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.