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.

Force spectroscopy measurements of the rupture of the molecular bond between biotin and streptavidin often results in a wide distribution of rupture forces. We attribute the long tail of high rupture forces to the nearly simultaneous rupture of more than one molecular bond. To decrease the number of possible bonds, we employed hydrophilic polymeric tethers to attach biotin molecules to the atomic force microscope probe. It is shown that the measured distributions of rupture forces still contain high forces that cannot be described by the forced dissociation from a deep potential well. We employed a recently developed analytical model of simultaneous rupture of two bonds connected by polymer tethers with uneven length to fit the measured distributions. The resulting kinetic parameters agree with the energy landscape predicted by molecular dynamics simulations. It is demonstrated that when more than one molecular bond might rupture during the pulling measurements there is a noise-limited range of probe velocities where the kinetic parameters measured by force spectroscopy correspond to the true energy landscape. Outside this range of velocities, the kinetic parameters extracted by using the standard most probable force approach might be interpreted as artificial energy barriers that are not present in the actual energy landscape. Factors that affect the range of useful velocities are discussed.

The hydrophobic effect is important for many biological and technological processes. Despite progress in theory, experimental data clarifying water structure and the interaction between hydrophobic solutes at the nanometer scale are scarce due to the very low solubility of hydrophobic species. This article describes an AFM single molecule force spectroscopy method to probe the interaction between molecules with low solubility and reports measurements of the strength and the length scale of the "hydrophobic bond" between hexadecane molecules. Hexadecane molecules are tethered by flexible poly(ethylene glycol) linkers to AFM probes and substrates, removing the aggregation state uncertainty of solution-based approaches as well as spurious surface effects. A shorter hydrophilic polymer layer is added to increase the accessibility of hydrophobic molecules for the force spectroscopy measurements. Statistical analysis of the rupture forces yields a barrier width of 0.24 nm, and a dissociation rate of 1.1 s(-1). The results of single molecule measurements are related to the theoretical predictions of the free energy of cavitation in water and to the empirical model of micellization of nonionic surfactants. It is estimated that approximately one-quarter of each molecule's surface is hydrated during forced dissociation, consistent with an extended (nonglobular) conformation of the hexadecane molecules in the dimer.

A force-spectroscopy-based approach is used to characterize separation between amyloidogenic peptide fragments of alpha-synuclein. Interactions between individual molecules are studied using a scanning-force-microscopy-based technique. Alpha-synuclein fragments are attached to the solid surfaces via flexible long poly-(ethylene glycol) linkers removing aggregation state uncertainty of solution-based approaches and spurious surface effects. Tethering one fragment to the scanning probe tip and another fragment to the second surface ensures that interactions between tethered molecules are studied. Control experiments with only one tethered peptide indicate peptide-peptide interactions as the source of observed interaction forces in the double-tether experiment. The temperature dependence of rupture forces from 17.5 degrees C to 40 degrees C reveals similar molecular parameters indicating that no significant conformational changes occur in the associated molecules over this temperature range. Rate-dependent measurements indicate conformational heterogeneity of joined peptide molecules.

Interactions between fullerene C60 molecules in water were measured by force spectroscopy. Fullerene molecules were covalently connected to bifunctional water-soluble poly(ethylene glycol) (PEG) linkers and subsequently tethered to the substrate and to the tip of the atomic force microscope to facilitate single molecule detection and avoid spurious surface effects. The distributions of rupture forces for substrates prepared with different incubation times of C60-PEG-NH2 exhibit high rupture forces that cannot be explained by the theoretical distribution of single molecule binding. Moreover, the relative amplitude of the high force peak in the histogram increases with incubation time. These observations are explained by attributing the measured high forces to the rupture of multiple bonds between fullerene molecules. Force spectroscopy data analysis based on the most probable forces gives significantly different dissociation rates for samples that exhibit different amplitudes of the high force peak. An approximate analytical model that considers ruptures of two bonds that are simultaneously loaded by tethers with different lengths is proposed. This model successfully fits the distributions of the rupture forces using the same set of kinetic parameters for samples prepared with different grafting densities. It is proposed that this model can be used as a common tool to analyze the probability distributions of rupture forces that contain peaks or shoulders on the high force side of the distribution.