Nonlinearly additive forces in multivalent ligand binding to a single protein revealed with force spectroscopy

We present evidence of multivalent interactions between a single protein molecule and multiple carbohydrates at a pH where the protein can bind four ligands. The evidence is based not only on measurements of the force required to rupture the bonds formed between concanavalin A (ConA) and alpha-D-mannose but also on an analysis of the polymer-extension force curves to infer the polymer architecture that binds the protein to the cantilever and the ligands to the substrate. We find that although the rupture forces for multiple carbohydrate connections to a single protein are larger than the rupture force for a single connection, they do not scale additively with increasing number. Specifically, the most common rupture forces are approximately 46, 68, and 85 pN at a loading rate of 650 +/- 25 pN/s, which we argue corresponds to 1, 2, and 3 ligands being pulled simultaneously from a single protein as corroborated by an analysis of the linkage architecture. As in our previous work polymer tethers allow us to discriminate between specific and nonspecific binding. We analyze the binding configuration (i.e., serial vs parallel connections) through fitting the polymer stretching data with modified wormlike chain (WLC) models that predict how the effective stiffness of the tethers is affected by multiple connections. This analysis establishes that the forces we measure are due to single proteins interacting with multiple ligands, the first force spectroscopy study that establishes single-molecule multivalent binding unambiguously.     

Rupture force analysis and the associated systematic errors in force spectroscopy by AFM

Force spectroscopy is a new and valuable tool in physical chemistry and biophysics. However, data analysis has yet to be standardized, hindering the advancement of the technique. In this article, treatment of the rupture forces is described in the framework of the Bell-Evans model, and the systematic errors associated with the tether effect for approaches that utilize the most probable, the median, and the mean rupture forces are compared. It is shown that significant systematic errors in the dissociation rate can result from nonlinear loading with polymeric tethers even if the apparent loading rate is used in the analysis. Analytical expressions for the systematic errors are provided for the most probable and median forces. The use of these expressions to correct the associated systematic errors is illustrated by the analysis of the measured rupture forces between single hexadecane molecules in water. It is noted that the measured distributions of rupture forces often contain high forces that are unaccounted for by theoretical models. Experimental data indicate that the most significant effect of the high forces "tail" is on the dissociation rate obtained from the median force analysis whereas the barrier width appears to be unaffected.     

Linker dependent bond rupture force measurements in single-molecule junctions

We use a modified conducting atomic force microscope to simultaneously probe the conductance of a single-molecule junction and the force required to rupture the junction formed by alkanes terminated with four different chemical link groups which vary in binding strength and mechanism to the gold electrodes. Molecular junctions with amine, methylsulfide, and diphenylphosphine terminated molecules show clear conductance signatures and rupture at a force that is significantly smaller than the measured 1.4 nN force required to rupture the single-atomic gold contact. In contrast, measurements with a thiol terminated alkane which can bind covalently to the gold electrode show conductance and force features unlike those of the other molecules studied. Specifically, the strong Au-S bond can cause structural rearrangements in the electrodes, which are accompanied by substantial conductance changes. Despite the strong Au-S bond and the evidence for disruption of the Au structure, the experiments show that on average these junctions also rupture at a smaller force than that measured for pristine single-atom gold contacts.     

On the detection of single bond ruptures in dynamic force spectroscopy by AFM

Force spectroscopy is a novel tool in physical chemistry and biophysics. This methodology is aimed at providing kinetic parameters of dissociation at a single-molecule level by rupturing molecular bonds subjected to different loading rates. One persistent problem in the implementation of this methodology is a question about the single-bond nature of the rupture events detected in experiments based on atomic force microscopy. Here we address this question by considering the probability that the nearly simultaneous rupture of two molecular bonds might appear as a single bond rupture in the experimental data, complicating the data analysis and contributing to systematic errors in the extracted kinetic parameters. An approximate analytical model predicts that such events might be common in experiments employing soft cantilever force sensors and short tethers to immobilize the interacting molecules. These findings are confirmed by a more elaborate numerical model providing valuable guidelines on performing single-molecule force spectroscopy experiments.     

Single-molecule measurement of the strength of a siloxane bond

Increasing the mechanical stability of artificial polymer materials is an important task in materials science, and for this a profound knowledge of the critical mechanoelastic properties of its constituents is vital. Here, we use AFM-based single-molecule force spectroscopy measurements to characterize the rupture of a single silicon-oxygen bond in the backbone of polydimethylsiloxane as well as the force-extension behavior of this polymer. PDMS is not only a polymer used in a large variety of products but also an important model system for highly flexible polymers. In our experiments, we probe the entire relevant force range from low forces dominated by entropy up to the rupture of the covalent Si-O bonds in the polymer backbone at high forces. The resulting rupture-force histograms are investigated with microscopic models of bond rupture under load and are compared to density functional theory calculations to characterize the free-energy landscape of the Si-O bond in the polymer backbone.     

Correction of systematic errors in single-molecule force spectroscopy with polymeric tethers by atomic force microscopy

Single-molecule force spectroscopy has become a valuable tool for the investigation of intermolecular energy landscapes for a wide range of molecular associations. Atomic force microscopy (AFM) is often used as an experimental technique in these measurements, and the Bell-Evans model is commonly used in the statistical analysis of rupture forces. Most applications of the Bell-Evans model consider a constant loading rate of force applied to the intermolecular bond. The data analysis is often inconsistent because either the probe velocity or the apparent loading rate is being used as an independent parameter. These approaches provide different results when used in AFM-based experiments. Significant variations in results arise from the relative stiffness of the AFM force sensor in comparison with the stiffness of polymeric tethers that link the molecules under study to the solid surfaces. An analytical model presented here accounts for the systematic errors in force-spectroscopy parameters arising from the nonlinear loading induced by polymer tethers. The presented analytical model is based on the Bell-Evans model of the kinetics of forced dissociation and on the asymptotic models of tether stretching. The two most common data reduction procedures are analyzed, and analytical expressions for the systematic errors are provided. The model shows that the barrier width is underestimated and that the dissociation rate is significantly overestimated when force-spectroscopy data are analyzed without taking into account the elasticity of the polymeric tether. Systematic error estimates for asymptotic freely jointed chain and wormlike chain polymer models are given for comparison. The analytical model based on the asymptotic freely jointed chain stretching is employed to analyze and correct the results of the double-tether force-spectroscopy experiments of disjoining "hydrophobic bonds" between individual hexadecane molecules that are covalently tethered via poly(ethylene glycol) linkers of different lengths to the substrates and to the AFM probes. Application of the correction algorithm decreases the spread of the data from the mean value, which is particularly important for measurements of the dissociation rate, and increases the barrier width to 0.43 nm, which might be indicative of the theoretically predicted hydrophobic dewetting.     

Activation of a Copper Biscarbene Mechano-Catalyst Using Single-Molecule Force Spectroscopy Supported by Quantum Chemical Calculations

Single-molecule force spectroscopy allows investigation of the effect of mechanical force on individual bonds. By determining the forces necessary to sufficiently activate bonds to trigger dissociation, it is possible to predict the behavior of mechanophores. The force necessary to activate a copper biscarbene mechano-catalyst intended for self-healing materials was measured. By using a safety line bypassing the mechanophore, it was possible to pinpoint the dissociation of the investigated bond and determine rupture forces to range from 1.6 to 2.6 nN at room temperature in dimethyl sulfoxide. The average length-increase upon rupture of the Cu−C bond, due to the stretching of the safety line, agrees with quantum chemical calculations, but the values exhibit an unusual scattering. This scattering was assigned to the conformational flexibility of the mechanophore, which includes formation of a threaded structure and recoiling of the safety line.     

Single-molecule force spectroscopy of β-peptides that display well-defined three-dimensional chemical patterns

Oligomers of β-amino acids ("β-peptides") can be designed to fold into stable helices that display side chains with a diverse range of chemical functionality in precise arrangements. We sought to determine whether the predictable, three-dimensional side-chain patterns generated by β-peptides could be used in combination with single-molecule force spectroscopy to quantify how changes in nanometer-scale chemical patterns affect intermolecular interactions. To this end, we synthesized β-peptides that were designed to be either globally amphiphilic (GA), i.e., display a global segregation of side chains bearing hydrophobic and cationic functional groups, or non-globally amphiphilic (iso-GA), i.e., display a more uniform distribution of hydrophobic and cationic functional groups in three-dimensions. Single-molecule force measurements of β-peptide interactions with hydrophobic surfaces through aqueous solution (triethanolamine buffer, pH 7.2) reveal that the GA and iso-GA isomers give rise to qualitatively different adhesion force histograms. The data are consistent with the display of a substantial nonpolar domain by the GA oligomer, which leads to strong hydrophobic interactions, and the absence of a comparable domain on the iso-GA oligomer. This interpretation is supported by force measurements in the presence of methanol, which is known to disrupt hydrophobic interactions. Our ability to associate changes in measured forces with changes in three-dimensional chemical nanopatterns projected from conformationally stable β-peptide helices highlights a contrast between this system and conventional peptides (α-amino acid residues): conventional peptides are more conformationally flexible, which leads to uncertainty in the three-dimensional nanoscopic chemical patterns that underlie measured forces. Overall, we conclude that β-peptide oligomers provide a versatile platform for quantifying intermolecular interactions that arise from specific functional group nanopatterns.     

Dynamic simulations of adhesion and friction in chemical force microscopy

A hybrid molecular simulation approach has been applied to investigate dynamic adhesion and friction between a chemical force microscope (CFM) tip and a substrate, both modified by self-assembled monolayers (SAMs) with hydrophobic methyl (CH(3)) or hydrophilic hydroxyl (OH) terminal groups. The method combines a dynamic model for the CFM tip-cantilever system and a molecular dynamics (MD) relaxation technique for SAMs on Au(111) at room temperature. The hybrid simulation method allows one to simulate force-distance curves (or adhesion) and friction loops (or friction coefficient) in the CFM on the experimental time scale for the first time. The simulation results also provide valuable molecular information at the interface that is not accessible in CFM experiments, such as the actual tip position with respect to the cantilever support position, molecular and hydrogen-bonding structures at the interface, and load distributions among different molecular chains (or single-molecule forces). Results show that the adhesion force and friction coefficient for the OH/OH contact pair are much larger than those for the CH(3)/CH(3) pair due to the formation of hydrogen bonds. During the retraction of a CFM tip from a surface, the CFM tip is away from the sample surface slightly while the spring undergoes dramatic elongation in the normal direction before rupture occurs. Single-molecule forces are distributed unevenly at the contact area. Surface energies calculated for functionalized surfaces compare well with those determined by experiments.     

Adjacent gauche stabilization in linear alkanes: implications for polymer models and conformational analysis

High-level ab initio quantum mechanical calculations are used to study various gauche conformational energies of n-pentane to n-decane. The destabilizing "pentane effect" (adjacent gauche states of opposite sign) for alkanes is confirmed, but the energies were found to depend slightly on chain length. In contrast, introducing an adjacent gauche of the same sign requires only 0.22-0.37 kcal/mol, approximately half of the single gauche state energy. This adjacent gauche stabilization should be taken into account when formulating or analyzing rotational isomeric models, carrying out conformational analysis, and developing force fields for alkanes, lipids, and related polymers.     

Confinement induced conformational changes in n-alkanes sequestered within a narrow carbon nanotube

While alkanes in solution exhibit predominantly extended conformations, nanoscale confinement of these chains within protein binding sites and synthetic receptors can significantly alter the conformer distribution. As a simple model for the effect of confinement on the conformation, we report molecular simulations of n-alkanes absorbed from a bulk solvent into narrow carbon nanotubes. We observe that confinement of butane, hexane, and tetracosane induces a trans to gauche conformational redistribution. Moreover, confined hexane and tetracosane exhibit cooperative interactions between neighboring dihedral angles, which promote a helical gauche conformation for the portions of the chain within the nanotube. Hexane absorbed into the nanotube from water or benzene exhibits essentially the same conformation regardless of the bulk solvent. The PMF between the nanotube and hexane along the central nanotube axis finds that nanotube absorption is favorable from aqueous solution but neutral from benzene. The interaction between hexane and the nanotube in water is dominated by the direct interaction between the alkane and the nanotube and weakly opposed by indirect water-mediated forces. In benzene, however, the direct alkane/nanotube interaction is effectively balanced by the indirect benzene-mediated interaction. Our simulations in water stand in difference to standard interpretations of the hydrophobic effect, which posit that the attraction between non-polar species in water is driven by their mutual insolubility.     

Detachment of Particles from Surfaces: An AFM Study

We have measured interactions between hydrophilic and hydrophobic surfaces in an aqueous medium at various pH and ionic strengths as well as in some organic solvents using atomic force microscopy and analyzed them in terms of particle adhesion and detachment from surfaces. In hydrophilic systems the forces observed were found to be well described by DLVO theory at large separation distances. Very long range hydrophobic forces were not observed in hydrophilic-hydrophobic systems. Nevertheless, the jump into contact was found to occur at distances greater that those predicted by just van der Waals attraction. The interaction between two hydrophobic surfaces was dominated by the long-range attraction due to hydrophobic forces. This interaction was found to be sensitive to the type of substrate as well as to the pH and electrolyte concentration. Measured pull-off forces showed poor reproducibility. However, average values showed clear trends and were used to estimate interfacial energies or work of adhesion for all systems studied by means of the Derjaguin approximation. These values were compared to those calculated by the surface tension component theory using the acid-base approach. Good qualitative agreement was obtained, giving support for the usefulness of this approach in estimating interfacial energies between surfaces in liquid media. A comparison of the measured adhesion force with hydrodynamic detachment experiments showed good qualitative agreement. Copyright 2001 Academic Press.     

Hydrophobic forces and hydrogen bonds in the adhesion between retinoid-coated surfaces

Interactions between hydrophobic chains of lipid monolayers and interactions between hydrophilic headgroups of lipid bilayers (with or without a molecular recognition step) are now well documented, especially for commonly used lipids. Here, we report force measurements between a new class of fluorinated lipid layers whose headgroups (synthetic ligands of retinoid receptors) display a very unusual polar/apolar character and can interact via a combination of hydrophobic forces and hydrogen bonds. Although these two interactions produce adhesion and are therefore not easily distinguishable, we show that it is possible to extract both contributions unambiguously. Experiments are performed both in pure water, where the adhesion is a combination of hydrophobic forces and hydrogen bonds, and in Tris buffer, where the hydrophobic effect is the dominant short-range attractive force. The contribution of hydrophobic forces scaled down to molecular interactions is deduced from force versus distance profiles, and the same value is found independently in pure water and Tris buffer, about 1 kBT. We also show that retinoid lipid layers attract each other through a very long-range (100 nm) exponential force, which is insensitive to the pH and the salinity. The origin of this long-range attraction is discussed on the basis of previously proposed mechanisms.     

Dynamic strength of the silicon-carbon bond observed over three decades of force-loading rates

The mechanical strength of individual Si-C bonds was determined as a function of the applied force-loading rate by dynamic single-molecule force spectroscopy, using an atomic force microscope. The applied force-loading rates ranged from 0.5 to 267 nN/s, spanning 3 orders of magnitude. As predicted by Arrhenius kinetics models, a logarithmic increase of the bond rupture force with increasing force-loading rate was observed, with average rupture forces ranging from 1.1 nN for 0.5 nN/s to 1.8 nN for 267 nN/s. Three different theoretical models, all based on Arrhenius kinetics and analytic forms of the binding potential, were used to analyze the experimental data and to extract the parameters fmax and D(e) of the binding potential, together with the Arrhenius A-factor. All three models well reproduced the experimental data, including statistical scattering; nevertheless, the three free parameters allow so much flexibility that they cannot be extracted unambiguously from the experimental data. Successful fits with a Morse potential were achieved with fmax = 2.0-4.8 nN and D(e) = 76-87 kJ/mol, with the Arrhenius A-factor covering 2.45 x 10(-10)-3 x 10(-5) s(-1), respectively. The Morse potential parameters and A-factor taken from gas-phase density functional calculations, on the other hand, did not reproduce the experimental forces and force-loading rate dependence.     

Predicting hydrophobic solvation by molecular simulation: 1. Testing united‐atom alkane models

We present a systematic test of the performance of three popular united‐atom force fields—OPLS‐UA, GROMOS and TraPPE—at predicting hydrophobic solvation, more precisely at describing the solvation of alkanes in alkanes. Gibbs free energies of solvation were calculated for 52 solute/solvent pairs from Molecular Dynamics simulations and thermodynamic integration making use of the IBERCIVIS volunteer computing platform. Our results show that all force fields yield good predictions when both solute and solvent are small linear or branched alkanes (up to pentane). However, as the size of the alkanes increases, all models tend to increasingly deviate from experimental data in a systematic fashion. Furthermore, our results confirm that specific interaction parameters for cyclic alkanes in the united‐atom representation are required to account for the additional excluded volume within the ring. Overall, the TraPPE model performs best for all alkanes, but systematically underpredicts the magnitude of solvation free energies by about 6% (RMSD of 1.2 kJ/mol). Conversely, both GROMOS and OPLS‐UA systematically overpredict solvation free energies (by ∼13% and 15%, respectively). The systematic trends suggest that all models can be improved by a slight adjustment of their Lennard‐Jones parameters. © 2016 Wiley Periodicals, Inc.     

Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules

A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/torsion, and angle/angle/ torsion cross-term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments. © 1994 by John Wiley & Sons, Inc.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.