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.     

Looking inside molecular bonds at biological interfaces with dynamic force spectroscopy

Weak non-covalent interactions between large molecules govern interfacial structure and adhesion in biology. Because of thermal activation, these bonds have modest lifetimes and bond lifetimes are progressively shortened under application of external force. Theory predicts that bond survival time depends on how fast the force is applied and the expected survival time specifies the most likely breakage force (strength) at a given loading rate (force/time). Plotted as a function of log(e) (loading rate), the dynamic spectrum of bond strength provides an image of the prominent barriers traversed in the energy landscape along the unbinding pathway, which establishes a direct link between measurements of bond force and molecular-scale chemistry. Experimentally, the challenge is to measure bond strength over several orders of magnitude in loading rate. With a recently designed probe technique, we have measured strengths of single receptor-ligand bonds and receptor-membrane anchoring over an enormous range of loading rates from 10(-1) pN/s to 10(5) pN/s, which reveals an inner view of the complexity of these interactions.     

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.     

Nano- to microscale dynamics of P-selectin detachment from leukocyte interfaces. II. Tether flow terminated by P-selectin dissociation from PSGL-1

We have used a biomembrane force probe decorated with P-selectin to form point attachments with PSGL-1 receptors on a human neutrophil (PMN) in a calcium-containing medium and then to quantify the forces experienced by the attachment during retraction of the PMN at fixed speed. From first touch to final detachment, the typical force history exhibited the following sequence of events: i), an initial linear-elastic displacement of the PMN surface, ii), an abrupt crossover to viscoplastic flow that signaled membrane separation from the interior cytoskeleton and the beginning of a membrane tether, and iii), the final detachment from the probe tip most often by one precipitous step of P-selectin:PSGL-1 dissociation. Analyzing the initial elastic response and membrane unbinding from the cytoskeleton in our companion article I, we focus in this article on the regime of tether extrusion that nearly always occurred before release of the extracellular adhesion bond at pulling speeds > or =1 microm/s. The force during tether growth appeared to approach a plateau at long times. Examined over a large range of pulling speeds up to 150 microm/s, the plateau force exhibited a significant shear thinning as indicated by a weak power-law dependence on pulling speed, f(infinity) = 60 pN(nu(pull)/microm/s)(0.25). Using this shear-thinning response to describe the viscous element in a nonlinear Maxwell-like fluid model, we show that a weak serial-elastic component with a stiffness of approximately 0.07 pN/nm provides good agreement with the time course of the tether force approach to the plateau under constant pulling speed.     

Cooperative adhesion of ligand-receptor bonds

Cooperative (simultaneous) breakage of multiple adhesive bonds has been proposed as a mechanism for enhanced binding strength between adhesion molecules on apposing cell surfaces. In this report, we used the atomic force microscopy (AFM) to study how changes in binding affinity and separation rate of force-induced ligand-receptor dissociation affect binding cooperativity. The AFM force measurements were carried out using (strept)avidin-functionalized cantilever tips and biotinylated agarose beads under conditions where multiple (strept)avidin-biotin linkages were formed following surface contact. At slow surface separation of the AFM cantilever from the bead's surface, the (strept)avidin-biotin linkages appeared to rupture sequentially. Increasing the separation rate from 210 to 1950 nm/s led to a linear increase in the average rupture force. Moreover, force histograms revealed a quantized force distribution that shifted toward higher values with increasing separation rate. In measurements of streptavidin-iminobiotin adhesion, the force distribution also shifted toward higher values when the buffer was adjusted to a higher pH to raise the binding affinity. Together, these results demonstrate that the cooperativity of ligand-receptor bonds is significantly enhanced by increases in surface separation rate and/or binding affinity.     

Forced detachment of the CD2-CD58 complex

The force-induced detachment of the adhesion protein complex CD2-CD58 was studied by steered molecular dynamics simulations. The forced detachment of CD2 and CD58 shows that the system can respond to an external force by two mechanisms, which depend on the loading rate. At the rapid loading rates of 70 and 35 pN/ps (pulling speeds of 1 and 0.5 A/ps) the two proteins unfold before they separate, whereas at slower loading rates of 7 and 3.5 pN/ps (pulling speeds of 0.1 and 0.05 A/ps), the proteins separate before the domains can unfold. When subjected to a constant force of 400 pN, the two proteins separated without significant structural distortion. These findings suggest that protein unfolding is not coupled to the adhesive function of CD2 and CD58. The simulations further confirm that salt bridges primarily determine the tensile strength of the protein-to-protein bond, and that the order of salt bridge rupture depends mainly on the position of the bond, relative to the line of action of the applied force. Salt bridges close to this line break first. The importance of each of the salt bridges for adhesion, determined from the simulations, correlates closely with their role in cell-to-cell adhesion and equilibrium binding determined by site-directed mutagenesis experiments.     

The coordination of spindle‐positioning forces during the asymmetric division of the Caenorhabditis elegans zygote

In Caenorhabditis elegans zygote, astral microtubules generate forces essential to position the mitotic spindle, by pushing against and pulling from the cortex. Measuring microtubule dynamics there, we revealed the presence of two populations, corresponding to pulling and pushing events. It offers a unique opportunity to study, under physiological conditions, the variations of both spindle‐positioning forces along space and time. We propose a threefold control of pulling force, by polarity, spindle position and mitotic progression. We showed that the sole anteroposterior asymmetry in dynein on‐rate, encoding pulling force imbalance, is sufficient to cause posterior spindle displacement. The positional regulation, reflecting the number of microtubule contacts in the posterior‐most region, reinforces this imbalance only in late anaphase. Furthermore, we exhibited the first direct proof that dynein processivity increases along mitosis. It reflects the temporal control of pulling forces, which strengthens at anaphase onset following mitotic progression and independently from chromatid separation. In contrast, the pushing force remains constant and symmetric and contributes to maintaining the spindle at the cell centre during metaphase.     

Monte Carlo simulation for single RNA unfolding by force

Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension ensemble, we focus on the mechanical behaviors of the RNA P5ab molecule, which include the unfolding force dependence on the pulling speed, the force-hysteresis phenomenon, and the coincidence of stretching-relaxing force-curves in thermal equilibrium. We particularly simulate the time traces of the end-to-end distance of the P5ab under the constant force in equilibrium, which also have been recorded in the recent experiment. The reaction rate constants for the folding and unfolding are calculated. Our results show that the agreement between the simulation and the experimental measurements is satisfactory.     

Nano- to microscale dynamics of P-selectin detachment from leukocyte interfaces. I. Membrane separation from the cytoskeleton

We have used a biomembrane force probe decorated with P-selectin to form point attachments with PSGL-1 receptors on a human neutrophil (PMN) in a calcium-containing medium and then to quantify the forces experienced by the attachment during retraction of the PMN at fixed speed. From first touch to final detachment, the typical force history exhibited the following sequence of events: i), an initial linear-elastic displacement of the PMN surface, ii), an abrupt crossover to viscoplastic flow that signaled membrane separation from the interior cytoskeleton and the beginning of a membrane tether, and iii), the final detachment from the probe tip by usually one precipitous step of P-selectin:PSGL-1 dissociation. In this first article I, we focus on the initial elastic response and its termination by membrane separation from the cytoskeleton, initiating tether formation. Quantifying membrane unbinding forces for rates of loading (force/time) in the elastic regime from 240 pN/s to 38,000 pN/s, we discovered that the force distributions agreed well with the theory for kinetically limited failure of a weak bond. The kinetic rate for membrane unbinding was found to increase as an exponential function of the pulling force, characterized by an e-fold scale in force of approximately 17 pN and a preexponential factor, or apparent unstressed off rate, of approximately 1/s. The rheological properties of tether growth subsequent to the membrane unbinding events are presented in a companion article II.     

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     

Exact low-force kinetics from high-force single-molecule unfolding events

Mechanical forces play a key role in crucial cellular processes involving force-bearing biomolecules, as well as in novel single-molecule pulling experiments. We present an exact method that enables one to extrapolate, to low (or zero) forces, entire time-correlation functions and kinetic rate constants from the conformational dynamics either simulated numerically or measured experimentally at a single, relatively higher, external force. The method has twofold relevance: 1), to extrapolate the kinetics at physiological force conditions from molecular dynamics trajectories generated at higher forces that accelerate conformational transitions; and 2), to extrapolate unfolding rates from experimental force-extension single-molecule curves. The theoretical formalism, based on stochastic path integral weights of Langevin trajectories, is presented for the constant-force, constant loading rate, and constant-velocity modes of the pulling experiments. For the first relevance, applications are described for simulating the conformational isomerization of alanine dipeptide; and for the second relevance, the single-molecule pulling of RNA is considered. The ability to assign a weight to each trace in the single-molecule data also suggests a means to quantitatively compare unfolding pathways under different conditions.     

Nucleosome dynamics between tension-induced states

We studied the dynamical behavior of a mononucleosome under tension using a theoretical model that takes into account the nucleosomal geometry, DNA elasticity, nonspecific DNA-protein binding, and effective repulsion between the two DNA turns. Using a dynamical Monte-Carlo simulation algorithm, we demonstrate that this model shows a behavior that for an appropriate set of parameters is in quantitative agreement with data from micromanipulation experiments on individual nucleosomes. All of the parameters of the model follow from the data obtained from two types of pulling experiments, namely, constant force and constant loading rate ensembles.     

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.     

Characterization of enhanced monovalent and bivalent thrombin DNA aptamer binding using single molecule force spectroscopy

Thrombin aptamer binding strength and stability is dependent on sterical parameters when used for atomic force microscopy sensing applications. Sterical improvements on the linker chemistry were developed for high-affinity binding. For this we applied single molecule force spectroscopy using two enhanced biotinylated thrombin aptamers, BFF and BFA immobilized on the atomic force microscopy tip via streptavidin. BFF is a dimer composed of two single-stranded aptamers (aptabody) connected to each other by a complementary sequence close to the biotinylated end. In contrast, BFA consists of a single DNA strand and a complementary strand in the supporting biotinylated part. By varying the pulling velocity in force-distance cycles the formed thrombin-aptamer complexes were ruptured at different force loadings allowing determination of the energy landscape. As a result, BFA aptamer showed a higher binding force at the investigated loading rates and a significantly lower dissociation rate constant, k_off, compared to BFF. Moreover, the potential of the aptabody BFF to form a bivalent complex could clearly be demonstrated.     

Use of the rat forelimb compression model to create discrete levels of bone damage in vivo

Skeletal responses to damage are significant for understanding the etiology of stress fractures and possibly osteoporotic fractures. We refined the rat forelimb-loading model to produce a range of sub-fracture damage levels during in vivo cyclic loading. A total of 98 right forelimbs of anesthetized, male, 5-month old Fischer rats were loaded cyclically (2 Hz) in axial compression. Rats were killed immediately after loading. In the first experiment, forelimbs were loaded to fracture, which occurred after an increase in peak displacement of 2.0+/-0.2 mm, independent of peak force or cycle number. In the next experiment, we loaded forelimbs at a constant peak force until the peak displacement increased by 0.6-1.8 mm (30-90% of fracture displacement). Mechanical properties of the loaded (right) and contralateral control (left) ulnae were determined ex vivo using three-point bending, and cracks were analyzed using micro-computed tomography. Results demonstrated a dose-response between increased forelimb displacement and increased ulnar damage, with four discrete damage levels. "Low" damage was produced by cyclic loading to 30% of fracture displacement, with no visible cracks and a 10% strength loss. "Mild" damage was produced by loading to 45% of fracture displacement, with variable linear cracks and 20% strength loss. "Moderate" damage was produced by loading to 60-75% of fracture displacement, with consistent linear cracks and 40% strength loss. "High" damage was produced by loading to 85-90% of fracture displacement, with branching cracks and 60% strength loss. This loading model will be useful for examining biological responses to a range of sub-fracture damage levels in future experiments.     

Force spectroscopy of LFA-1 and its ligands, ICAM-1 and ICAM-2

Single-molecule measurements of the interaction of leukocyte function-associated antigen-1 (LFA-1), expressed on Jurkat T cells, with intercellular adhesion molecules-1 and -2 (ICAM-1 and ICAM-2) were conducted using atomic force microscopy (AFM). The force spectra (i.e., unbinding force versus loading rate) of both the LFA-1/ICAM-1 and LFA-1/ICAM-2 interactions were acquired at a loading rate range covering 3 orders of magnitude (50-60,000 pN/s) and revealed a fast loading regime and a slow loading regime. This indicates that the dissociation of both complexes involves overcoming a steep inner and a wide outer activation barrier. LFA-1 binding to ICAM-1 and ICAM-2 was strengthened in the slow loading regime by the addition of Mg(2+). Differences in the dynamic strength of the LFA-1/ICAM-1 and LFA-1/ICAM-2 interactions can be attributed to the presence of wider barriers in the ICAM-2 complex, making it more responsive to a pulling force than the ICAM-1 complex.     

The solution to the streptavidin-biotin paradox: the influence of history on the strength of single molecular bonds

In the past few years, many studies have attempted to measure the strength of a single molecular bond. In general, these experiments consisted in pulling on the bond and measuring the force necessary to dissociate the molecules. However, seemingly contradictory experimental results led to draw the intriguing conclusion that the strength of the bond could depend on the experiment even if the pulling conditions are similar: this paradox was first observed on the widely used streptavidin-biotin bond. Here, by doing supplementary measurements and by reanalyzing the controversial experimental results using Kramers' theory, we show that they can be conciliated. This allows us to show that the strength of a bond is very sensitive to the history of its formation, which is the key to the paradox.     

Force spectroscopy of the leukocyte function-associated antigen-1/intercellular adhesion molecule-1 interaction

Interactions between leukocyte function-associated antigen-1 (LFA-1) with its cognate ligand, intercellular adhesion molecule-1 (ICAM-1) play a crucial role in leukocyte adhesion. Because the cell and its adhesive components are subject to external perturbation from the surrounding flow of blood, it is important to understand the binding properties of the LFA-1/ICAM-1 interaction in both steady state and in the presence of an external pulling force. Here we report on atomic force microscopy (AFM) measurements of the unbinding of LFA-1 from ICAM-1. The single molecule measurements revealed the energy landscape corresponding to the dissociation of the LFA-1/ICAM-1 complex and provided the basis for defining the energetic determinants of the complex at equilibrium and under the influence of an external force. The AFM force measurements were performed in an experimental system consisting of an LFA-1-expressing T cell hybridoma, 3A9, attached to the end of the AFM cantilever and an apposing surface expressing ICAM-1. In measurements covering three orders of magnitude change in force loading rate, the LFA-1/ICAM-1 force spectrum (i.e., unbinding force versus loading rate) revealed a fast and a slow loading regime that characterized a steep inner activation barrier and a wide outer activation barrier, respectively. The addition of Mg(2+), a cofactor that stabilizes the LFA-1/ICAM-1 interaction, elevated the unbinding force of the complex in the slow loading regime. In contrast, the presence of EDTA suppressed the inner barrier of the LFA-1/ICAM-1 complex. These results suggest that the equilibrium dissociation constant of the LFA-1/ICAM-1 interaction is regulated by the energetics of the outer activation barrier of the complex, while the ability of the complex to resist a pulling force is determined by the divalent cation-dependent inner activation barrier.     

Two-dimensional kinetics of inter-connexin interactions from single-molecule force spectroscopy

Gap junction channels are intercellular channels that form by docking the extracellular loops of connexin protein subunits. While the structure and function of gap junctions as intercellular channels have been characterized using different techniques, the physics of the inter-connexin interaction remain unknown. Moreover, as far as we know, the capacity of gap junction channels to work as adhesion complexes supporting pulling forces has not yet been quantitatively addressed. We report the first quantitative characterization of the kinetics and binding strength of the interaction of a short peptide mimicking extracellular loop 2 of Cx26 with membrane-reconstituted Cx26, combining the imaging and force spectroscopy capabilities of atomic force microscopy. The fast dissociation rate inferred a dynamic bond, while the slow association rate reflected the reduced flexibility and small size of extracellular loops. Our results propose the gap junction channel as an adhesion complex that associates slowly and dissociates fast at low force but is able to support important pulling forces in its native, hexameric form.