinetics of dissociation from the substrate of transiently tethered cells also increased more rapidly as a function of shear stress for antibodies than for selectins. These comparisons emphasize a number of remarkable features of selectins, including the lack of development of firm adhesion, and suggest that specialized molecular or cellular mechanisms must be required to explain their ability to support rolling over a wide range of environmental variables.

Dynamic strength of molecular adhesion bonds

In biology, molecular linkages at, within, and beneath cell interfaces arise mainly from weak noncovalent interactions. These bonds will fail under any level of pulling force if held for sufficient time. Thus, when tested with ultrasensitive force probes, we expect cohesive material strength and strength of adhesion at interfaces to be time- and loading rate-dependent properties. To examine what can be learned from measurements of bond strength, we have extended Kramers' theory for reaction kinetics in liquids to bond dissociation under force and tested the predictions by smart Monte Carlo (Brownian dynamics) simulations of bond rupture. By definition, bond strength is the force that produces the most frequent failure in repeated tests of breakage, i.e., the peak in the distribution of rupture forces. As verified by the simulations, theory shows that bond strength progresses through three dynamic regimes of loading rate. First, bond strength emerges at a critical rate of loading (> or = 0) at which spontaneous dissociation is just frequent enough to keep the distribution peak at zero force. In the slow-loading regime immediately above the critical rate, strength grows as a weak power of loading rate and reflects initial coupling of force to the bonding potential. At higher rates, there is crossover to a fast regime in which strength continues to increase as the logarithm of the loading rate over many decades independent of the type of attraction. Finally, at ultrafast loading rates approaching the domain of molecular dynamics simulations, the bonding potential is quickly overwhelmed by the rapidly increasing force, so that only naked frictional drag on the structure remains to retard separation. Hence, to expose the energy landscape that governs bond strength, molecular adhesion forces must be examined over an enormous span of time scales. However, a significant gap exists between the time domain of force measurements in the laboratory and the extremely fast scale of molecular motions. Using results from a simulation of biotin-avidin bonds (Izrailev, S., S. Stepaniants, M. Balsera, Y. Oono, and K. Schulten. 1997. Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J., this issue), we describe how Brownian dynamics can help bridge the gap between molecular dynamics and probe tests.

Rheology of rat basophilic leukemia cells

Rat basophilic leukemia (RBL) cells, decorated with IgE, have been shown to bind irreversibly to antigen-coated substrates. In this paper we measured RBL cell deformability and demonstrated that this irreversible binding is not due to a compliant cellular rheology of these cells. The rheological properties of RBL cells were assessed with single-cell micropipette aspiration. Small-sized (G1/G0 phase) cells were found to be more deformable than medium-sized (S phase) cells. No changes in cellular rheology were observed after binding of anti-dinitrophenol IgE to Fce receptors. Furthermore, cytoplasmic viscosity mu showed power-law dependence on mean shear rate gama m: mu = mu c(gamma m/gamma c)-b, where mu c is a characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. All the cells exhibited similar dependence on shear rate (b approximately 0.5). When gamma c was set to 1 s-1. mu c = 480 +/- 10,560 +/- 40 and 490 +/- 10 Pa.s for G1/G0, S cells, and G1/G0 cells treated with the antibody, respectively. In general. RBL cells were much more rigid than normal neutrophils (mu c = 130 +/- 20 Pa, s b = 0.5). Thus the biochemistry of the adhesion molecules, not the cellular deformability of the cell, is the cause of the irreversibility of RBL cell adhesion under flow.

Variation in the velocity, deformation, and adhesion energy density of leukocytes rolling within venules

Leukocyte rolling along the endothelium in inflammation is caused by continuous formation and breakage of bonds between selectin adhesion molecules and their ligands. We investigated trauma-induced leukocyte rolling in venules (diameter, 23 to 58 microns; wall shear stress, 1.2 to 35 dyne/cm2) of the exteriorized rat mesentery using high-resolution intravital microscopy. While rolling, the leukocytes deformed into a tear-droplike shape. Deformation continued to increase with shear stress up to the highest values observed (35 dyne/cm2). Successive leukocytes had similar rolling velocities at the same axial positions along each vessel, suggesting that heterogeneity of endothelial adhesiveness is responsible for velocity variation. Adhesion energy density varied inversely with instantaneous rolling velocity and directly with instantaneous deformation. Adhesion energy density reached a maximum of 0.36 dyne/cm, similar to values found for lymphocyte function-associated antigen-1-dependent adhesion of stimulated T cells to isolated intercellular adhesion molecule-1. We conclude that selectin-mediated adhesion during rolling produces adhesion energy densities comparable to those observed for integrin-mediated adhesion events in other experimental systems.

Effect of receptor-ligand affinity on the strength of endothelial cell adhesion

The objective of this study was to determine the effect of receptor-ligand affinity on the strength of endothelial cell adhesion. Linear and cyclic forms of the fibronectin (Fn) cell-binding domain peptide Arg-Gly-Asp (RGD) were covalently immobilized to glass, and Fn was adsorbed onto glass slides. Bovine aortic endothelial cells attached to the surfaces for 15 min. The critical wall shear stress at which 50% of the cells detached increased nonlinearly with ligand density and was greater with immobilized cyclic RGD than with immobilized linear RGD or adsorbed Fn. To directly compare results for the different ligand densities, the receptor-ligand dissociation constant and force per bond were estimated from data for the critical shear stress and contact area. Total internal reflection fluorescence microscopy was used to measure the contact area as a function of separation distance. Contact area increased with increasing ligand density. Contact areas were similar for the immobilized peptides but were greater on surfaces with adsorbed Fn. The dissociation constant was determined by nonlinear regression of the net force on the cells to models that assumed that bonds were either uniformly stressed or that only bonds on the periphery of the contact region were stressed (peeling model). Both models provided equally good fits for cells attached to immobilized peptides whereas the peeling model produced a better fit of data for cells attached to adsorbed Fn. Cyclic RGD and linear RGD both bind to the integrin alpha v beta 3, but immobilized cyclic RGD exhibited a greater affinity than did linear RGD. Receptor affinities of Fn adsorbed to glycophase glass and Fn adsorbed to glass were similar. The number of bonds was calculated assuming binding equilibrium. The peeling model produced good linear fits between bond force and number of bonds. Results of this study indicate that 1) bovine aortic endothelial cells are more adherent on immobilized cyclic RGD peptide than linear RGD or adsorbed Fn, 2) increased adhesion is due to a greater affinity between cyclic RGD and its receptor, and 3) the affinity of RGD peptides and adsorbed Fn for their receptors is increased after immobilization.

Micropipette suction for measuring piconewton forces of adhesion and tether formation from neutrophil membranes

A new method for measuring piconewton-scale forces that employs micropipette suction is presented here. Spherical cells or beads are used directly as force transducers, and forces as small as 10-20 pN can be imposed. When the transducer is stationary in the pipette, the force is simply the product of the suction pressure and the cross-sectional area of the pipette minus a small correction for the narrow gap that exists between the transducer and the pipette wall. When the transducer is moving along the pipette, the force on it is corrected by a factor that is proportional to the ratio of its velocity relative to its drag-free velocity. With this technique, the minimum force required to form a membrane tether from neutrophils is determined (45 pN), and the length of the microvilli on the surface of neutrophils is inferred. The strength of this technique is in its simplicity and its ability to measure forces between cells without requiring a separate theory or a calibration against an external standard and without requiring the use of a solid surface.

Kinetics and locus of failure of receptor-ligand-mediated adhesion between latex spheres. I. Protein-carbohydrate bond

We previously described the use of a counter-rotating cone and plate rheoscope to measure the time and force dependence of break-up of doublets of sphered, swollen, and fixed red cells (SSRC) cross-linked by monoclonal IgM antibody. It has been shown that doublet break-up can occur by extraction of receptors from the membrane, rather than by antibody-antigen bond break-up, and is a stochastic process. We therefore prepared 4.62-microns carboxyl modified latex spheres with a covalently coupled synthetic blood group B antigen trisaccharide. Using a two-step carbodiimide process, ethylene diamine was covalently linked to the carboxyl modified latex spheres, and the trisaccharide, having an eight carbon spacer modified to bear a terminal carboxyl group, was linked to the ethylene diamine. Using these antigen spheres we carried out studies in Couette flow, in a transparent cone and plate rheoscope, of the shear-induced break-up of doublets cross-linked by monoclonal IgM anti-B antibody in 19% and 15% Dextran 40. As previously found with SSRC, over a range of normal force from 55 to 175 pN, there was a distribution in times to break-up. However, the fraction of antigen sphere doublets broken up, which increased from 0.08 to 0.43 at 75 pM IgM, and from 0.06 to 0.20 at 150 pM IgM, was significantly lower than that for the SSRC, where the fraction broken up at 150 pM IgM increased from 0.10 to 0.47. Thus, significantly higher forces were required to achieve the same degree of break-up for doublets of antigen-linked spheres than for SSRC. Computer simulation using a stochastic model of break-up showed that the differences between antigen sphere and SSRC doublet break-up were due to a change in bond character (the range and depth of the bond energy minimum) rather than to an increase in the number of bonds linking antigen-sphere doublets. This supports the notion that antibody-antigen bonds are ruptured in the case of antigen spheres, whereas antigen is able to be extracted from the membrane of SSRC, although changes of receptor substrate from cell to latex and the possibility of latex strand extraction from the microspheres are potential complicating factors.

Avidin-biotin interactions at vesicle surfaces: adsorption and binding, cross-bridge formation, and lateral interactions

Densely packed domains of membrane proteins are important structures in cellular processes that involve ligand-receptor binding, receptor-mediated adhesion, and macromolecule aggregation. We have used the biotin-avidin interaction at lipid vesicle surfaces to mimic these processes, including the influence of a surface grafted polymer, polyethyleneglycol (PEG). Single vesicles were manipulated by micropipette in solutions of fluorescently labeled avidin to measure the rate and give an estimate of the amount of avidin binding to a biotinylated vesicle as a function of surface biotin concentration and surface-grafted PEG as PEG-lipid. The rate of avidin adsorption was found to be four times less with 2 mol% PEG750 than for the unmodified surface, and 10 mol% PEG completely inhibited binding of avidin to biotin for a 2-min incubation. Using two micropipettes, an avidin-coated vesicle was presented to a biotinylated vesicle. In this vesicle-vesicle adhesion test, the accumulation of avidin in the contact zone was observed, again by using fluorescent avidin. More importantly, by controlling the vesicle membrane tension, this adhesion test provided a direct measure of the spreading pressure of the biotin-avidin-biotin cross-bridges confined in the contact zone. Assuming ideality, this spreading pressure gives the concentration of avidin cross-bridges in the contact zone. The rate of cross-bridge accumulation was consistent with the diffusion of the lipid-linked "receptors" into the contact zone. Once adherent, the membranes failed in tension before they could be peeled apart. PEG750 did not influence the mechanical equilibrium because it was not compressed in the contact zone, but it did perform an important function by eliminating all nonspecific adhesion. This vesicle-vesicle adhesion experiment, with a lower tension limit of 0.01 dyn/cm, now provides a new and useful method with which to measure the spreading pressures and therefore colligative properties of a range of membrane-bound macromolecules.

Selectin- and integrin-mediated T-lymphocyte rolling and arrest on TNF-alpha-activated endothelium: augmentation by erythrocytes

The adhesive and hemodynamic forces that lead to lymphocyte rolling and arrest on activated endothelium and the biophysical role of various adhesion molecules and blood elements in this process are poorly understood. By quantifying their behaviour both in vivo and in vitro, we show here that erythrocytes facilitate selectin- and integrin-mediated rolling and binding of T-lymphocytes on tumor necrosis factor alpha-activated endothelium. The relative contribution of selectins and integrins to this process can be distinguished by using a simple mathematical expression of lymphocyte capture within the range of physiological shear stress. The need for selectin participation in lymphocyte capture increases with shear stress (> 1 dyn/cm2), and both beta 1 and beta 2 integrins act in synergy to produce adhesive drag on captured cells. These findings are potentially useful in developing strategies for intervening with T-cells in a variety of normal and pathological responses as well as for the delivery of genetically modified T-cells to their targets in vivo.

A stochastic model of leukocyte rolling

Selectin-mediated leukocyte rolling under flow is an important process in leukocyte recruitment during inflammation. The rolling motion of individual cells has been observed to fluctuate randomly both in vivo and in vitro. This paper presents a stochastic model of the micromechanics of cell rolling and provides an analytical method of treating experimental data. For a homogeneous cell population, the velocity distribution is obtained in an analytical form, which is in good agreement with experimentally determined velocity histograms obtained previously. For a heterogeneous cell population, the model provides a simple, analytical method of separating the contributions of temporal fluctuations and population heterogeneity to the variance of measured rolling velocities. The model also links the mean and variance of rolling velocities to the molecular events underlying the observed cellular motion, allowing characterization of the distribution and release rate of the clusters of molecular bonds that tether the cell to substratum. Applying the model to the analysis of data obtained for neutrophils rolling on an E-selectin-coated surface at a wall shear stress of 1.2 dyn/cm2 yields estimations of the average distance between bond clusters (approximately micron) and the average time duration of a bond cluster resisting the applied fluid force (approximately 0.5 s).

Molecular mechanisms determining the strength of receptor-mediated intermembrane adhesion

The strength of receptor-mediated cell adhesion is directly controlled by the mechanism of cohesive failure between the cell surface and underlying substrate. Unbinding can occur either at the locus of the specific bond or within the bilayer, which results in tearing the hydrophobic anchors from the membrane interior. In this work, the surface force apparatus has been used to investigate the relationship between the receptor-ligand bond affinities and the dominant mechanism of receptor-coupled membrane detachment. The receptors and ligands used in this study were membrane-bound streptavidin and biotin analogs, respectively, with solution affinities ranging over 10 orders of magnitude. With the optical technique of the surface force apparatus, the occurrence of membrane rupture was directly visualized in situ. The latter observations together with measurements of the corresponding intermembrane adhesive strengths were used to identify the dominant failure pathway for each streptavidin-analog pair. Even in cases where the membrane pull-out energy exceeded the equilibrium bond energy, cohesive failure occurred within the membrane interior at nearly all bond affinities considered. These results are consistent with previous findings and provide direct support for the commonly held view that, under nonequilibrium conditions of applied external stress, the gradient of the bond energy, not the equilibrium bond energy alone, determines the adhesive strength. Furthermore, our findings directly demonstrate that, in the presence of competing failure mechanisms, the preferred detachment mechanism- hence, the adhesive strength-will be determined by the bond that exhibits the weakest tensile strength. Because the tensile strength is determined by the gradient of the unbinding energy, the critical detachment force will be determined by both the bond energy and the effective bond length.

Modeling of molecular mechanisms of cell adhesion

Cellular adhesion is a process of great importance in biology. We present a simple model of the adhesion process in which the molecular mechanisms involve a receptor, a ligand, and the cytoskeleton of the cell. Based on the energetic consideration of the process, we propose a molecular interpretation of the existing experimental data. The model suggests that the interaction of the receptor and (or) receptor-ligand with the cytoskeleton can have important influence on the formation and strength of the adhesion complex as well as on the subsequent interaction with different ligands. When conformational changes take place during the adhesion process, the characterization of the adhesion bonds based on chemical kinetics alone seems to be incomplete and must be supplemented by parameters, describing the functionality of the complex, i.e., change of the affinity for different ligands, as in the signal transduction, or the strength of the bond, as in the adhesion process.

Kinetics of cell detachment: effect of ligand density

Cell adhesion to substratum is often mediated by binding between cell surface receptors and substrate ligands. Substrates can be derivatized with different types and densities of ligands, but how substrate chemistry determines cellular function, such as adhesion strength, has not been demonstrated quantitatively. We employ a numerical methodology developed by Dembo and colleagues (9), who investigated membrane peeling under conditions of excess ligand density, to investigate the kinetics and strength of cell peeling from ligand coated surfaces for arbitrary ligand density. We show there are two asymptotic limits to peeling strength, as quantified by the critical tension: a high ligand density limit, where the critical tension is independent of ligand density and depends logarithmically on the receptor density; and a low ligand density limit, in which the critical tension depends logarithmically on the ligand density but is independent of receptor density. In between these limits, we numerically determine the critical tension. The critical tension is always a weak function of the dissociation constant between ligand and receptor. Furthermore, we show how the rate of peeling, for tensions above the critical tension, depends on ligand density and the mechanical properties of the receptor-ligand bonds. Interestingly, we illustrate when small increases in ligand density should alter cellular behavior, inducing a change to spreading onto a substrate from peeling up from a substrate. In total the predictions of this paper provide criteria for the design of ligand-coated substrate that provide for the proper adhesion strength and dynamics of detachment of cells from surfaces.

Kinetics of cell detachment: peeling of discrete receptor clusters

Clustering of cell surface adhesion receptors is an essential step in the development of focal contacts, specialized cell-substrate attachment sites where receptors are simultaneously linked to extracellular ligand and cytoskeletal proteins. Previously, we examined the effect of receptor clustering on attachment strength. Here, we employ the numerical methodology developed by Dembo and colleagues (Dembo, M., D.C. Torney, K. Saxman, and D. Hammer. 1988. Proc. R. Soc. Lond. B. 234:55-83) to investigate the kinetics of cell detachment when receptors are clustered into discrete patches. We show that the membrane peeling velocity decreases if receptors are clustered within a patch located inside the contact region. Peeling of clusters is influenced by the chemistry and mechanics of receptor-ligand bonds within the patch. Detachment is also prohibited if the applied tension equals the critical tension of the patch, unless the patch length is small compared with the boundary length over which membrane bending occurs, in which case the patch will peel. Peeling of these short patches only occurs when the mechanical stiffness of clustered bonds is within an optimal range. We compare our model predictions with experimental measurements of T lymphocyte detachment from ICAM-1 substrates. We demonstrate that if discrete patches of receptors are present, detachment occurs through intervals of slow and fast peeling, similar to the dynamics of T lymphocyte peeling, indicating that clustering of LFA-1 receptors is one possible explanation for the observed detachment kinetics in this system.

1992 ALZA Distinguished Lecture: bioengineering and vascular biology

The vascular system is naturally dynamic; fluid mechanics and mass transfer are closely integrated with blood and vascular cell function. We are beginning to understand how local wall shear stress and strain modulate endothelial cell metabolism at the gene level. This knowledge may help explain the focal nature of many vascular pathologies, including atherosclerosis. Understanding mechanical control of gene regulation at the level of specific promoter elements and transcription factors involved will lead to development of novel constructs for localized delivery of specific gene products in regions of high or low shear stress or strain in the vascular system. In addition, recent research has shown how local fluid mechanics can alter receptor specificity in cell-to-cell and cell-to-matrix protein adhesion and aggregation. Knowledge of the specific molecular sequences involved in cell-to-cell recognition will allow development of targeted therapeutics, with applications in thrombosis, inflammation, cancer metastasis, and sickle-cell anemia. Bioengineers are uniquely qualified to be leaders in this field, because advances require a synthesis of cell and molecular biology with systems analysis, transport phenomena, and quantitative modeling. Rapid progress in tissue engineering applications will require this new kind of biomedical engineer, which represents both a challenge and an opportunity for our profession.

Relationship between receptor/ligand binding affinity and adhesion strength

Receptor-mediated cell adhesion is a central phenomenon in many physiological and biotechnological processes. Mechanical strength of adhesion is generally presumed to be related to chemical affinity of receptor/ligand bonds, but no experimental study has been previously directed toward this issue. Here we investigate the dependence of receptor/ligand adhesion strength on bond affinity using a radial fluid flow chamber assay to measure the force needed to detach polystyrene beads covalently coated with immunoglobulin G from glass surfaces covalently coated with protein A. A spectrum of animal species sources for immunoglobulin G permits examination of three decades of protein A/immunoglobulin G binding affinity. Our results for this model system demonstrate that adhesion strength varies with the logarithm of the binding affinity, consistent with a prediction from the theoretical model by Dembo et al. (Dembo, M., D.C. Torney, K. Saxman, and D. Hammer. 1988. Proc. R. Soc. Lond. Ser. B 234:55-83).

Interaction forces between red cells agglutinated by antibody. IV. Time and force dependence of break-up

We report on an extension of a previously described method to measure the hydrodynamic force to separate doublets of fixed, sphered and swollen red cells cross-linked by antibody (S. P. Tha, J. Shuster, and H. L. Goldsmith. 1986. Biophys. J. 50:1117-1126). With a traveling microtube apparatus, doublets are tracked and videotaped in a slowly accelerating Poiseuille flow in 150-microns-diameter tubes, and the hydrodynamic normal force at break-up, Fn, is computed from the measured doublet velocity and radial position. Previous results showed a large range of Fn, the mean of which increased with [antiserum], and an absence of clustering at discrete values of Fn. Since it was assumed that the cells separate the instant a critical force to break all crossbridges was reached, lack of clustering could have been due to the use of a polyclonal antiserum. We therefore studied the effect of monoclonal IgM or IgA antibody on the distribution of Fn. The results showed that the data are as scattered as ever, with Fn varying from 2 to 200 pN, and exhibit no evidence of clustering. However, the scatter in Fn could be due to the stochastic nature of intercellular bonds (E. Evans, D. Berk, and A. Leung. 1991a. Biophys. J. 59:838-848). We therefore studied the force dependence of the time to break-up under constant shear stress (Fn from 30 to 200 pN), both in Poiseuille and Couette flow, the latter by using a counter-rotating cone and plate rheoscope. When 280 doublets were rapidly accelerated in the traveling microtube and then allowed to coast in steady flow for up to 180 s, 91% survived into the constant force region; 16% of these broke up after time intervals, tP, of 2-30s. Of 340 doublets immediately exposed to constant shear in the rheoscope, 37% broke after time intervals, tc, from < 1 to 10 s. Thus, doublets do indeed break up under a constant shear stress, if given time. The average time to break-up decreased significantly with increasing force, while the fraction of doublets broken up increased. At a given Fn, the fraction of break-ups decreased with increasing [IgM], suggesting that the average number of bonds had also increased. Using a stochastic model of break-up (G. I. Bell. 1978. Science (Washington DC). 200:618-627; E. Evans, D. Berk,and A. Leung. 1991. Biophys. J. 59:838-848) and a Poisson distribution for the number of bonds, Nb, break-up in slowly accelerating Poiseuille flow and in immediate shear application in Couette flow was simulated. In Poiseuille flow, the observed range and scatter in Fn could be reproduced assuming (Nb) > 5. In the rheoscope, the time intervals and number of rotations to break-up, tc, were quite well reproduced assuming (Nb) = 4. The similarity of (Fn) for monoclonal IgM and IgA for doublet break-up under constant slow acceleration is compatible with the conclusion of Evans et al. (1991 a) for normal red cells and Xia et al. (manuscript submitted for publication) for sphered and swollen red cells, that the applied force extracts the antigen from the cell membrane.

A stochastic model for adhesion-mediated cell random motility and haptotaxis

The active migration of blood and tissue cells is important in a number of physiological processes including inflammation, wound healing, embryogenesis, and tumor cell metastasis. These cells move by transmitting cytoplasmic force through membrane receptors which are bound specifically to adhesion ligands in the surrounding substratum. Recently, much research has focused on the influence of the composition of extracellular matrix and the distribution of its components on the speed and direction of cell migration. It is commonly believed that the magnitude of the adhesion influences cell speed and/or random turning behavior, whereas a gradient of adhesion may bias the net direction of the cell movement, a phenomenon known as haptotaxis. The mechanisms underlying these responses are presently not understood. A stochastic model is presented to provide a mechanistic understanding of how the magnitude and distribution of adhesion ligands in the substratum influence cell movement. The receptor-mediated cell migration is modeled as an interrelation of random processes on distinct time scales. Adhesion receptors undergo rapid binding and transport, resulting in a stochastic spatial distribution of bound receptors fluctuating about some mean distribution. This results in a fluctuating spatio-temporal pattern of forces on the cell, which in turn affects the speed and turning behavior on a longer time scale. The model equations are a system of nonlinear stochastic differential equations (SDE's) which govern the time evolution of the spatial distribution of bound and free receptors, and the orientation and position of the cell. These SDE's are integrated numerically to simulate the behavior of the model cell on both a uniform substratum, and on a gradient of adhesion ligand concentration. Furthermore, analysis of the governing SDE system and corresponding Fokker-Planck equation (FPE) yields analytical expressions for indices which characterize cell movement on multiple time scales in terms of cell cytomechanical, morphological, and receptor binding and transport parameters. For a uniform adhesion ligand concentration, this analysis provides expressions for traditional cell movement indices such as mean speed, directional persistence time, and random motility coefficient. In a small gradient of adhesion, a perturbation analysis of the FPE yields a constitutive cell flux expression which includes a drift term for haptotactic directional cell migration. The haptotactic drift contains terms identified as contributions from directional orientation bias (taxis), kinesis, and orthotaxis, of which taxis appears to be predominant given estimates of the model parameters.