What is the biological relevance of the specific bond properties revealed by single-molecule studies?

During the last decade, many authors took advantage of new methodologies based on atomic force microscopy (AFM), biomembrane force probes (BFPs), laminar flow chambers or optical traps to study at the single-molecule level the formation and dissociation of bonds between receptors and ligands attached to surfaces. Experiments provided a wealth of data revealing the complexity of bond response to mechanical forces and the dependence of bond rupture on bond history. These results supported the existence of multiple binding states and/or reaction pathways. Also, single bond studies allowed us to monitor attachments mediated by a few bonds. The aim of this review is to discuss the impact of this new information on our understanding of biological molecules and phenomena. The following points are discussed: (i) which parameters do we need to know in order to predict the behaviour of an encounter between receptors and ligands, (ii) which information is actually yielded by single-molecule studies and (iii) is it possible to relate this information to molecular structure?     

Flow-enhanced adhesion regulated by a selectin interdomain hinge

L-selectin requires a threshold shear to enable leukocytes to tether to and roll on vascular surfaces. Transport mechanisms govern flow-enhanced tethering, whereas force governs flow-enhanced rolling by prolonging the lifetimes of L-selectin-ligand complexes (catch bonds). Using selectin crystal structures, molecular dynamics simulations, site-directed mutagenesis, single-molecule force and kinetics experiments, Monte Carlo modeling, and flow chamber adhesion studies, we show that eliminating a hydrogen bond to increase the flexibility of an interdomain hinge in L-selectin reduced the shear threshold for adhesion via two mechanisms. One affects the on-rate by increasing tethering through greater rotational diffusion. The other affects the off-rate by strengthening rolling through augmented catch bonds with longer lifetimes at smaller forces. By forcing open the hinge angle, ligand may slide across its interface with L-selectin to promote rebinding, thereby providing a mechanism for catch bonds. Thus, allosteric changes remote from the ligand-binding interface regulate both bond formation and dissociation.     

Elasticity-associated rebinding rate of molecular bonds between soft elastic media

A quantitative understanding of how cells interact with their extracellular matrix via molecular bonds is fundamental for many important processes in cell biology and engineering. In these interactions, the deformability of cells and matrix are usually comparable with that of the bonds, making their rebinding events globally coupled with the deformation states of whole systems. Unfortunately, this important principle is not realized or adopted in most conventional theoretical models for analyzing cellular adhesions. In this study, we considered a new theoretical model of a cluster of ligand-receptor bonds between two soft elastic bodies, in which the rebinding rates of ligands to receptors are described, by considering the deformation of the overall system under the influence of bond distributions. On the basis of theory of continuum and statistical mechanics, we obtained an elasticity-associated rebinding rate of open bonds in a closed analytical form that highly depends on the binding states and distributions of all other bonds as well as on the overall deformation energy stored in the elastic bodies and all closed bonds. On the basis of this elasticity-associated rebinding rate and by performing Monte Carlo simulations, we uncovered new mechanisms underlying the adhesion stability of molecular-bond clusters associated with deformable elastic bodies. Moreover, we revealed that the rebinding processes of molecular bonds is not only dependent on interfacial separation but is related to overall energy. This newly proposed rebinding rate may substantially improve our understanding of how cells adapt to their microenvironments by adjusting their mechanical properties through cytoskeleton remodeling.     

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).     

Force history dependence of receptor-ligand dissociation

Receptor-ligand bonds that mediate cell adhesion are often subjected to forces that regulate their dissociation via modulating off-rates. Off-rates control how long receptor-ligand bonds last and how much force they withstand. One should therefore be able to determine off-rates from either bond lifetime or unbinding force measurements. However, substantial discrepancies exist between the force dependence of off-rates derived from the two types of measurements even for the same interactions, e.g., selectins dissociating from their ligands, which mediate the tethering and rolling of leukocytes on vascular surfaces during inflammation and immune surveillance. We used atomic force microscopy to measure survival times of P-selectin dissociating from P-selectin glycoprotein ligand 1 or from an antibody in both bond lifetime and unbinding force experiments. By a new method of data analysis, we showed that the discrepancies resulted from the assumption that off-rates were functions of force only. The off-rates derived from forced dissociation data depended not only on force but also on the history of force application. This finding provides a new paradigm for understanding how force regulates receptor-ligand interactions.     

Specific molecular interactions by force spectroscopy: from single bonds to collective properties

Interactions involving multiple bonds occur throughout biology, and have distinct properties that are fundamentally different from those present in single bond systems. We have developed a new method to analyse the AFM force measurements in order to extract relevant information and to characterise the interactions involving from single to multiple bonds. Our study reveals a surprising behaviour in the presence of multiple bonds with a high rebinding probability: the mean binding forces increase with decreasing pulling velocity. Such behaviour is different from the force dependence on the loading rate for single bond rupture or existing models for multiple bonds rupture.     

Triphasic Force Dependence of E-Selectin/Ligand Dissociation Governs Cell Rolling under Flow

During inflammation, flowing leukocytes tether to and roll on vascular surfaces through the association and dissociation of selectin/ligand bonds. The interactions of P- and L- selectins with their respective ligands exhibit catch-slip bonds, such that increasing force initially prolongs and then shortens bond lifetimes. In addition, catch-slip bonds have been shown to govern L-selectin-mediated cell rolling. Using a flow chamber and biomembrane force probe, we show a triphasic force dependence of E-selectin/ligand dissociation that initially behaves as slip bonds, then transitions to catch bonds, and finally transitions again to slip bonds as the force increases. These transitions govern the velocities of neutrophils, HL-60 cells, and Colo-205 cells rolling on E-selectin, as evidenced by the fact that their velocities exhibited a triphasic force dependence that inversely matched the triphasic lifetime-force relationship. At low forces, slip bonds may also precede catch bonds for interactions of P- and L-selectin with their ligands.     

Hidden multiple bond effects in dynamic force spectroscopy

In dynamic force spectroscopy, a (bio-)molecular complex is subjected to a steadily increasing force until the chemical bond breaks. Repeating the same experiment many times results in a broad distribution of rupture forces, whose quantitative interpretation represents a formidable theoretical challenge. In this study we address the situation that more than a single molecular bond is involved in one experimental run, giving rise to multiple rupture events that are even more difficult to analyze and thus are usually eliminated as far as possible from the further evaluation of the experimental data. We develop and numerically solve a detailed model of a complete dynamic force spectroscopy experiment including a possible clustering of molecules on the substrate surface, the formation of bonds, their dissociation under load, and the postprocessing of the force extension curves. We show that the data, remaining after elimination of obvious multiple rupture events, may still contain a considerable number of hidden multiple bonds, which are experimentally indistinguishable from true single bonds, but which have considerable effects on the resulting rupture force statistics and its consistent theoretical interpretation.     

Single molecule adhesion measurements reveal two homophilic neural cell adhesion molecule bonds with mechanically distinct properties

Neural cell adhesion molecule (NCAM) is a cell surface adhesion glycoprotein that plays an important role in the development and stability of nervous tissue. The homophilic binding mechanism of NCAM is still a subject of debate on account of findings that appear to support different mechanisms. This paper describes single molecule force measurements with both full-length NCAM and NCAM mutants that lack different immunoglobulin (Ig) domains. By systematically applying an external, time-dependent force to the bond, we obtained parameters that describe the energy landscape of NCAM-NCAM bonds. Histograms of the rupture forces between the full-length NCAM extracellular domains revealed two binding events, one rupturing at higher forces than the other. These bond rupture data show that the two bonds have the same dissociation rates. Despite the energetic and kinetic similarities, the bond strengths differ significantly, and are mechanically distinct. Measurements with NCAM domain deletion mutants mapped the weaker bond to the Ig1-2 segment, and the stronger bond to the Ig3 domain. Finally, the quantitative agreement between the fragment adhesion and the strengths of both NCAM bonds shows that the domain deletions considered in this study do not alter the intrinsic strengths of either of the two bonds.     

Kinetics of the Multistep Rupture of Fibrin ‘A-a’ Polymerization Interactions Measured Using Atomic Force Microscopy

Fibrin, the structural scaffold of blood clots, spontaneously polymerizes through the formation of ‘A-a’ knob-hole bonds. When subjected to external force, the dissociation of this bond is accompanied by two to four abrupt changes in molecular dimension observable as rupture events in a force curve. Herein, the configuration, molecular extension, and kinetic parameters of each rupture event are examined. The increases in contour length indicate that the D region of fibrinogen can lengthen by ∼50% of the length of a fibrin monomer before rupture of the ‘A-a’ interaction. The dependence of the dissociation rate on applied force was obtained using probability distributions of rupture forces collected at different pull-off velocities. These distributions were fit using a model in which the effects of the shape of the binding potential are used to quantify the kinetic parameters of forced dissociation. We found that the weak initial rupture (i.e., event 1) was not well approximated by these models. The ruptured bonds comprising the strongest ruptures, events 2 and 3, had kinetic parameters similar to those commonly found for the mechanical unfolding of globular proteins. The bonds ruptured in event 4 were well described by these analyses, but were more loosely bound than the bonds in events 2 and 3. We propose that the first event represents the rupture of an unknown interaction parallel to the ‘A-a’ bond, events 2 and 3 represent unfolding of structures in the D region of fibrinogen, and event 4 is the rupture of the ‘A-a’ knob-hole bond weakened by prior structural unfolding. Comparison of the activation energy obtained via force spectroscopy measurements with the thermodynamic free energy of ‘A-a’ bond dissociation indicates that the ‘A-a’ bond may be more resistant to rupture by applied force than to rupture by thermal dissociation.     

Strength of multiple parallel biological bonds

Multivalent interactions play a critical role in a variety of biological processes on both molecular and cellular levels. We have used molecular force spectroscopy to investigate the strength of multiple parallel peptide-antibody bonds using a system that allowed us to determine the rupture forces and the number of ruptured bonds independently. In our experiments the interacting molecules were attached to the surfaces of the probe and sample of the atomic force microscope with flexible polymer tethers, and the unique mechanical signatures of the tethers determined the number of ruptured bonds. We show that the rupture forces increase with the number of interacting molecules and that the measured forces obey the predictions of a Markovian model for the strength of multiple parallel bonds. We also discuss the implications of our results to the interpretation of force spectroscopy measurements in multiple bond systems.     

Detachment of agglutinin-bonded red blood cells. I. Forces to rupture molecular-point attachments.

A simple micromechanical method has been developed to measure the rupture strength of a molecular-point attachment (focal bond) between two macroscopically smooth membrane capsules. In the procedure, one capsule is prepared with a low density coverage of adhesion molecules, formed as a stiff sphere, and held at fixed position by a micropipette. The second capsule without adhesion molecules is pressurized into a spherical shape with low suction by another pipette. This capsule is maneuvered to initiate point contact at the pole opposite the stiff capsule which leads to formation of a few (or even one) molecular attachments. Then, the deformable capsule is slowly withdrawn by displacement of the pipette. Analysis shows that the end-to-end extension of the capsule provides a direct measure of the force at the point contact and, therefore, the rupture strength when detachment occurs. The range for point forces accessible to this technique depends on the elastic moduli of the membrane, membrane tension, and the size of the capsule. For biological and synthetic vesicle membranes, the range of force lies between 10(-7)-10(-5) dyn (10(-12)-10(-10) N) which is 100-fold less than presently measurable by Atomic Force Microscopy! Here, the approach was used to study the forces required to rupture microscopic attachments between red blood cells formed by a monoclonal antibody to red cell membrane glycophorin, anti-A serum, and a lectin from the snail-helix pomatia. Failure of the attachments appeared to be a stochastic function of the magnitude and duration of the detachment force. We have correlated the statistical behavior observed for rupture with a random process model for failure of small numbers of molecular attachments. The surprising outcome of the measurements and analysis was that the forces deduced for short-time failure of 1-2 molecular attachments were nearly the same for all of the agglutinin, i.e., 1-2 x 10(-6) dyn. Hence, microfluorometric tests were carried out to determine if labeled agglutinins and/or labeled surface molecules were transferred between surfaces after separation of large areas of adhesive contact. The results showed that the attachments failed because receptors were extracted from the membrane.     

Long-Lived, High-Strength States of ICAM-1 Bonds to β2 Integrin, II: Lifetimes of LFA-1 Bonds Under Force in Leukocyte Signaling

Using single-molecule force spectroscopy to probe ICAM-1 interactions with recombinant α_Lβ₂ immobilized on microspheres and β₂ integrin on neutrophils, we quantified an impressive hierarchy of long-lived, high-strength states of the integrin bond, which start from basal levels with activation in solutions of divalent cations and shift dramatically upward to hyperactivated states with cell signaling. Taking advantage of very rare events, we used repeated measurements of bond lifetimes under steady ramps of force to achieve a direct assay for the off-rates of ICAM-1 from β₂ integrin throughout the course of each experiment. In our companion article I, we demonstrate the assay using results from tests of a monovalent ICAM-1 probe against recombinant α_Lβ₂ on microspheres in millimolar solutions of divalent cations (Ca²⁺, Mg²⁺, Mn²⁺). In this article, we examine the impact of inside-out and outside-in signaling in neutrophils on the lifetimes and mechanical strengths of ICAM-1 bonds to β₂ integrin on the cell surface. Even though ICAM-1 bonds to recombinant α_Lβ₂ on microspheres in Mg²⁺ or Mn²⁺ can live for long periods of time under slow pulling, here we show that stimulation of neutrophils in Mg²⁺ plus the chemokine IL-8 (i.e., inside-out signaling) induces several-hundred-fold longer lifetimes for ICAM-1 attachments to LFA-1, creating strong bonds at very slow pulling speeds where none are perceived in Mg²⁺ or Mn²⁺ alone. Similar changes are observed with outside-in signaling, i.e., long lifetimes and increased bond strength also occur when neutrophils are bound with the activating (anti-CD18) monoclonal 240Q. Limiting our investigation to rare events using very dilute ICAM-1 probes, we show that although the prolonged lifetimes of cell surface attachments for both inside-out and outside-in signaling exhibit single-bond-like statistics for dissociation under force, they are consistent with a tightly coupled dimeric ICAM-1 interaction with a pair of LFA-1 heterodimers.     

Effects of multiple-bond ruptures on kinetic parameters extracted from force spectroscopy measurements: revisiting biotin-streptavidin interactions

Force spectroscopy measurements of the rupture of the molecular bond between biotin and streptavidin often results in a wide distribution of rupture forces. We attribute the long tail of high rupture forces to the nearly simultaneous rupture of more than one molecular bond. To decrease the number of possible bonds, we employed hydrophilic polymeric tethers to attach biotin molecules to the atomic force microscope probe. It is shown that the measured distributions of rupture forces still contain high forces that cannot be described by the forced dissociation from a deep potential well. We employed a recently developed analytical model of simultaneous rupture of two bonds connected by polymer tethers with uneven length to fit the measured distributions. The resulting kinetic parameters agree with the energy landscape predicted by molecular dynamics simulations. It is demonstrated that when more than one molecular bond might rupture during the pulling measurements there is a noise-limited range of probe velocities where the kinetic parameters measured by force spectroscopy correspond to the true energy landscape. Outside this range of velocities, the kinetic parameters extracted by using the standard most probable force approach might be interpreted as artificial energy barriers that are not present in the actual energy landscape. Factors that affect the range of useful velocities are discussed.     

FimH forms catch bonds that are enhanced by mechanical force due to allosteric regulation

The bacterial adhesive protein, FimH, is the most common adhesin of Escherichia coli and mediates weak adhesion at low flow but strong adhesion at high flow. There is evidence that this occurs because FimH forms catch bonds, defined as bonds that are strengthened by tensile mechanical force. Here, we applied force to single isolated FimH bonds with an atomic force microscope in order to test this directly. If force was loaded slowly, most of the bonds broke up at low force (<60 piconewtons of rupture force). However, when force was loaded rapidly, all bonds survived until much higher force (140-180 piconewtons of rupture force), behavior that indicates a catch bond. Structural mutations or pretreatment with a monoclonal antibody, both of which allosterically stabilize a high affinity conformation of FimH, cause all bonds to survive until high forces regardless of the rate at which force is applied. Pretreatment of FimH bonds with intermediate force has the same strengthening effect on the bonds. This demonstrates that FimH forms catch bonds and that tensile force induces an allosteric switch to the high affinity, strong binding conformation of the adhesin. The catch bond behavior of FimH, the amount of force needed to regulate FimH, and the allosteric mechanism all provide insight into how bacteria bind and form biofilms in fluid flow. Additionally, these observations may provide a means for designing antiadhesive mechanisms.     

Receptor aggregation by intermembrane interactions: a Monte Carlo study

The lateral organization of receptors on cell surfaces is critically important to their function; many receptors transmit transmembrane signals when redistributed into clusters, while the response of others is potentiated by their aggregation. Cell-cell contact can play a crucial role in receptor aggregation, even when the bonds between receptors on one cell and ligands on the other are monovalent. Monte Carlo simulations on a two-membrane model were carried out to determine whether weak enthalpic interactions among receptors in one membrane, and among ligands in another, can work synergistically to give large-scale clustering when the two membranes are brought into contact. The simulations give support to such a clustering mechanism. In addition, because clustering is a cooperative process akin to a phase separation, individual receptors and ligands may undergo repeated binding and unbinding while in a clustered "phase," and a single ligand could interact with multiple different receptor partners. The results suggest a resolution of the dichotomy between serial triggering and aggregation models of T cell activation.     

Ligand interactions of the cation-dependent mannose 6-phosphate receptor. Comparison with the cation-independent mannose 6-phosphate receptor

The interactions of the bovine cation-dependent mannose 6-phosphate receptor with monovalent and divalent ligands have been studied by equilibrium dialysis. This receptor appears to be a homodimer or a tetramer. Each mole of receptor monomer bound 1.2 mol of the monovalent ligands, mannose 6-phosphate and pentamannose phosphate with Kd values of 8 X 10(-6) M and 6 X 10(-6) M, respectively and 0.5 mol of the divalent ligand, a high mannose oligosaccharide with two phosphomonoesters, with a Kd of 2 X 10(-7) M. When Mn2+ was replaced by EDTA in the dialysis buffer, the Kd for pentamannose phosphate was 2.5 X 10(-5) M. By measuring the affinity of the cation-dependent and cation-independent mannose 6-phosphate receptors for a variety of mannose 6-phosphate analogs, we conclude that the 6-phosphate and the 2-hydroxyl of mannose 6-phosphate each contribute approximately 4-5 kcal/mol of Gibb's free energy to the binding reaction. Neither receptor appears to interact substantially with the anomeric oxygen of mannose 6-phosphate. The receptors differ in that the cation-dependent receptor displays no detectable affinity for N-acetylglucosamine 1'-(alpha-D-methylmannopyranose 6-monophosphate) whereas this ligand binds to the cation-independent receptor with a poor, but readily measurable Kd of about 0.1 mM. The spacing of the mannose 6-phosphate-binding sites relative to each other may also differ for the two receptors.     

Multi-scale simulation of L-selectin–PSGL-1-dependent homotypic leukocyte binding and rupture

L-selectin–PSGL-1-mediated polymorphonuclear (PMN) leukocyte homotypic interactions potentiate the extent of PMN recruitment to endothelial sites of inflammation. Cell–cell adhesion is a complex phenomenon involving the interplay of bond kinetics and hydrodynamics. As a first step, a 3-D computational model based on the Immersed Boundary Method is developed to simulate adhesion-detachment of two PMN cells in quiescent conditions. Our simulations predict that the total number of bonds formed is dictated by the number of available receptors (PSGL-1) when ligands (L-selectin) are in excess, while the excess amount of ligands influences the rate of bond formation. Increasing equilibrium bond length results in a higher number of receptor–ligand bonds due to an increased intercellular contact area. On-rate constants determine the rate of bond formation, while off-rates control the average number of bonds by modulating bond lifetimes. Application of an external pulling force leads to time-dependent on- and off-rates and causes bond rupture. Moreover, the time required for bond rupture in response to an external force is inversely proportional to the applied load and decreases with increasing off-rate.     

Detection and localization of single molecular recognition events using atomic force microscopy

Because of its piconewton force sensitivity and nanometer positional accuracy, the atomic force microscope (AFM) has emerged as a powerful tool for exploring the forces and the dynamics of the interaction between individual ligands and receptors, either on isolated molecules or on cellular surfaces. These studies require attaching specific biomolecules or cells on AFM tips and on solid supports and measuring the unbinding forces between the modified surfaces using AFM force spectroscopy. In this review, we describe the current methodology for molecular recognition studies using the AFM, with an emphasis on strategies available for preparing AFM tips and samples, and on procedures for detecting and localizing single molecular recognition events.