Dependence of Work on the Pulling Speed in Mechanical Ligand Unbinding

[Image: see text] In single-molecule force spectroscopy, the rupture force F(max) required for mechanical unfolding of a biomolecule or for pulling a ligand out of a binding site depends on the pulling speed V and, in the linear Bell–Evans regime, F(max) ∼ ln(V). Recently, it has been found that non-equilibrium work W is better than F(max) in describing relative ligand binding affinity, but the dependence of W on V remains unknown. In this paper, we developed an analytical theory showing that in the linear regime, W ∼ c(1) ln(V) + c(2) ln(2)(V), where c(1) and c(2) are constants. This quadratic dependence was also confirmed by all-atom steered molecular dynamics simulations of protein–ligand complexes. Although our theory was developed for ligand unbinding, it is also applicable to other processes, such as mechanical unfolding of proteins and other biomolecules, due to its universality.