Yielding Elastic Tethers Stabilize Robust Cell Adhesion

Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds.     

For catch bonds, it all hinges on the interdomain region

Tensile mechanical force was long assumed to increase the detachment rates of biological adhesive bonds (Bell, 1978). However, in the last few years, several receptor-ligand pairs were shown to form "catch bonds," whose lifetimes are enhanced by moderate amounts of force. These include the bacterial adhesive protein FimH binding to its ligand mannose (Thomas et al., 2002; Thomas et al., 2006), blood cell adhesion proteins P- and L-selectin binding to sialyl Lewis X (sLe(X))-containing ligands (Marshall et al., 2003; Evans et al., 2004; Sarangapani et al., 2004), and the myosin-actin motor protein interaction (Guo and Guilford, 2006). The structural mechanism behind this counterintuitive force-enhanced catch bond behavior is of great interest.     

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.     

Stick and grip: measurement systems and quantitative analyses of integrin-mediated cell adhesion strength

Cell adhesion to extracellular matrix components involves integrin receptor-ligand binding and adhesion strengthening, comprising receptor clustering, cytoskeletal interactions, and cell spreading. Although elucidation of the biochemical events in adhesive interactions is rapidly advancing, the mechanical processes and mechanisms of adhesion strengthening remain poorly understood. Because the biochemical and biophysical processes in adhesive interactions are tightly coupled, mechanical analyses of adhesion strength provide critical information on structure-function relationships. This review focuses on (a) measurement systems for cell adhesion strength and (b) quantitative analyses of integrin-mediated strengthening to extracellular matrix components.     

A semianalytic model of leukocyte rolling

Rolling allows leukocytes to maintain adhesion to vascular endothelium and to molecularly coated surfaces in flow chambers. Using insights from adhesive dynamics, a computational method for simulating leukocyte rolling and firm adhesion, we have developed a semianalytic model for the steady-state rolling of a leukocyte. After formation in a force-free region of the contact zone, receptor-ligand bonds are transported into the trailing edge of the contact zone. Rolling velocity results from a balance of the convective flux of bonds and the rate of dissociation at the back edge of the contact zone. We compare the model's results to that of adhesive dynamics and to experimental data on the rolling of leukocytes, with good agreement. We calculate the dependence of rolling velocity on shear rate, intrinsic forward and reverse reaction rates, bond stiffness, and reactive compliance, and use the model to calculate a state diagram relating molecular parameters and the dynamic state of adhesion. A dimensionless form of the analytic model permits exploration of the parameters that control rolling. The chemical affinity of a receptor-ligand pair does not uniquely determine rolling velocity. We elucidate a fundamental relationship between off-rate, ligand density, and reactive compliance at the transition between firm and rolling adhesion. The model provides a rapid method for screening system parameters for the potential to mediate rolling.     

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.     

Effects of curvature and cell–cell interaction on cell adhesion in microvessels

It has been found that both circulating blood cells and tumor cells are more easily adherent to curved microvessels than straight ones. This motivated us to investigate numerically the effect of the curvature of the curved vessel on cell adhesion. In this study, the fluid dynamics was carried out by the lattice Boltzmann method (LBM), and the cell dynamics was governed by the Newton’s law of translation and rotation. The adhesive dynamics model involved the effect of receptor-ligand bonds between circulating cells and endothelial cells (ECs). It is found that the curved vessel would increase the simultaneous bond number, and the probability of cell adhesion is increased consequently. The interaction between traveling cells would also affect the cell adhesion significantly. For two-cell case, the simultaneous bond number of the rear cell is increased significantly, and the curvature of microvessel further enhances the probability of cell adhesion.     

Cell Adhesion Strength Is Controlled by Intermolecular Spacing of Adhesion Receptors

Spatial patterning of biochemical cues on the micro- and nanometer scale controls numerous cellular processes such as spreading, adhesion, migration, and proliferation. Using force microscopy we show that the lateral spacing of individual integrin receptor-ligand bonds determines the strength of cell adhesion. For spacings ≥90 nm, focal contact formation was inhibited and the detachment forces as well as the stiffness of the cell body were significantly decreased compared to spacings ≤50 nm. Analyzing cell detachment at the subcellular level revealed that rupture forces of focal contacts increase with loading rate as predicted by a theoretical model for adhesion clusters. Furthermore, we show that the weak link between the intra- and extracellular space is at the intracellular side of a focal contact. Our results show that cells can amplify small differences in adhesive cues to large differences in cell adhesion strength.     

Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities.(ABSTRACT TRUNCATED AT 250 WORDS)     

Uncoiling mechanics of Escherichia coli type I fimbriae are optimized for catch bonds

We determined whether the molecular structures through which force is applied to receptor–ligand pairs are tuned to optimize cell adhesion under flow. The adhesive tethers of our model system, Escherichia coli, are type I fimbriae, which are anchored to the outer membrane of most E. coli strains. They consist of a fimbrial rod (0.3–1.5 μm in length) built from a helically coiled structural subunit, FimA, and an adhesive subunit, FimH, incorporated at the fimbrial tip. Previously reported data suggest that FimH binds to mannosylated ligands on the surfaces of host cells via catch bonds that are enhanced by the shear-originated tensile force. To understand whether the mechanical properties of the fimbrial rod regulate the stability of the FimH–mannose bond, we pulled the fimbriae via a mannosylated tip of an atomic force microscope. Individual fimbriae rapidly elongate for up to 10 μm at forces above 60 pN and rapidly contract again at forces below 25 pN. At intermediate forces, fimbriae change length more slowly, and discrete 5.0 ± 0.3–nm changes in length can be observed, consistent with uncoiling and coiling of the helical quaternary structure of one FimA subunit at a time. The force range at which fimbriae are relatively stable in length is the same as the optimal force range at which FimH–mannose bonds are longest lived. Higher or lower forces, which cause shorter bond lifetimes, cause rapid length changes in the fimbria that help maintain force at the optimal range for sustaining the FimH–mannose interaction. The modulation of force and the rate at which it is transmitted from the bacterial cell to the adhesive catch bond present a novel physiological role for the fimbrial rod in bacterial host cell adhesion. This suggests that the mechanical properties of the fimbrial shaft have codeveloped to optimize the stability of the terminal adhesive under flow.     

Uncoiling Mechanics of Escherichia coli Type I Fimbriae Are Optimized for Catch Bonds

We determined whether the molecular structures through which force is applied to receptor–ligand pairs are tuned to optimize cell adhesion under flow. The adhesive tethers of our model system, Escherichia coli, are type I fimbriae, which are anchored to the outer membrane of most E. coli strains. They consist of a fimbrial rod (0.3–1.5 μm in length) built from a helically coiled structural subunit, FimA, and an adhesive subunit, FimH, incorporated at the fimbrial tip. Previously reported data suggest that FimH binds to mannosylated ligands on the surfaces of host cells via catch bonds that are enhanced by the shear-originated tensile force. To understand whether the mechanical properties of the fimbrial rod regulate the stability of the FimH–mannose bond, we pulled the fimbriae via a mannosylated tip of an atomic force microscope. Individual fimbriae rapidly elongate for up to 10 μm at forces above 60 pN and rapidly contract again at forces below 25 pN. At intermediate forces, fimbriae change length more slowly, and discrete 5.0 ± 0.3–nm changes in length can be observed, consistent with uncoiling and coiling of the helical quaternary structure of one FimA subunit at a time. The force range at which fimbriae are relatively stable in length is the same as the optimal force range at which FimH–mannose bonds are longest lived. Higher or lower forces, which cause shorter bond lifetimes, cause rapid length changes in the fimbria that help maintain force at the optimal range for sustaining the FimH–mannose interaction. The modulation of force and the rate at which it is transmitted from the bacterial cell to the adhesive catch bond present a novel physiological role for the fimbrial rod in bacterial host cell adhesion. This suggests that the mechanical properties of the fimbrial shaft have codeveloped to optimize the stability of the terminal adhesive under flow.     

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.(ABSTRACT TRUNCATED AT 250 WORDS)     

Simulation of cell rolling and adhesion on surfaces in shear flow: general results and analysis of selectin-mediated neutrophil adhesion.

The receptor-mediated adhesion of cells to ligand-coated surfaces in viscous shear flow is an important step in many physiological processes, such as the neutrophil-mediated inflammatory response, lymphocyte homing, and tumor cell metastasis. This paper describes a calculational method which simulates the interaction of a single cell with a ligand-coated surface under flow. The cell is idealized as a microvilli-coated hard sphere covered with adhesive springs. The distribution of microvilli on the cell surface, the distribution of receptors on microvilli tips, and the forward and reverse reaction between receptor and ligand are all simulated using random number sampling of appropriate probability functions. The velocity of the cell at each time step in the simulation results from a balance of hydrodynamic, colloidal and bonding forces; the bonding force is derived by summing the individual contributions of each receptor-ligand tether. The model can simulate the effect of many parameters on adhesion, such as the number of receptors on microvilli tips, the density of ligand, the rates of reaction between receptor and ligand, the stiffness of the resulting receptor-ligand springs, the response of springs to strain, and the magnitude of the bulk hydrodynamic stresses. The model can successfully recreate the entire range of expected and observed adhesive phenomena, from completely unencumbered motion, to rolling, to transient attachment, to firm adhesion. Also, the method can generate meaningful statistical measures of adhesion, including the mean and variance in velocity, rate constants for cell attachment and detachment, and the frequency of adhesion. We find a critical modulating parameter of adhesion is the fractional spring slippage, which relates the strain of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same strain. Our analysis of neutrophil adhesive behavior on selectin-coated (CD62-coated) surfaces in viscous shear flow reported by Lawrence and Springer (Lawrence, M.B., and T.A. Springer 1991. Cell. 65:859-874) shows the fractional spring slippage of the CD62-LECAM-1 bond is likely below 0.01. We conclude the unique ability of this selectin bond to cause neutrophil rolling under flow is a result of its unique response to strain. Furthermore, our model can successfully recreate data on neutrophil rolling as function of CD62 surface density.     

Simultaneous tether extraction from endothelial cells and leukocytes: observation, mechanics, and significance

It has been hypothesized, from earlier studies on single-tether extraction from individual leukocytes and human umbilical vein endothelial cells, that during rolling of leukocytes on the endothelium, simultaneous extraction of membrane nanotubes (tethers) occurs, resulting in enhancement of the force decrease on the adhesive bond. In this study, using the micropipette aspiration technique and fluorescence microscopy, we show that tethers are indeed extracted simultaneously when an endothelial cell and a leukocyte are separated after brief contact and adhesion, and the endothelial cell contributes much more to the composite tether length. In addition, the constitutive relationship for simultaneous tether extraction is determined with neutrophils and T-lymphocytes as force transducers, and cytokine-stimulated human umbilical vein and dermal microvascular endothelial cells as substrates, respectively. This relationship is consistent with that derived theoretically from the constitutive equations for single-tether extraction from either cell alone. Moreover, we show that simultaneous tether extraction was likely terminated by receptor-ligand bond dissociation. With a biomechanical model of leukocyte rolling, we predict the force history of the adhesive receptor-ligand bond and show that it is remarkably similar for different leukocyte-endothelial cell pairs. Simultaneous tether extraction therefore represents a generic mechanism for stabilizing leukocyte rolling on the endothelium.     

An analytical model for determining two-dimensional receptor-ligand kinetics

Cell-cell adhesive interactions play a pivotal role in major pathophysiological vascular processes, such as inflammation, infection, thrombosis, and cancer metastasis, and are regulated by hemodynamic forces generated by blood flow. Cell adhesion is mediated by the binding of receptors to ligands, which are both anchored on two-dimensional (2-D) membranes of apposing cells. Biophysical assays have been developed to determine the unstressed (no-force) 2-D affinity but fail to disclose its dependence on force. Here we develop an analytical model to estimate the 2-D kinetics of diverse receptor-ligand pairs as a function of force, including antibody-antigen, vascular selectin-ligand, and bacterial adhesin-ligand interactions. The model can account for multiple bond interactions necessary to mediate adhesion and resist detachment amid high hemodynamic forces. Using this model, we provide a generalized biophysical interpretation of the counterintuitive force-induced stabilization of cell rolling observed by a select subset of receptor-ligand pairs with specific intrinsic kinetic properties. This study enables us to understand how single-molecule and multibond biophysics modulate the macroscopic cell behavior in diverse pathophysiological processes.     

Receptor-ligand binding in the cell-substrate contact zone: a quantitative analysis using CX3CR1 and CXCR1 chemokine receptors

Receptor-ligand binding analyses have generally used soluble components to measure thermodynamic binding constants. In their biological context, adhesion receptors bind to an immobile ligand and the binding reaction is confined to the cell-substrate contact zone. We have developed a new procedure based on the spinning disk technology to measure the number of receptor-ligand bonds in the contact zone. Application of this methodology to the CX3CR1-fractalkine and the CXCR1-IL-8 receptor-ligand systems demonstrated that the level of binding to an immobilized ligand is reduced by several orders of magnitude in comparison to solution binding. A comparison of the solution binding and contact zone binding constants shows that the effect of ligand immobilization was similar for each system. In contrast, although the CXCR1-IL-8 bond had the higher affinity, the average bond strength was only 10% of that for the CX3CR1 bond. Because fractalkine can be expressed as a cell surface-bound protein, CX3CR1 has been proposed to function as an adhesion receptor. The higher bond strength suggests that the bond architecture has also evolved to serve an adhesion function.     

Catch bonds: physical models and biological functions

Force can shorten the lifetimes of receptor-ligand bonds by accelerating their dissociation. Perhaps paradoxical at first glance, bond lifetimes can also be prolonged by force. This counterintuitive behavior was named catch bonds, which is in contrast to the ordinary slip bonds that describe the intuitive behavior of lifetimes being shortened by force. Fifteen years after their theoretical proposal, catch bonds have finally been observed. In this article we review recently published data that have demonstrated catch bonds in the selectin system and suggested catch bonds in other systems, the theoretical models for their explanations, and their function as a mechanism for flow-enhanced adhesion.     

A 3-D computational model predicts that cell deformation affects selectin-mediated leukocyte rolling

Leukocyte recruitment to sites of inflammation is initiated by their tethering and rolling on the activated endothelium under flow. Even though the fast kinetics and high tensile strength of selectin-ligand bonds are primarily responsible for leukocyte rolling, experimental evidence suggests that cellular properties such as cell deformability and microvillus elasticity actively modulate leukocyte rolling behavior. Previous theoretical models either assumed cells as rigid spheres or were limited to two-dimensional representations of deformable cells with deterministic receptor-ligand kinetics, thereby failing to accurately predict leukocyte rolling. We therefore developed a three-dimensional computational model based on the immersed boundary method to predict receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions. Our model predicts for the first time that the rolling of more compliant cells is relatively smoother and slower compared to cells with stiffer membranes, due to increased cell-substrate contact area. At the molecular level, we show that the average number of bonds per cell as well as per single microvillus decreases with increasing membrane stiffness. Moreover, the average bond lifetime decreases with increasing shear rate and with increasing membrane stiffness, due to higher hydrodynamic force experienced by the cell. Taken together, our model captures the effect of cellular properties on the coupling between hydrodynamic and receptor-ligand bond forces, and successfully explains the stable leukocyte rolling at a wide range of shear rates over that of rigid microspheres.     

Enforced detachment of red blood cells adhering to surfaces: statics and dynamics

We investigated the mechanical strength of adhesion and the dynamics of unbinding of red blood cells to solid surfaces. Two different situations were tested: 1), native red blood cells nonspecifically adhered to glass surfaces coated with positively charged polymers and 2), biotinylated red blood cells specifically adhered to glass surfaces decorated with streptavidin, which has a high binding affinity for biotin. We used micropipette manipulation for forming and subsequently breaking the adhesive contact through a stepwise micromechanical procedure. Analysis of cell deformations provided the relation between force and contact radius, which was found to be in good agreement with theoretical predictions. We further demonstrated that the separation energy could be precisely derived from the measure of rupture forces and the cell shape. Finally, the dynamics of detachment was analyzed as a function of the applied force and the initial size of the adhesive patch. Our experiments were supported by original theoretical predictions, which allowed us to correlate the measured separation times with the molecular parameters (e.g., activation barrier, receptor-ligand characteristic length) derived from force measurements at the single bond level.