Dependence of Work on the Pulling Speed in Mechanical Ligand Unbinding

Abstract

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.

Antibody–nanobody combination increases their neutralizing activity against SARS-CoV-2 and nanobody H11-H4 is effective against Alpha, Kappa and Delta variants

“…W increased rapidly until the pulled molecule (H11-H4, CR3022 or RBD) left the binding region, reaching a stable value when two subsystems ceased to interact (Fig. 3 B), and also increases with v 74 . For v = 0.5 nm/ns, we obtained W = 101.6 ± 3.4, 208.6 ± 5.3 and 461.3 ± 5.7 kcal/mol for H11-H4–RBD, CR3022–RBD, and H11-H4 + CR3022–RBD, respectively (Table 2 ).…”

Point mutations in SARS-CoV-2 variants induce long-range dynamical perturbations in neutralizing antibodies

“…While it is true that explicit solvent gives more accurate thermodynamics, when pulling a ligand through water the rate of pulling must be accounted for. 59 Implicit solvents permit instantaneous ("adiabatic") rearrangement of the "water", while explicit water imposes a limit to the speed with which the ligand can be pulled (i.e., slower than the structural relaxation of the explicit water molecules). As a consequence, the absolute work will be different due to interaction with the water molecules during the pulling.…”

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“…These numerical errors are exacerbated by larger systems which effect larger fluctuations and require even longer pulling distances to fully unravel. The speed of the pulling of the nonequilibrium trajectories has also been seen to affect convergence, as, for example, Li et al found that fast pulling can affect the PMF results when a limited number of realizations are performed. Specifically, as the pulling speed V is increased, the nonequilibrium work values used to determine the JA increase in concert as a quadratic function of ln­( V ) .…”

“…The speed of the pulling of the nonequilibrium trajectories has also been seen to affect convergence, as, for example, Li et al found that fast pulling can affect the PMF results when a limited number of realizations are performed. Specifically, as the pulling speed V is increased, the nonequilibrium work values used to determine the JA increase in concert as a quadratic function of ln­( V ) . Thus, a low pulling speed and a reasonably large number of trajectories are often needed to obtain accurate results through SMD, which in turn requires significant to inaccessibly large computational resources.…”

“…Specifically, as the pulling speed V is increased, the nonequilibrium work values used to determine the JA increase in concert as a quadratic function of ln( V ). 44 Thus, a low pulling speed and a reasonably large number of trajectories are often needed to obtain accurate results through SMD, which in turn requires significant to inaccessibly large computational resources.…”