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.