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.     

Application of atomic force microscopy for characteristics of single intermolecular interactions

Atomic force microscopy (AFM) can be used to make measurements in vacuum, air, and water. The method is able to gather information about intermolecular interaction forces at the level of single molecules. This review encompasses experimental and theoretical data on the characterization of ligand-receptor interactions by AFM. The advantage of AFM in comparison with other methods developed for the characterization of single molecular interactions is its ability to estimate not only rupture forces, but also thermodynamic and kinetic parameters of the rupture of a complex. The specific features of force spectroscopy applied to ligand-receptor interactions are examined in this review from the stage of the modification of the substrate and the cantilever up to the processing and interpretation of the data. We show the specificities of the statistical analysis of the array of data based on the results of AFM measurements, and we discuss transformation of data into thermodynamic and kinetic parameters (kinetic dissociation constant, Gibbs free energy, enthalpy, and entropy). Particular attention is paid to the study of polyvalent interactions, where the definition of the constants is hampered due to the complex stoichiometry of the reactions.     

Dynamic force spectroscopy of the digoxigenin-antibody complex

Small ligands and their receptors are widely used non-covalent couplers in various biotech applications. One prominent example, the digoxigenin-antibody complex, was often used to immobilize samples for single molecule force measurements by optical trap or AFM. Here, we employed dynamic AFM spectroscopy to demonstrate that a single digoxigenin-antibody bond is likely to fail even under moderate loading rates. This effect potentially could lower the yield of measurements or even obscure the unbinding data of the sample by the rupture events of the coupler. Immobilization by multiple antibody-antigen bonds, therefore, is highly recommended. The analysis of our data revealed a pronounced loading rate dependence of the rupture force, which we analyzed based on the well-established Bell-Evans-model with two subsequent unbinding barriers. We could show that the first barrier has a width of Deltax(1)=1.15 nm and a spontaneous rate of k(off1)=0.015 s(-1) and the second has a width of Deltax(2)=0.35 nm and a spontaneous rate of k(off2)=4.56 s(-1). In the crossover region between the two regimes, we found a marked discrepancy between the predicted bond rupture probability density and the measured rupture force histograms, which we discuss as non-Markovian contribution to the unbinding process.     

Effect of viscoelasticity on the analysis of single-molecule force spectroscopy on live cells

Single-molecule force spectroscopy is used to probe the kinetics of receptor-ligand bonds by applying mechanical forces to an intermediate media on which the molecules reside. When this intermediate media is a live cell, the viscoelastic properties can affect the calculation of rate constants. We theoretically investigate the effect of media viscoelasticity on the common assumption that the bond force is equal to the instantaneous applied force. Dynamic force spectroscopy is simulated between two cells of varying micromechanical properties adhered by a single bond with a constant kinetic off-rate. We show that cell and microvilli deformation, and hydrodynamic drag contribute to bond forces that can be 28-90% lower than the applied force for loading rates of 10(3)-10(7) pN/s, resulting in longer bond lifetimes. These longer bond lifetimes are not caused by changes in bond kinetics; rather, they are due to the mechanical response of the intermediate media on which the bonds reside. Under the assumption that the instantaneous bond force is equal to the applied force--thereby ignoring viscoelasticity--leads to 14-39% error in the determination of off-rates. We present an approach that incorporates viscoelastic properties in calculating the instantaneous bond force and kinetic dissociation parameter of the intermolecular bond.     

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.     

Direct measurements of the mechanical stability of zinc-thiolate bonds in rubredoxin by single-molecule atomic force microscopy

Zinc (Zn) is one of the most abundant metals and is essential for life. Through ligand interactions, often with thiolate from cysteine residues in proteins, Zn can play important structural roles in organizing protein structure and augmenting protein folding and stability. However, it is difficult to separate the contributions of Zn-ligand interactions from those originating from intrinsic protein folding in experimental studies of Zn-containing metalloproteins, which makes the study of Zn-ligand interactions in proteins challenging. Here, we used single-molecule force spectroscopy to directly measure the mechanical rupture force of the Zn-thiolate bond in Zn-rubredoxin. Our results show that considerable force is needed to rupture Zn-thiolate bonds (∼170 pN, which is significantly higher than the force necessary to rupture the coordination bond between Zn and histidines). To our knowledge, our study not only provides new information about Zn-thiolate bonds in rubredoxin, it also opens a new avenue for studying metal-ligand bonds in proteins using single-molecule force spectroscopy.     

Biomolecule Association Rates Do Not Provide a Complete Description of Bond Formation

The efficiency of many cell-surface receptors is dependent on the rate of binding soluble or surface-attached ligands. Much effort was exerted to measure association rates between soluble molecules (three-dimensional k_on) and, more recently, between surface-attached molecules (two-dimensional [2D] k_on). According to a generally accepted assumption, the probability of bond formation between receptors and ligands is proportional to the first power of encounter duration. Here we provide new experimental evidence and review published data demonstrating that this simple assumption is not always warranted. Using as a model system the (2D) interaction between ICAM-1-coated surfaces and flowing microspheres coated with specific anti-ICAM-1 antibodies, we show that the probability of bond formation may scale as a power of encounter duration that is significantly higher than 1. Further, we show that experimental data may be accounted for by modeling ligand-receptor interaction as a displacement along a single path of a rough energy landscape. Under a wide range of conditions, the probability that an encounter of duration t resulted in bond formation varied as erfc[(t₀/t)^1/2], where t₀ was on the order of 10 ms. We conclude that the minimum contact time for bond formation may be a useful parameter to describe a ligand-receptor interaction, in addition to conventional association rates.     

Dynamic strength of the interaction between lung surfactant protein D (SP-D) and saccharide ligands

In order to investigate the dynamic strength of the interaction between lung surfactant protein D (SP-D) and different sugars, maltose, mannose, glucose, and galactose, we have used an atomic force microscope to monitor the interaction on a single molecule scale. The experiment is performed by measuring the rupture force when the SP-D-sugar bond is subjected to a continuously increasing force. Under these dynamic conditions, SP-D binds strongest to d-mannose and weakest to maltose and d-galactose. These results differ from equilibrium measurements wherein SP-D exhibits preference for maltose. On the basis of this finding, we propose that the binding of the disaccharide maltose to SP-D, which is energetically stronger than the binding of any of the monosacchrides, alters the structure of the binding site in a way that lowers the dynamic strength of the bond. We conclude that determining the strength of a protein-ligand bond under dynamic stress using an atomic force microscope is possibly more relevant for mimicking the actual nonequilibrium physiological situation in the lungs.     

Catch Bond Interaction between Cell-Surface Sulfatase Sulf1 and Glycosaminoglycans

In biological adhesion, the biophysical mechanism of specific biomolecular interaction can be divided in slip and catch bonds, respectively. Conceptually, slip bonds exhibit a reduced bond lifetime under increased external force and catch bonds, in contrast, exhibit an increased lifetime (for a certain force interval). Since 2003, a handful of biological systems have been identified to display catch bond properties. Upon investigating the specific interaction between the unique hydrophilic domain (HD) of the human cell-surface sulfatase Sulf1 against its physiological glycosaminoglycan (GAG) target heparan sulfate (HS) by single molecule force spectroscopy (SMFS), we found clear evidence of catch bond behavior in this system. The HD, ∼320 amino acids long with dominant positive charge, and its interaction with sulfated GAG-polymers were quantitatively investigated using atomic force microscopy (AFM) based force clamp spectroscopy (FCS) and dynamic force spectroscopy (DFS). In FCS experiments, we found that the catch bond character of HD against GAGs could be attributed to the GAG 6-O-sulfation site whereas only slip bond interaction can be observed in a GAG system where this site is explicitly lacking. We interpreted the binding data within the theoretical framework of a two state two path model, where two slip bonds are coupled forming a double-well interaction potential with an energy difference of ΔE ≈ 9 k_BT and a compliance length of Δx ≈ 3.2 nm. Additional DFS experiments support this assumption and allow identification of these two coupled slip-bond states that behave consistently within the Kramers-Bell-Evans model of force-mediated dissociation.     

The role of flexible tethers in multiple ligand-receptor bond formation between curved surfaces

Ligands mounted to surfaces via extensible tethers are present in nature and represent a growing class of molecules used to engineer adhesion in drug targeting, biosensing, self-assembling nanostructures, and in other biophysical research. Using a continuum approach with geometric and thermodynamic arguments, we derive a number of analytical expressions that relate key properties of single-tethered ligand-receptor interactions to multiple bond formation between curved surfaces. The theoretical predictions are in good agreement with measurements made with the surface forces apparatus. We establish that, when ligated, many tethers commonly used in biophysical research exhibit a discrete binding range that can be accurately measured with force spectroscopy. The distribution of bound ligated tethers is independent of the surfaces' interaction radius, R. The bridging force scales linearly with R, the tether's effective spring constant and grafting density, and with the ligand-receptor bond energy when the surfaces are in direct contact. These results are contrasted to bridging forces that evolve between plane-parallel geometries. Last, we show how our simple analytical reductions can be used to predict adhesive forces for STEALTH liposomes and other targeted and self-assembled nanoparticles.     

Two Barriers or not? Dynamic Force Spectroscopy on the Integrin α7β1 Invasin Complex

Dynamic force spectroscopy was used to test force-induced dissociation of the complex between the integrin α₇β₁ and the bacterial protein invasin. Both proteins were used in truncated forms comprising the respective binding sites. Using the biomembrane force-probe, the bond system was exposed to 14 different loading rates ranging from 18 pN/s to 5.3 nN/s. At each rate, bond rupture spectra were collected. Median forces ranged from 8 to 72 pN. These showed two linear regimes when plotted against the logarithm of the force-loading rate. However, a statistical analysis of the full rupture force spectra including the detection limits of the setup showed that all measured data are well described by dissociation over a single barrier.     

Methods and estimations of uncertainties in single-molecule dynamic force spectroscopy

In dynamic force spectroscopy, access to the characteristic parameters of single molecular bonds requires nontrivial measurements and data processing as the rupture forces are found not only to be distributed over a wide range, but are also dependent on the loading rate. The choice of measurement procedure and data processing methods has a considerable impact on the accuracy and precision of the final results. We analyze, by means of numerical simulations, methods to minimize and assess the magnitude of the expected errors for different combinations of experimental and evaluation methods. It was found that the choice of fitting function is crucial to extract correct parameter values. Applying a Gaussian function, which is a common practice, is equivalent to introducing a systematic error, and leads to a consequent overestimation of the thermal off-rate by more than 30%. We found that the precision of the bond length and the thermal off-rate, in presence of unbiased noise, were improved by reducing the number of loading rates for a given number of measurements. Finally, the results suggest that the minimum number of measurements needed to obtain the bond strength, with acceptable precision, exceeds the common number of ~100 reported in literature.     

Single-molecule recognition force spectroscopy of transmembrane transporters on living cells

Atomic force microscopy (AFM) has proven to be a powerful tool in biological sciences. Its particular advantage over other high-resolution methods commonly used is that biomolecules can be investigated not only under physiological conditions but also while they perform their biological functions. Single-molecule force spectroscopy with AFM tip-modification techniques can provide insight into intermolecular forces between individual ligand-receptor pairs of biological systems. Here we present protocols for force spectroscopy of living cells, including cell sample preparation, tip chemistry, step-by-step AFM imaging, force spectroscopy and data analysis. We also delineate critical steps and describe limitations that we have experienced. The entire protocol can be completed in 12 h. The model studies discussed here demonstrate the power of AFM for studying transmembrane transporters at the single-molecule level.     

Energy landscape of streptavidin-biotin complexes measured by atomic force microscopy

The dissociation of ligand and receptor involves multiple transitions between intermediate states formed during the unbinding process. In this paper, we explored the energy landscape of the streptavidin-biotin interaction by using the atomic force microscope (AFM) to measure the unbinding dynamics of individual ligand-receptor complexes. The rupture force of the streptavidin-biotin bond increased more than 2-fold over a range of loading rates between 100 and 5000 pN/s. Moreover, the force measurements showed two regimes of loading in the streptavidin-biotin force spectrum, revealing the presence of two activation barriers in the unbinding process. Parallel experiments carried out with a streptavidin mutant (W120F) were used to investigate the molecular determinants of the activation barriers. From these experiments, we attributed the outer activation barrier in the energy landscape to the molecular interaction of the '3-4' loop of streptavidin that closes behind biotin.     

Direct and Model Free Calculation of Force-Dependent Dissociation Rates from Force Spectroscopic Data

Force spectroscopy allows testing the free energy landscapes of molecular interactions. Usually, the dependency of the most probable rupture force on the force rate or the shape of the rupture force histogram is fitted with different models that contain approximations and basic assumptions. We present a simple and model free approach to extract the force-dependent dissociation rates directly from the force curve data. Simulations show that the dissociation rates at any force are given directly by the ratio of the number of detected rupture events to the time this force was acting on the bond. To calculate these total times of acting forces, all force curve data points of all curves measured are taken into account, which significantly increases the amount of information which is considered for data analysis compared to other methods. Moreover, by providing force-dependent dissociation rates this method allows direct testing and validating of any energy landscape model.     

Model energy landscapes and the force-induced dissociation of ligand-receptor bonds

We discuss models for the force-induced dissociation of a ligand-receptor bond, occurring in the context of cell adhesion or single molecule unbinding force measurements. We consider a bond with a structured energy landscape which is modeled by a network of force dependent transition rates between intermediate states. The behavior of a model with only one intermediate state and a model describing a molecular zipper is studied. We calculate the bond lifetime as a function of an applied force and unbinding forces under an increasing applied load and determine the relationship between both quantities. The dissociation via an intermediate state can lead to distinct functional relations of the bond lifetime on force. One possibility is the occurrence of three force regimes where the lifetime of the bond is determined by different transitions within the energy landscape. This case can be related to recent experimental observations of the force-induced dissociation of single avidin-biotin bonds.     

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.     

原子力显微镜单分子力谱研究生物分子间相互作用

原子力显微镜单分子力谱是近年来发展起来的能在单分子水平研究生物分子相互作用的新工具。本文综述了单分子力谱的测定原理、方法及其在研究蛋白．蛋白、蛋白-DNA相互作用,蛋白质去折叠和活细胞上配体／受体结合中的应用进展。     

Two Barriers or not? Dynamic Force Spectroscopy on the Integrin α7β1 Invasin Complex

Dynamic force spectroscopy was used to test force-induced dissociation of the complex between the integrin α₇β₁ and the bacterial protein invasin. Both proteins were used in truncated forms comprising the respective binding sites. Using the biomembrane force-probe, the bond system was exposed to 14 different loading rates ranging from 18 pN/s to 5.3 nN/s. At each rate, bond rupture spectra were collected. Median forces ranged from 8 to 72 pN. These showed two linear regimes when plotted against the logarithm of the force-loading rate. However, a statistical analysis of the full rupture force spectra including the detection limits of the setup showed that all measured data are well described by dissociation over a single barrier.