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.     

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.     

Temperature Dependence of Unbinding Forces between Complementary DNA Strands

Force probe techniques such as atomic force microscopy can directly measure the force required to rupture single biological ligand receptor bonds. Such forces are related to the energy landscape of these weak, noncovalent biological interactions. We report unbinding force measurements between complementary strands of DNA as a function of temperature. Our measurements emphasize the entropic contributions to the energy landscape of the bond.     

Investigating the binding behaviour of two avidin‐based testosterone binders using molecular recognition force spectroscopy

Molecular recognition force spectroscopy, a biosensing atomic force microscopy technique allows to characterise the dissociation of ligand–receptor complexes at the molecular level. Here, we used molecular recognition force spectroscopy to study the binding capability of recently developed testosterone binders. The two avidin‐based proteins called sbAvd‐1 and sbAvd‐2 are expected to bind both testosterone and biotin but differ in their binding behaviour towards these ligands. To explore the ligand binding and dissociation energy landscape of these proteins, we tethered biotin or testosterone to the atomic force microscopy probe while the testosterone‐binding protein was immobilized on the surface. Repeated formation and rupture of the ligand–receptor complex at different pulling velocities allowed determination of the loading rate dependence of the complex‐rupturing force. In this way, we obtained the molecular dissociation rate (k_off) and energy landscape distances (x_β) of the four possible complexes: sbAvd‐1‐biotin, sbAvd‐1‐testosterone, sbAvd‐2‐biotin and sbAvd‐2‐testosterone. It was found that the kinetic off‐rates for both proteins and both ligands are similar. In contrast, the x_β values, as well as the probability of complex formations, varied considerably. In addition, competitive binding experiments with biotin and testosterone in solution differ significantly for the two testosterone‐binding proteins, implying a decreased cross‐reactivity of sbAvd‐2. Unravelling the binding behaviour of the investigated testosterone‐binding proteins is expected to improve their usability for possible sensing applications. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

Association Kinetics from Single Molecule Force Spectroscopy Measurements

Single molecule force spectroscopy is often used to study the dissociation of single molecules by applying mechanical force to the intermolecular bond. These measurements provide the kinetic parameters of dissociation. We present what to our knowledge is a new atomic force microscopy-based approach to obtain the activation energy of the association reaction and approximate grafting density of reactive receptors using the dependence of the probability to form molecular bonds on probe velocity when one of the interacting molecules is tethered by a flexible polymeric linker to the atomic force microscopy probe. Possible errors in the activation energy measured with this approach are considered and resulting corrections are included in the data analysis. This new approach uses the same experimental setup as traditional force spectroscopy measurements that quantify dissociation kinetics. We apply the developed methodology to measure the activation energy of biotin-streptavidin association (including a contribution from the steric factor) and obtain a value of 8 ± 1 kT. This value is consistent with the association rate measured previously in solution. Comparison with the solution-derived activation energy indicates that kinetics of biotin-streptavidin binding is mainly controlled by the reaction step.     

Direct measurement of the interaction force between immunostimulatory CpG-DNA and TLR9 fusion protein

The specific interaction between human Toll-like receptor 9 (TLR9)-ectodomain (ECD)-fusion protein and immunostimulatory CpG-DNA was measured using force spectroscopy. Flexible tethers were used between receptors and surface as well as between DNA and atomic force microscope tip to make efficient recognition studies possible. The molecular recognition forces detected are in the range of 50 to 150 ± 20 pN at the used force-loading rates, and the molecular interaction probability was much reduced when the receptors were blocked with free CpG-DNA. A linear increase of the unbinding force with the logarithm of the loading rate was found over the range 0.1 to 30 nN/s. This indicates a single potential barrier characterizing the energy landscape and no intermediate state for the unbinding pathway of CpG-DNA from the TLR9-ECD. Two important kinetic parameters for CpG-DNA interaction with TLR9-ECD were determined from the force-loading rate dependency: an off-rate of k(off) = 0.14 ± 0.10 s(-1) and a binding interaction length of x(β) = 0.30 ± 0.03 nm, which are consistent with literature values. Various models for the molecular interaction of this innate immune receptor binding to CpG-DNA are discussed.     

Hydrodynamic effects in fast AFM single-molecule force measurements

Atomic force microscopy (AFM) allows the critical forces that unfold single proteins and rupture individual receptor–ligand bonds to be measured. To derive the shape of the energy landscape, the dynamic strength of the system is probed at different force loading rates. This is usually achieved by varying the pulling speed between a few nm/s and a few m/s, although for a more complete investigation of the kinetic properties higher speeds are desirable. Above 10 m/s, the hydrodynamic drag force acting on the AFM cantilever reaches the same order of magnitude as the molecular forces. This has limited the maximum pulling speed in AFM single-molecule force spectroscopy experiments. Here, we present an approach for considering these hydrodynamic effects, thereby allowing a correct evaluation of AFM force measurements recorded over an extended range of pulling speeds (and thus loading rates). To support and illustrate our theoretical considerations, we experimentally evaluated the mechanical unfolding of a multi-domain protein recorded at 30 m/s pulling speed.Abbrevations AFM atomic force micrcoscopy - pN piconewton - BR bacteriorhodopsin - DFS dynamic force spectroscopy - Ig27 immunoglobulin 27 - If27-8 immunoglobulin 27 octameric construct - BFP biomembrane force probe     

Force-Induced Lysozyme—HyHEL5 Antibody Dissociation and Its Analysis by Means of a Cooperative Binding Model

Dynamic force spectroscopy probes the kinetic properties of molecules interacting with each other such as antibody-antigen, receptor-ligand, etc. In this article, a statistical model for the dissociation of such cooperative systems is presented. The partner molecules are assumed to be linked by a number of relatively weak bonds that can be grouped together into cooperative units. Single bonds are assumed to open and close statistically. Our model was used to analyze molecular recognition experiments of single receptor-ligand pairs in which the two molecules are brought into contact using an atomic force microscope, which leads to the formation of a strong and specific bond. Then a prescribed time-dependent force is applied to the complex and the statistical distribution of forces needed to pull the molecules completely apart is measured. This quantity is also calculated from our model. Furthermore, its dependence on the model parameters, such as binding free energy, number of bonds and groups, number of cooperative elementary bonds and degree of cooperativity within a group, influence of the force on the binding free energy, and the rate of change of the pulling force, is determined.     

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.     

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.     

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.     

Multiple-bond kinetics from single-molecule pulling experiments: evidence for multiple NCAM bonds

The kinetic parameters of single bonds between neural cell adhesion molecules were determined from atomic force microscope measurements of the forced dissociation of the homophilic protein-protein bonds. The analytical approach described provides a systematic procedure for obtaining rupture kinetics for single protein bonds from bond breakage frequency distributions obtained from single-molecule pulling experiments. For these studies, we used the neural cell adhesion molecule (NCAM), which was recently shown to form two independent protein bonds. The analysis of the bond rupture data at different loading rates, using the single-bond full microscopic model, indicates that the breakage frequency distribution is most sensitive to the distance to the transition state and least sensitive to the molecular spring constant. The analysis of bond failure data, however, motivates the use of a double-bond microscopic model that requires an additional kinetic parameter. This double-bond microscopic model assumes two independent NCAM-NCAM bonds, and more accurately describes the breakage frequency distribution, particularly at high loading rates. This finding agrees with recent surface-force measurements, which showed that NCAM forms two spatially distinct bonds between opposed proteins.     

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.     

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.     

Molecular dynamics study of unbinding of the avidin-biotin complex.

We report molecular dynamics simulations that induce, over periods of 40-500 ps, the unbinding of biotin from avidin by means of external harmonic forces with force constants close to those of AFM cantilevers. The applied forces are sufficiently large to reduce the overall binding energy enough to yield unbinding within the measurement time. Our study complements earlier work on biotin-streptavidin that employed a much larger harmonic force constant. The simulations reveal a variety of unbinding pathways, the role of key residues contributing to adhesion as well as the spatial range over which avidin binds biotin. In contrast to the previous studies, the calculated rupture forces exceed by far those observed. We demonstrate, in the framework of models expressed in terms of one-dimensional Langevin equations with a schematic binding potential, the associated Smoluchowski equations, and the theory of first passage times, that picosecond to nanosecond simulation of ligand unbinding requires such strong forces that the resulting protein-ligand motion proceeds far from the thermally activated regime of millisecond AFM experiments, and that simulated unbinding cannot be readily extrapolated to the experimentally observed rupture.     

Graphical method for force analysis: macromolecular mechanics with atomic force microscopy

We present a graphical method for a unifying, quantitative analysis of molecular bonding-force measurements by atomic force microscopy (AFM). The method is applied to interpreting a range of phenomena commonly observed in the experimental AFM measurements of noncovalent, weak bonds between biological macromolecules. The analysis suggests an energy landscape underlying the intermolecular force and demonstrates that many observations, such as "snaps-on," "jumps-off," and hysteresis loops, are different manifestations of a double-well energy landscape. The analysis gives concrete definitions for the operationally defined "attractive" and "adhesive" forces in terms of molecular parameters. It is shown that these operationally defined quantities are usually functions of the experimental setup, such as the stiffness of the force probe and the rate of its movement. The analysis reveals a mechanical instability due to the multistate nature of molecular interactions and provides new insight into macromolecular viscosity. The graphical method can equally be applied to a quantitative analysis of multiple unfolding of subunits of the giant muscle protein titin under AFM.     

Force spectroscopy of the double-tethered concanavalin-A mannose bond

We present the measurement of the force required to rupture a single protein-sugar bond using a methodology that provides selective discrimination between specific and nonspecific binding events and helps verify the presence of a single functional molecule on the atomic force microscopy tip. In particular, the interaction force between a polymer-tethered concanavalin-A protein (ConA) and a similarly tethered mannose carbohydrate was measured as 47 +/- 9 pN at a bond loading rate of approximately 10 nN/s. Computer simulations of the polymer molecular configurations were used to determine the angles that the polymers could sweep out during binding and, in conjunction with mass spectrometry, used to separate the angular effects from the effects due to a distribution of tether lengths. We find that when using commercially available polymer tethers that vary in length from 19 to 29 nm, the angular effects are relatively small and the rupture distributions are dominated by the 10-nm width of the tether length distribution. In all, we show that tethering both a protein and its ligand allows for the determination of the single-molecule bond rupture force with high sensitivity and includes some validation for the presence of a single-tethered functional molecule on the atomic force microscopy tip.     

Temperature softening of a protein in single-molecule experiments

Mechanical flexibility is crucial for the function of proteins. However, such material properties are not easily accessible experimentally. We used single-molecule force spectroscopy to study the stiffness of a single domain of Dictyostelium discoideum filamin (ddFLN4) in a temperature range from 5 degrees C to 37 degrees C. Analyzing the distributions of unfolding forces allowed us to extract transition barrier heights and positions of the underlying energy landscape. We found a marked narrowing of unfolding force distributions with increasing temperature. This narrowing reflects an increase in transition state position from 2.7 A to 7.8 A and thus a reduction of the molecular spring constant of the protein by a factor of 7. We suggest this temperature softening reflects a shift in the nature of the interactions responsible for mechanical stability from hydrogen bonds to hydrophobic interactions. This result has important consequences for all interpretations of protein mechanical studies if experimental results obtained at room temperature are to be transferred to physiological temperatures.