A single-molecule stretching method for lateral and normal AFM lever calibration

Angle-dependent strength of a single chemical bond by stereographic force spectroscopy

A wealth of chemical bonds and polymers have been studied with single-molecule force spectroscopy, usually by applying a force perpendicular to the anchoring surface. However, the direction-dependence of the bond strength lacks fundamental understanding. Here we establish stereographic force spectroscopy to study the single-bond strength for various pulling angles. Surprisingly, we find that the apparent bond strength increases with increasing pulling angle relative to the anchoring surface normal, indicating a sturdy mechanical anisotropy of a chemical bond. This finding can be rationalized by a fixed pathway for the rupture of the bond, resulting in an effective projection of the applied pulling force onto a nearly fixed rupture direction. Our study is fundamental for the molecular understanding of the role of the direction of force application in molecular adhesion and friction. It is also a prerequisite for the nanoscale tailoring of the anisotropic strength of bottom-up designed materials.

Stereographic force spectroscopy reveals that a chemical bond ruptures along a fixed pathway such that the apparent bond strength strongly depends on the angle of force application.

Calibration of T-shaped atomic force microscope cantilevers using the thermal noise method

The tip-sample interaction force measurements in atomic force microscopy (AFM) provide information about materials' properties with nanoscale resolution. The T-shaped cantilevers used in Torsional-Harmonic AFM allow measuring the rapidly changing tip-sample interaction forces using the torsional (twisting) deflections of the cantilever due to the off-axis placement of the sharp tip. However, it has been difficult to calibrate these cantilevers using the commonly used thermal noise-based calibration method as the mechanical coupling between flexural and torsional deflections makes it challenging to determine the deflection sensitivities from force-distance curves. Here, we present thermal noise-based calibration of these T-shaped AFM cantilevers by simultaneously analyzing flexural and torsional thermal noise spectra, along with deflection signals during a force-distance curve measurement. The calibration steps remain identical to the conventional thermal noise method, but a computer performs additional calculations to account for mode coupling. We demonstrate the robustness of the calibration method by determining the sensitivity of calibration results to the laser spot position on the cantilever, to the orientation of the cantilever in the cantilever holder, and by repeated measurements. We validated the quantitative force measurements against the known unfolding force of a protein, the I91 domain of titin, which resulted in consistent unfolding force values among six independently calibrated cantilevers.

Probing fibronectin-antibody interactions using AFM force spectroscopy and lateral force microscopy

The first experiment showing the effects of specific interaction forces using lateral force microscopy (LFM) was demonstrated for lectin-carbohydrate interactions some years ago. Such measurements are possible under the assumption that specific forces strongly dominate over the non-specific ones. However, obtaining quantitative results requires the complex and tedious calibration of a torsional force. Here, a new and relatively simple method for the calibration of the torsional force is presented. The proposed calibration method is validated through the measurement of the interaction forces between human fibronectin and its monoclonal antibody. The results obtained using LFM and AFM-based classical force spectroscopies showed similar unbinding forces recorded at similar loading rates. Our studies verify that the proposed lateral force calibration method can be applied to study single molecule interactions.

Precise and direct method for the measurement of the torsion spring constant of the atomic force microscopy cantilevers

A direct method for the evaluation of the torsional spring constants of the atomic force microscope cantilevers is presented in this paper. The method uses a nanoindenter to apply forces at the long axis of the cantilever and in the certain distance from it. The torque vs torsion relation is then evaluated by the comparison of the results of the indentations experiments at different positions on the cantilever. Next, this relation is used for the precise determination of the torsional spring constant of the cantilever. The statistical analysis shows that the standard deviation of the calibration measurements is equal to approximately 1%. Furthermore, a simple method for calibration of the photodetector's lateral response is proposed. The overall procedure of the lateral calibration constant determination has the accuracy approximately equal to 10%.