Dependence of Work on the Pulling Speed in Mechanical Ligand Unbinding.

In single-molecule force spectroscopy, the rupture force Fmax 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, Fmax ∼ ln(V). Recently, it has been found that non-equilibrium work W is better than Fmax 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 ∼ c1 ln(V) + c2 ln2(V), where c1 and c2 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.