Fundamental High-Speed Limits in Single-Molecule, Single-Cell, and Nanoscale Force Spectroscopies

Force spectroscopy is enhancing our understanding of single-biomolecule, single-cell, and nanoscale mechanics. Force spectroscopy postulates the proportionality between the interaction force and the instantaneous probe deflection. By studying the probe dynamics, we demonstrate that the total force acting on the probe has three different components: the interaction, the hydrodynamic, and the inertial. The amplitudes of those components depend on the ratio between the resonant frequency and the frequency at which the data are measured. A force-distance curve provides a faithful measurement of the interaction force between two molecules when the inertial and hydrodynamic components are negligible. Otherwise, force spectroscopy measurements will underestimate the value of unbinding forces. Neglecting the above force components requires the use of frequency ratios in the 50-500 range. These ratios will limit the use of high-speed methods in force spectroscopy. The theory is supported by numerical simulations.