Dynamic Force Spectroscopy Research Articles

Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis

Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification.

Noncontact friction via capillary shear interaction at nanoscale

Friction in an ambient condition involves highly nonlinear interactions of capillary force, induced by the capillary-condensed water nanobridges between contact or noncontact asperities of two sliding surfaces. Since the real contact area of sliding solids is much smaller than the apparent contact area, the nanobridges formed on the distant asperities can contribute significantly to the overall friction. Therefore, it is essential to understand how the water nanobridges mediate the ‘noncontact' friction, which helps narrow the gap between our knowledge of friction on the microscopic and macroscopic scales. Here we show, by using noncontact dynamic force spectroscopy, the single capillary bridge generates noncontact friction via its shear interaction. The pinning–depinning dynamics of the nanobridge's contact line produces nonviscous damping, which occurs even without normal load and dominates the capillary-induced hydrodynamic damping. The novel nanofriction mechanism may provide a deeper microscopic view of macroscopic friction in air where numerous asperities exist.

AFM force spectroscopy reveals how subtle structural differences affect the interaction strength between Candida albicans and DC-SIGN.

The fungus Candida albicans is the most common cause of mycotic infections in immunocompromised hosts. Little is known about the initial interactions between Candida and immune cell receptors, such as the C-type lectin dendritic cell-specific intracellular cell adhesion molecule-3 (ICAM-3)-grabbing non-integrin (DC-SIGN), because a detailed characterization at the structural level is lacking. DC-SIGN recognizes specific Candida-associated molecular patterns, that is, mannan structures present in the cell wall of Candida. The molecular recognition mechanism is however poorly understood. We postulated that small differences in mannan-branching may result in considerable differences in the binding affinity. Here, we exploit atomic force microscope-based dynamic force spectroscopy with single Candida cells to gain better insight in the carbohydrate recognition capacity of DC-SIGN. We demonstrate that slight differences in the N-mannan structure of Candida, that is, the absence or presence of a phosphomannan side chain, results in differences in the recognition by DC-SIGN as follows: (i) it contributes to the compliance of the outer cell wall of Candida, and (ii) its presence results in a higher binding energy of 1.6 kB T. The single-bond affinity of tetrameric DC-SIGN for wild-type C. albicans is ~10.7 kB T and a dissociation constant kD of 23 μM, which is relatively strong compared with other carbohydrate-protein interactions described in the literature. In conclusion, this study shows that DC-SIGN specifically recognizes mannan patterns on C. albicans with high affinity. Knowledge on the binding pocket of DC-SIGN and its pathogenic ligands will lead to a better understanding of how fungal-associated carbohydrate structures are recognized by receptors of the immune system and can ultimately contribute to the development of new anti-fungal drugs.

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 kBT 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.

Shear-stress function approach of hydration layer based on the Green-Kubo formula.

We present the analytic expression of the stress correlation (SC) function for the ubiquitous hydration water layer (HWL) using the Green-Kubo equation and the shear modulus of HWL. The SC function is then experimentally obtained by measuring the viscoelastic properties of HWL using shear-mode dynamic force spectroscopy. Interestingly, the SC changes sign from positive to negative as the HWL thickness increases, where the shear stresses acting on the HWLs bound to two nearby surfaces are out of phase. We also suggest that the repulsive hydration force originates from the SC of HWL. Our results provide the first demonstration of the microscopic understanding of the HWL viscoelasticity and may allow a deeper insight on the HWL dynamics as well as the complex liquids.

Multi-Ligand-Binding Flavoprotein Dodecin as a Key Element for Reversible Surface Modification in Nano-biotechnology.

In this paper the multiple (re)programming of protein-DNA nanostructures comprising generation, deletion, and reprogramming on the same flavin-DNA-modified surface is introduced. This work is based on a systematic study of the binding affinity of the multi-ligand-binding flavoprotein dodecin on flavin-terminated DNA monolayers by surface plasmon resonance and quartz crystal microbalance with dissipation (QCM-D) measurements, surface plasmon fluorescence spectroscopy (SPFS), and dynamic AFM force spectroscopy. Depending on the flavin surface coverage, a single apododecin is captured by one or more surface-immobilized flavins. The corresponding complex binding and unbinding rate constants kon(QCM) = 7.7 × 10(3) M(-1)·s(-1) and koff(QCM) = 4.5 × 10(-3) s(-1) (Kd(QCM) = 580 nM) were determined by QCM and were found to be in agreement with values for koff determined by SPFS and force spectroscopy. Even though a single apododecin-flavin bond is relatively weak, stable dodecin monolayers were formed on flavin-DNA-modified surfaces at high flavin surface coverage due to multivalent interactions between apododecin bearing six binding pockets and the surface-bound flavin-DNA ligands. If bi- or multivalent flavin ligands are adsorbed on dodecin monolayers, stable sandwich-type surface-DNA-flavin-apododecin-flavin ligand arrays are obtained. Nevertheless, the apododecin flavin complex is easily and quantitatively disassembled by flavin reduction. Binding and release of apododecin are reversible processes, which can be carried out alternatingly several times to release one type of ligand by an external redox trigger and subsequently replace it with a different ligand. Hence the versatile concept of reprogrammable functional biointerfaces with the multi-ligand-binding flavoprotein dodecin is demonstrated.

Reconciling bond strength of a slip bond at low loading rates with rebinding

Conventional theory predicts that molecular bond strength becomes trivial at very low loading rates, which, however, failed in some experiments probably due to hidden rebinding. Here we propose average bond strength as an alternative physical quantity to be measured in dynamic force spectroscopy experiments. Our analysis indicates that there exists an asymptotic value of average bond strength at low loading rates, which, nevertheless, increases with the spring constant of the loading system. This finding is subsequently confirmed with the Monte Carlo simulation. The proposed average bond strength can be informative in the understanding of the intriguing behaviors of molecular bonds at low loading rates.

Crucial Roles of Bond Rebinding in Rupture Behaviors of Single Molecular Bond at Ultralow Loading Rates

Single-molecule dynamic force spectroscopy (DFS) is a powerful tool for studying mechanical forces of molecular interactions. Recently, the important role of bond rebinding in DSF experiments was recognized, which intrigued mounting researches in this direction. In this work, we study how the bond rebinding influences the strength of single-molecular bonds using Brownian dynamics (BD) simulations and theoretical modeling. Our results show that bond rebinding significantly enhances the strength of single-molecular bond at ultralow loading rates. The rebinding behavior strongly depends on the loading stiffness, suggesting that the strength of single-molecular bond is not only dependent on its intrinsic property, but also the stiffness of loading device. By connecting our new model with conventional theories that did not consider the rebinding effect and are only applied to high loading rates, we propose a unified scheme to predict the rupture forces in a full range of loading rate in DSF experiments and simulations.

Investigation of the heparin–thrombin interaction by dynamic force spectroscopy

BackgroundThe interaction between heparin and thrombin is a vital step in the blood (anti)coagulation process. Unraveling the molecular basis of the interactions is therefore extremely important in understanding the mechanisms of this complex biological process. MethodsIn this study, we use a combination of an efficient thiolation chemistry of heparin, a self-assembled monolayer-based single molecule platform, and a dynamic force spectroscopy to provide new insights into the heparin–thrombin interaction from an energy viewpoint at the molecular scale. ResultsWell-separated single molecules of heparin covalently attached to mixed self-assembled monolayers are demonstrated, whereby interaction forces with thrombin can be measured via atomic force microscopy-based spectroscopy. Further these interactions are studied at different loading rates and salt concentrations to directly obtain kinetic parameters. ConclusionsAn increase in the loading rate shows a higher interaction force between the heparin and thrombin, which can be directly linked to the kinetic dissociation rate constant (koff). The stability of the heparin/thrombin complex decreased with increasing NaCl concentration such that the off-rate was found to be driven primarily by non-ionic forces. General significanceThese results contribute to understanding the role of specific and nonspecific forces that drive heparin–thrombin interactions under applied force or flow conditions.

High-Speed Force Spectroscopy Unbinds Streptavidin-Biotin at the Velocity of Molecular Dynamics Simulations

The forced disruption of the (strept)avidin-biotin complex by atomic force microscopy (AFM) and other techniques opened the field and established the basis of single molecule force spectroscopy (1-3). Steered molecular dynamics (SMD) simulations provided atomic description of the unbinding process (4). However, the maximum experimental AFM velocities were typically of 10 µm/s, while SMD simulations were performed in the range of 1 m/s to 10 m/s. Recent development of high-speed force spectroscopy (HS-FS) using HS-AFM allowed velocities in the mm/s range (5). We have applied HS-FS to probe the binding strength of the streptavidin-biotin complex at velocities up to ∼8 mm/s, paralleled by SMD simulations. The experimental dynamic force spectrum of the unbinding process is compared with SMD simulations. The combination of HS-FS and SMD at overlapping velocities provides an atomic description of the unbinding process measured by experiment.1. Merkel, R., P. Nassoy, A. Leung, K. Ritchie, and E. Evans. 1999. Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy. Nature 397:50-53.2. Florin, E. L., V. T. Moy, and H. E. Gaub. 1994. Adhesion Forces Between Individual Ligand-Receptor Pairs. Science 264:415-417.3. Lee, G. U., D. A. Kidwell, and R. J. Colton. 1994. Sensing Discrete Streptavidin Biotin Interactions with Atomic-Force Microscopy. Langmuir 10:354-357.4. Grubmuller, H., B. Heymann, and P. Tavan. 1996. Ligand binding: Molecular mechanics calculation of the streptavidin biotin rupture force. Science 271:997-999.5. Rico, F., L. Gonzalez, I. Casuso, M. Puig-Vidal, and S. Scheuring. 2013. High-Speed Force Spectroscopy Unfolds Titin at the Velocity of Molecular Dynamics Simulations. Science 342:741-743.

In situ single molecule detection of insulin receptors on erythrocytes from a type 1 diabetes ketoacidosis patient by atomic force microscopy.

Type 1 diabetes is an insulin-dependent metabolic disorder always associated with ketoacidosis and a high morbidity rate in teenagers. The in situ single molecule detection of insulin receptors on healthy and diseased erythrocytes is helpful to understand the pathomechanism of type 1 diabetes ketoacidosis (T1-DKA), which would also benefit the diagnosis and treatment of T1-DKA. Here, we demonstrated, for the first time, the single molecule interaction between insulin and insulin receptor on erythrocytes from a healthy volunteer and a T1-DKA patient using high sensitivity atomic force microscopy (AFM) in PBS solution. The single molecule force results demonstrated the decreased binding force and binding probability between insulin and insulin receptor on T1-DKA erythrocytes, implying the deficit of insulin receptor functions in T1-DKA. The binding kinetic parameters calculated from dynamic force spectroscopy indicated that the insulin-insulin receptor complexes on T1-DKA erythrocytes were less stable than those from healthy volunteer. Using high resolution AFM imaging, a decreased roughness was found both in intact T1-DKA erythrocytes and in the purified membrane of T1-DKA erythrocytes, and an increased stiffness was also found in T1-DKA erythrocytes. Moreover, AFM, which was used to investigate the single molecule interactions between insulin-insulin receptor, cell surface ultrastructure and stiffness in healthy and diseased erythrocytes, was expected to develop into a potential nanotool for pathomechanism studies of clinical samples at the nanoscale.

Time and Space resolved Methods: general discussion.

Jim De Yoreo presented some slides on in situ AFM, TEM, dynamic force spectroscopy (DFS) and optical spectroscopy investigations of nucleation in the calcium carbonate system: The free energy barrier to homogeneous nucleation of calcite calculated within the framework of classical nucleation theory (CNT) is prohibitive, even at concentrations exceeding the solubility limits of the amorphous phases. Consistent with this analysis, during nucleation in pure solutions, in our in situ TEM experiments we observed direct formation of all phases, including amorphous calcium carbonate (ACC), as well as the three predominant crystalline phases: calcite, vaterite, and aragonite, even under conditions in which ACC readily forms. In addition to direct formation pathways, we observed indirect pathways in which ACC transforms to aragonite and vaterite through nucleation within or on the precursors, rather than via dissolution and reprecipitation. We also observed aragonate transformation to calcite, but never recorded an instance in which ACC transforms into calcite, except via dissolution–reprecipitation reactions.

Probing of PNA-DNA Hybrid Duplex Stability with AFM Force Spectroscopy

Peptide nucleic acids (PNA) are synthetic polymers the neutral peptide backbone of which provides elevated stability to PNA-PNA and hybrid PNA-DNA duplex. It was demonstrated recently (J.Org.Chem.2011, 76, 5614-5627) that additional modification of the backbone such as incorporation of diethylene glycol (miniPEG) further increases the duplex thermal stability, so the hybrid duplex with 10 miniPEG units (γ-PNA) has the melting temperature 23°C higher compared to the regular PNA-DNA duplex. Here we applied AFM force spectroscopy to probe the strength of the γ-PNA-DNA duplex (5′GAGTAG GTAG-3’) containing ten miniPEG-modified units. Single-stranded PNA and DNA oligonucleotides containing terminal thiol groups were immobilized on amino-functionalized AFM tip and mica substrate, respectively via bifunctional PEG tethers and the interaction between the DNA and γ-PNA polymers was analyzed by multiple approach retraction cycles over various locations on the mica substrate. Such single molecule probing experiments produced force curves with well-defined rupture events corresponding to the dissociation of the duplex formed during the approach step. The experiments were performed at various pulling rates (300-3000 nm/sec) enabled us to characterize the hybrid duplex stability using dynamic force spectroscopy (DFS) approach. The DFS measurements yielded rupture forces varying in the range 60-70 pN. The data analyzed in the framework of the Bell-Evans approach yielded a dissociation constant, koff ∼ 10−9 sec−1 and rupture distance x-1∼ 1.7 nm. Similar published DFS measurements of DNA duplex are characterized by koff with ∼ 108 times less values, which is in line with elevated stabilities of the γ-PNA-DNA duplexes compared with the DNA duplexes.The work was supported by NIH grants 5P01 GM091743-03 and 5R01 GM096039-04 to YLL. γ-PNA was synthesized at PNA innovation.

Time and space resolved methods: general discussion.

Jim De Yoreo presented some slides on in situ AFM, TEM, dynamic force spectroscopy (DFS) and optical spectroscopy investigations of nucleation in the calcium carbonate system: The free energy barrier to homogeneous nucleation of calcite calculated within the framework of classical nucleation theory (CNT) is prohibitive, even at concentrations exceeding the solubility limits of the amorphous phases. Consistent with this analysis, during nucleation in pure solutions, in our in situ TEM experiments we observed direct formation of all phases, including amorphous calcium carbonate (ACC), as well as the three predominant crystalline phases: calcite, vaterite, and aragonite, even under conditions in which ACC readily forms. In addition to direct formation pathways, we observed indirect pathways in which ACC transforms to aragonite and vaterite through nucleation within or on the precursors, rather than via dissolution and reprecipitation. We also observed aragonate transformation to calcite, but never recorded an instance in which ACC transforms into calcite, except via dissolution–reprecipitation reactions.

Study of the interactions between endolysin and bacterial peptidoglycan on S. aureus by dynamic force spectroscopy.

The cell wall binding domain (CBD) of bacteriophage lysins can recognize target bacteria with extraordinary specificity through binding to bacterial peptidoglycan, thus it is a promising new probe to identify the corresponding bacterial pathogen. In this work, we used atomic force microscopy (AFM) based single-molecule force spectroscopy to investigate the interaction between the CBD of lysin PlyV12 (PlyV12C) and pathogenic bacterium Staphylococcus aureus (S. aureus). The binding forces of PlyV12C with S. aureus have been measured, and the dissociation process of their binding complex has been characterized. Furthermore, we compared the interactions of PlyV12C-S. aureus and antibody-S. aureus. It is revealed that PlyV12C has a comparable affinity to bacterial peptidoglycans as that of the S. aureus antibody. The results provide new information on the binding properties of lysin CBD with bacterium, and the application of lysin CBD in bacterium detection.

Surface conformations of an anti-ricin aptamer and its affinity for ricin determined by atomic force microscopy and surface plasmon resonance.

We used atomic force microscopy (AFM) and surface plasmon resonance (SPR) to study the surface conformations of an anti-ricin aptamer and its specific binding affinity for ricin molecules. The effect of surface modification of the Au(111) substrate on the aptamer affinity was also estimated. The AFM topography images had a resolution high enough to distinguish different aptamer conformations. The specific binding site on the aptamer molecule was clearly located by the AFM recognition images. The aptamer on a Au(111) surface modified with carboxymethylated-dextran (CD) showed both similarities to and differences from the one without CD modification. The influence of CD modification was evaluated using AFM images of various aptamer conformations on the Au(111) surface. The affinity between ricin and the anti-ricin aptamer was estimated using the off-rate values measured using AFM and SPR. The SPR measurements of the ricin sample were conducted in the range from 83.3 pM to 8.33 nM, and the limit of detection was estimated as 25 pM (1.5 ng mL(-1)). The off-rate values of the ricin-aptamer interactions were estimated using both single-molecule dynamic force spectroscopy (DFS) and SPR as (7.3 ± 0.4) × 10(-4) s(-1) and (1.82 ± 0.067) × 10(-2) s(-1), respectively. The results show that single-molecule measurements can obtain different reaction parameters from bulk solution measurements. In AFM single-molecule measurements, the various conformations of the aptamer immobilized on the gold surface determined the availability of each specific binding site to the ricin molecules. The SPR bulk solution measurements averaged the signals from specific and non-specific interactions. AFM images and DFS measurements provide more specific information on the interactions of individual aptamer and ricin molecules.

Dynamic single-molecule force spectroscopy of rhodopsin in native membranes.

Membrane proteins are an important class of proteins in biology and therapeutics. Understanding the dynamic nature of the molecular interactions that stabilize membrane protein structure is critical to dissect the mechanism of action and dysfunction of these proteins. Single-molecule force spectroscopy (SMFS) and dynamic SMFS (DFS) are emerging nanotechniques that allow the study of membrane proteins under the physiologically relevant conditions of a lipid bilayer and buffer conditions. These techniques directly probe the molecular interactions underlying protein structure and reveal unique insights about their properties. Outlined in this report will be procedures on how to conduct SMFS and DFS on rhodopsin in native retinal membranes. Rhodopsin is a membrane protein belonging to the G protein-coupled receptor family of proteins, one of the largest families of proteins in nature.

Probing Protein-Lipid Interactions at the Single Molecule Level

Cell membranes consist mostly of lipids and embedded proteins, forming a shell around the cell that controls information and material fluxes into and out of the cell. Protein-lipid interactions thus play a crucial role in numerous cellular mechanisms. Understanding these interactions would provide basic biophysical knowledge in addition to advance pharmaceutical developments, many of which target membranes. Despite their significance, protein-lipid interactions are not fully understood and have not yet been fully investigated from a mechanistic standpoint. In this study we investigated synthesized peptide constructs that insert into lipid bilayers via force spectroscopy. The constructs used here are based on SecA, a membrane-associated ATPase of the general secretory system. We investigated the first 10 amino terminal residues of SecA (SecA2-11) in three different arrangements to provide control experiments and guide interpretation. In one arrangement, two copies of SecA2-11 were covalently linked in series to the atomic force microscope tip, in another, they were linked in parallel. In all cases the constructs were brought into close proximity of a supported POPC lipid bilayer and the mechanical interaction between the peptide and lipid was recorded using single-molecule dynamic force spectroscopy. Investigating chemically similar yet geometrically different constructs provides important benchmarks for the interpretation of future studies involving longer constructs such as full length SecA.

Energetic basis for the molecular-scale organization of bone

The remarkable properties of bone derive from a highly organized arrangement of coaligned nanometer-scale apatite platelets within a fibrillar collagen matrix. The origin of this arrangement is poorly understood and the crystal structures of hydroxyapatite (HAP) and the nonmineralized collagen fibrils alone do not provide an explanation. Moreover, little is known about collagen-apatite interaction energies, which should strongly influence both the molecular-scale organization and the resulting mechanical properties of the composite. We investigated collagen-mineral interactions by combining dynamic force spectroscopy (DFS) measurements of binding energies with molecular dynamics (MD) simulations of binding and atomic force microscopy (AFM) observations of collagen adsorption on single crystals of calcium phosphate for four mineral phases of potential importance in bone formation. In all cases, we observe a strong preferential orientation of collagen binding, but comparison between the observed orientations and transmission electron microscopy (TEM) analyses of native tissues shows that only calcium-deficient apatite (CDAP) provides an interface with collagen that is consistent with both. MD simulations predict preferred collagen orientations that agree with observations, and results from both MD and DFS reveal large values for the binding energy due to multiple binding sites. These findings reconcile apparent contradictions inherent in a hydroxyapatite or carbonated apatite (CAP) model of bone mineral and provide an energetic rationale for the molecular-scale organization of bone.

Atomic force microscopy measurements reveal multiple bonds between Helicobacter pylori blood group antigen binding adhesin and Lewis b ligand.

The strength of binding between the Helicobacter pylori blood group antigen-binding adhesin (BabA) and its cognate glycan receptor, the Lewis b blood group antigen (Le(b)), was measured by means of atomic force microscopy. High-resolution measurements of rupture forces between single receptor-ligand pairs were performed between the purified BabA and immobilized Le(b) structures on self-assembled monolayers. Dynamic force spectroscopy revealed two similar but statistically different bond populations. These findings suggest that the BabA may form different adhesive attachments to the gastric mucosa in ways that enhance the efficiency and stability of bacterial adhesion.