Interpretation of Different Force Application Modes in Single Molecule Force Spectroscopy

Mechanical forces play an important part in biology at the molecular level. Numerous biological macromolecules, such as protein, RNA, and polysaccharides function under load in living cells. Single molecule force spectroscopy (SMFS) has emerged in the last two decades as a highly advantageous methodology of studying macromolecules with sub-nano resolution. In this technique, an external controlled vectorial force is applied to a molecule, while recording its conformational response. The most frequent mode is by pulling it at constant velocity (FX) or at constant force (FC). In the case of proteins, kinetic and thermodynamic information is then extracted from the unfolding forces histograms. This pose a difficulty, since the force dependent unfolding rate is given in terms of the applied force rate, Ḟ = dF/dt in [pN/s], while the experiments are performed under constant pulling velocity, v, in [nm/s]. To accommodate this requirement, the rate is approximated by Ḟ ~ K_s^.v, where K_s is the spring constant of the AFM tip. However, in FC experiments, through the use of a PID controller, one can directly set Ḟ, while recording the end-to-end length evolution of the molecule is recorded. In this work, we aim at comparing actual the corrections applied to the models in the FX mode to those measured under controlled Ḟ in the FC mode.