Extending Bell's model: how force transducer stiffness alters measured unbinding forces and kinetics of molecular complexes

Forced unbinding of complementary macromolecules such as ligand-receptor complexes can reveal energetic and kinetic details governing physiological processes ranging from cellular adhesion to drug metabolism. Although molecular-level experiments have enabled sampling of individual ligand-receptor complex dissociation events, disparities in measured unbinding force F_R among these methods lead to marked variation in inferred binding energetics and kinetics at equilibrium. These discrepancies are documented for even the ubiquitous ligand-receptor pair, biotin-streptavidin. We investigated these disparities and examined atomic-level unbinding trajectories via steered molecular dynamics simulations, as well as via molecular force spectroscopy experiments on biotin-streptavidin. In addition to the well-known loading rate dependence of F_R predicted by Bell's model, we find that experimentally accessible parameters such as the effective stiffness of the force transducer k can significantly perturb the energy landscape and the apparent unbinding force of the complex for sufficiently stiff force transducers. Additionally, at least 20% variation in unbinding force can be attributed to minute differences in initial atomic positions among energetically and structurally comparable complexes. For force transducers typical of molecular force spectroscopy experiments and atomistic simulations, this energy barrier perturbation results in extrapolated energetic and kinetic parameters of the complex that depend strongly on k. We present a model that explicitly includes the effect of k on apparent unbinding force of the ligand-receptor complex, and demonstrate that this correction enables prediction of unbinding distances and dissociation rates that are decoupled from the stiffness of actual or simulated molecular linkers.     

Membrane-based actuation for high-speed single molecule force spectroscopy studies using AFM

Atomic force microscopy (AFM)-based dynamic force spectroscopy of single molecular interactions involves characterizing unbinding/unfolding force distributions over a range of pulling speeds. Owing to their size and stiffness, AFM cantilevers are adversely affected by hydrodynamic forces, especially at pulling speeds >10 μm/s, when the viscous drag becomes comparable to the unbinding/unfolding forces. To circumvent these adverse effects, we have fabricated polymer-based membranes capable of actuating commercial AFM cantilevers at speeds ≥100 μm/s with minimal viscous drag effects. We have used FLUENT^®, a computational fluid dynamics (CFD) software, to simulate high-speed pulling and fast actuation of AFM cantilevers and membranes in different experimental configurations. The simulation results support the experimental findings on a variety of commercial AFM cantilevers and predict significant reduction in drag forces when membrane actuators are used. Unbinding force experiments involving human antibodies using these membranes demonstrate that it is possible to achieve bond loading rates ≥10⁶ pN/s, an order of magnitude greater than that reported with commercial AFM cantilevers and systems.     

Exploring the Energy Profile of Human IgG/Rat Anti-human IgG Interactions by Dynamic Force Spectroscopy

Interactions between antibody and antigen molecules play essential roles in biological recognition processes as well as medical diagnosis. Therefore, an understanding of the underlying mechanism of antibody?Cantigen interactions at the single molecular level would be beneficial. In the present study, human immunoglobulin (IgG) tethered cantilevers and rat anti-human IgG functionalized gold surfaces were fabricated by using self-assembled monolayers method. Dynamic force spectroscopy was employed to characterize the interactions between human (IgG) and rat anti-human IgG at the single-molecule level. The unbinding forces were determined to be 44.6?±?0.8, 65.8?±?3.0, 108.1?±?4.1, 131.1?±?11.2, 149.5?±?4.7, 239.5?±?3.1 and 294.7?±?7.7?pN with ramping loading rates of 514, 1,127, 3,058, 7,215, 15,286, 31,974 and 50,468?pN?s^-1, respectively. In addition, the unbinding forces were found to be increasing with the logarithm of apparent loading rates in a linear way. Fitting data group resulted in two distinct linear parts, suggesting there are two energy barriers. The corresponding distances in the bound and transition states (x _?? ) and the dissociation rates (K _off ) were calculated to be 0.129?±?0.006?nm, 3.986?±?0.162?s^?1 for the outer barrier and 0.034?±?0.001?nm, 36.754?±?0.084?s^?1 for the inner barrier. Such findings hold promise of screening novel drugs and discerning different unbinding modes of biological molecules.     

Force-based analysis of multidimensional energy landscapes: application of dynamic force spectroscopy and steered molecular dynamics simulations to an antibody fragment-peptide complex

Multidimensional energy landscapes are an intrinsic property of proteins and define their dynamic behavior as well as their response to external stimuli. In order to explore the energy landscape and its implications on the dynamic function of proteins dynamic force spectroscopy and steered molecular dynamics (SMD) simulations have proved to be important tools. In this study, these techniques have been employed to analyze the influence of the direction of the probing forces on the complex of an antibody fragment with its peptide antigen. Using an atomic force microscope, experiments were performed where the attachment points of the 12 amino acid long peptide antigen were varied. These measurements yielded clearly distinguishable basal dissociation rates and potential widths, proving that the direction of the applied force determines the unbinding pathway. Complementary atomistic SMD simulations were performed, which also show that the unbinding pathways of the system are dependent on the pulling direction. However, the main barrier to be crossed was independent of the pulling direction and is represented by a backbone hydrogen bond between Gly^H-H40 of the antibody fragment and Glu^Oε-6_peptide of the peptide. For each pulling direction, the observed barriers can be correlated with the rupture of specific interactions, which stabilize the bound complex. Furthermore, although the SMD simulations were performed at loading rates exceeding the experimental rates by orders of magnitude due to computational limitations, a detailed comparison of the barriers that were overcome in the SMD simulations with the data obtained from the atomic force microscope unbinding experiments show excellent agreement.     

Molecular recognition force spectroscopy study of the dynamic interaction between aptamer GBI‐10 and extracellular matrix protein tenascin‐C on human glioblastoma cell

Molecular recognition force spectroscopy (MR‐FS) was applied to investigate the dynamic interaction between aptamer GBI‐10 and tenascin‐C (TN‐C) on human glioblastoma cell surface at single‐molecule level. The unbinding force between aptamer GBI‐10 and TN‐C was 39 pN at the loading rate of 0.3 nN sec^?1. A series of kinetic parameters concerning interaction process such as the unbinding force f_u, the association rate constant k_on, dissociation rate constant at zero force k_off, and dissociation constant K_D for aptamer GBI‐10/TN‐C complexes were acquired. In addition, the interaction of aptamer GBI‐10 with TN‐C depended on the presence of Mg²⁺. This work demonstrates that MR‐FS can be used as an attractive tool for exploring the interaction forces and dynamic process of aptamer and ligand at the single‐molecule level. As a future perspective, MR‐FS may be used as a potential diagnostic and therapeutic tool by combining with other techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic response of glucagon/anti-glucagon pairs to pulling velocity and pH studied by atomic force microscopy

We used atomic force microscopy (AFM) to measure the unbinding force between antigen coupled to an AFM tip and antibody coated on the substrate surface. Dynamic responses of glucagon/anti-glucagon pairs with multiple pull-off steps to pH and pulling velocity were studied by AFM. Force-distance curves of a specific glucagon-anti-glucagon interaction system with mono-, di-, and multi-unbinding events were recorded, which may be attributed to a single, sequential or multiple breaking of interacting bond(s) between glucagon and anti-glucagon. We studied the dynamic response of glucagon-anti-glucagon pairs to various pulling velocities (16.7-166.7 nm/s). It was found that the mean value of the unbinding force was shifted toward higher values with increasing pulling velocity at each pH. This indicates that the friction force between glucagon and anti-glucagon may contribute to the unbinding force. Moreover, the dynamic response of glucagon-anti-glucagon pairs to pH (4-10) with different pulling velocities was studied. Within the acid range, the bond strength between the glucagon/anti-glucagon complex showed a rapid increase from pH 4 to 7 and reached a maximum (256.4+/-48.9 pN at 166.7 nm/s) at neutrality, followed by a sharp decrease with increasing pH (pH 7-10). This could be attributed to the conformational change that occurred in glucagon when the pH value in solution was varied from the reference level at neutrality. This study demonstrated that the pH dependence of multiple antigen-antibody bond-rupture forces could be measured by a force-based AFM biosensor. Unraveling the relationship between inter-molecular force and intra-molecular conformational change in acid, neutral, and alkaline environments may provide new directions for future application of force measurements by AFM in proteomics or in the development of a clinical cantilever-based mechanical biosensor.     

Weak pulling forces exerted on Nin-orientated transmembrane segments during co-translational insertion into the inner membrane of Escherichia coli

Transmembrane helices (TMHs) in membrane proteins can be orientated with their N-terminus towards the cytoplasm (N_in), or facing the non-cytoplasmic side (N_out). Most membrane proteins are inserted co-translationally into membranes, aided by Sec-type translocons. Since the final orientation of N_in- and N_out-orientated TMHs differs, they could also interact differently with the translocon and the surrounding membrane during insertion. We measured pulling forces exerted on N_in-orientated TMHs during co-translational insertion into the inner membrane of Escherichia coli. Our results demonstrate that N_in-orientated TMHs experience a weaker pulling force but retain the overall biphasic force profile seen previously for N_out-orientated TMHs (Ismail et al., 2012 [1]).     

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.     

Integrin-based mechanosensing through conformational deformation

Conversion of integrins from low to high affinity states, termed activation, is important in biological processes, including immunity, hemostasis, angiogenesis, and embryonic development. Integrin activation is regulated by large-scale conformational transitions from closed, low affinity states to open, high affinity states. Although it has been suggested that substrate stiffness shifts the conformational equilibrium of integrin and governs its unbinding, here, we address the role of integrin conformational activation in cellular mechanosensing. Comparison of wild-type versus activating mutants of integrin αVβ3 show that activating mutants shift cell spreading, focal adhesion kinase activation, traction stress, and force on talin toward high stiffness values at lower stiffness. Although all activated integrin mutants showed equivalent binding affinity for soluble ligands, the β3 S243E mutant showed the strongest shift in mechanical responses. To understand this behavior, we used coarse-grained computational models derived from molecular level information. The models predicted that wild-type integrin αVβ3 displaces under force and that activating mutations shift the required force toward lower values, with S243E showing the strongest effect. Cellular stiffness sensing thus correlates with computed effects of force on integrin conformation. Together, these data identify a role for force-induced integrin conformational deformation in cellular mechanosensing.     

Probing effects of pH change on dynamic response of Claudin-2 mediated adhesion using single molecule force spectroscopy

Claudins belong to a large family of transmembrane proteins that localize at tight junctions (TJs) where they play a central role in regulating paracellular transport of solutes and nutrients across epithelial monolayers. Their ability to regulate the paracellular pathway is highly influenced by changes in extracellular pH. However, the effect of changes in pH on the strength and kinetics of claudin mediated adhesion is poorly understood. Using atomic force microscopy, we characterized the kinetic properties of homophilic trans-interactions between full length recombinant GST tagged Claudin-2 (Cldn2) under different pH conditions. In measurements covering three orders of magnitude change in force loading rate of 10²–10⁴ pN/s, the Cldn2/Cldn2 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 throughout pH range of 4.5–8. Comparing to the neutral condition (pH 6.9), differences in the inner energy barriers for the dissociation of Cldn2/Cldn2 mediated interactions at acidic and alkaline environments were found to be < 0.65 k_BT, which is much lower than the outer dissociation energy barrier (> 1.37 k_BT). The relatively stable interaction of Cldn2/Cldn2 in neutral environment suggests that electrostatic interactions may contribute to the overall adhesion strength of Cldn2 interactions. Our results provide an insight into the changes in the inter-molecular forces and adhesion kinetics of Cldn2 mediated interactions in acidic, neutral and alkaline environments.     

Direct force measurement of single DNA–peptide interactions using atomic force microscopy

The selective interactions between DNA and miniature (39 residues) engineered peptide were directly measured at the single‐molecule level by using atomic force microscopy. This peptide (p007) contains an α‐helical recognition site similar to leucine zipper GCN4 and specifically recognizes the ATGAC sequence in the DNA with nanomolar affinity. The average rupture force was 42.1 pN, which is similar to the unbinding forces of the digoxigenin–antidigoxigenin complex, one of the strongest interactions in biological systems. The single linear fit of the rupture forces versus the logarithm of pulling rates showed a single energy barrier with a transition state located at 0.74 nm from the bound state. The smaller k_off compared with that of other similar systems was presumably due to the increased stability of the helical structure by putative folding residues in p007. This strong sequence‐specific DNA–peptide interaction has a potential to be utilized to prepare well‐defined mechanically stable DNA–protein hybrid nanostructures. Copyright © 2013 John Wiley & Sons, Ltd.     

Dissociation of Bimolecular ��IIb��3-Fibrinogen Complex under a Constant Tensile Force

The regulated ability of integrin αIIbβ3 to bind fibrinogen plays a crucial role in platelet aggregation, adhesion, and hemostasis. Employing an optical-trap-based electronic force clamp, we studied the thermodynamics and kinetics of αIIbβ3-fibrinogen bond formation and dissociation under constant unbinding forces, mimicking the forces of physiologic blood shear on a thrombus. The distribution of bond lifetimes was bimodal, indicating that the αIIbβ3-fibrinogen complex exists in two bound states with different mechanical stability. The αIIbβ3 antagonist, abciximab, inhibited binding without affecting the unbinding kinetics, whereas Mn²⁺ biased the αIIbβ3-fibrinogen complex to the strong bound state with reduced off-rate. The average bond lifetimes decreased exponentially with increasing pulling force from ∼5 pN to 50 pN, suggesting that in this force range the αIIbβ3-fibrinogen interactions are classical slip bonds. We found no evidence for catch bonds, which is consistent with the known lack of shear-enhanced platelet adhesion on fibrinogen-coated surfaces. Taken together, these data provide important quantitative and qualitative characteristics of αIIbβ3-fibrinogen binding and unbinding that underlie the dynamics of platelet adhesion and aggregation in blood flow.     

Force Spectroscopy Shows Dynamic Binding of Influenza Hemagglutinin and Neuraminidase to Sialic Acid

The influenza A virus infects target cells through multivalent interactions of its major spike proteins, hemagglutinin (HA) and neuraminidase (NA), with the cellular receptor sialic acid (SA). HA is known to mediate the attachment of the virion to the cell, whereas NA enables the release of newly formed virions by cleaving SA from the cell. Because both proteins target the same receptor but have antagonistic functions, virus infection depends on a properly tuned balance of the kinetics of HA and NA activities for viral entry to and release from the host cell. Here, dynamic single-molecule force spectroscopy, based on scanning force microscopy, was employed to determine these bond-specific kinetics, characterized by the off rate k_off, rupture length x_β and on rate k_on, as well as the related free-energy barrier ΔG and the dissociation constant K_D. Measurements were conducted using surface-immobilized HA and NA of the influenza A virus strain A/California/04/2009 and a novel, to our knowledge, synthetic SA-displaying receptor for functionalization of the force probe. Single-molecule force spectroscopy at force loading rates between 100 and 50,000 pN/s revealed most probable rupture forces of the protein-SA bond in the range of 10–100 pN. Using an extension of the widely applied Bell-Evans formalism by Friddle, De Yoreo, and co-workers, it is shown that HA features a smaller x_β, a larger k_off and a smaller ΔG than NA. Measurements of the binding probability at increasing contact time between the scanning force microscopy force probe and the surface allow an estimation of K_D, which is found to be three times as large for HA than for NA. This suggests a stronger interaction for NA-SA than for HA-SA. The biological implications in regard to virus binding to the host cell and the release of new virions from the host cell are discussed.     

Absence of multiple forms of ribulose 15-bisphosphate carboxylase/oxygenase in mung bean

Ribulose 1,5-bisphosphate carboxylase/oxygenase has been reported to occur in multiple forms in mung bean (Phaseolus aureus) using Sephadex G-200 chromatography. We have isolated this enzyme by identical methodology. The profile from Sephadex G-200 chromatography shows only one peak in contrast to the previous report and we find no evidence to corroborate the conclusions. Where V_c, V_o and K_c, K_o represent V_max and Michaelis constants, respectively, the constant V_cK_o/V_oK_c for the single form is 70 at 40 μM CO₂ and 1200 μM O₂.     

Order Statistics Theory of Unfolding of Multimeric Proteins

Dynamic force spectroscopy has become indispensable for the exploration of the mechanical properties of proteins. In force-ramp experiments, performed by utilizing a time-dependent pulling force, the peak forces for unfolding transitions in a multimeric protein (D)_N are used to map the free energy landscape for unfolding for a protein domain D. We show that theoretical modeling of unfolding transitions based on combining the observed first (f₁), second (f₂), …, N^th (f_N) unfolding forces for a protein tandem of fixed length N, and pooling the force data for tandems of different length, n₁ < n₂ < … < N, leads to an inaccurate estimation of the distribution of unfolding forces for the protein D, ψ_D(f). This problem can be overcome by using Order statistics theory, which, in conjunction with analytically tractable models, can be used to resolve the molecular characteristics that determine the unfolding micromechanics. We present a simple method of estimation of the parent distribution, ψ_D(f), based on analyzing the force data for a tandem (D)_n of arbitrary length n. Order statistics theory is exemplified through a detailed analysis and modeling of the unfolding forces obtained from pulling simulations of the monomer and oligomers of the all-β-sheet WW domain.     

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.     

The influence of foot position on body dynamics

During locomotion, the human body exhibits inherent dynamic properties such as mass (M), stiffness (K) and damping (B). During the gait cycle, foot contact with the ground progresses from the heel to the toe. Contact forces between the foot and ground are defined as ground reaction forces (GRF). It is unclear how body dynamics are affected by foot landing position. If the shape of GRF is indicative of body dynamics, our understanding of gait patterns in normal and pathologic conditions may improve. The aims of this study were to determine:(1) whether foot landing position affects the inherent dynamics of the human body and (2) the extent to which the GRF curve reflects the response of inherent body dynamics to sudden loading.Eight non-disabled control volunteers performed a series of small jumps and landed on one leg with a fully extended knee in three foot landing positions: heel, mid-foot, and toe. They then walked at self-paced velocity over force plates. For each foot landing position, values of K, B and the dimensionless damping coefficient, ξ, were calculated from the period of vertical body oscillations, T, and compared with an ANOVA test. In addition, the time between the two peaks of the vertical GRF, T_GRF, was compared with T. We found that that K and B decreased and ξ did not change (p<0.01) between heel to toe-landing positions. T_GRF was not different than T for the toe-landing position, which suggests that the dynamic body response has major impact on the shape of GRF.     

Electrokinetics of Miniature K+ Channel: Open-State V Sensitivity and Inhibition by K+ Driving Force

Kcv, isolated from a Chlorella virus, is the smallest known K⁺ channel. When Kcv is expressed in Xenopus oocytes and exposed to 50 mM [K⁺]_o, its open-state current-voltage relationship (I-V) has the shape of a “tilted S” between ?200 and +120 mV. Details of this shape depend on the conditioning voltage (V _c) immediately before an I-V recording. Unexpectedly, the I-V relationships, recorded in different [K⁺]_o, do intersect. These characteristics are numerically described here by fits of a kinetic model to the experimental data. In this model, the V _c sensitivity of I-V is mainly assigned to an affinity increase of external K⁺ association at more positive voltages. The general, tilted-S shape as well as the unexpected intersections of the I-V relationships are kinetically described by a decrease of the cord conductance by the electrochemical driving force for K⁺ in either direction, like in fast V-dependent blocking by competing ions.