Trust the force, but pull wisely: Structural insights into non-equilibrium response forces from pulling MD simulations

We analyze the coarse-grained equations of motion of molecular systems subject to external driving. As exemplary processes, we study by means of targeted and steered molecular dynamics simulations the dissociation of a sodium-chloride ion pair in water and ligand-protein unbinding of trypsin-benzamidine. We derive an exact generalization of Mori's Langevin equation that contains the memory kernel of the stationary process, an additive driving force, and a non-equilibrium response force describing the effects of the perturbed environment. We show that both the fluctuating force in the stationary case and the non-equilibrium response force in the driven cases exhibit spatial structure in their first and second moments. The latter depends sensitively on the employed driving protocols. For sodium chloride, we find that the first moment of the non-equilibrium response force matches the mean force for slow constrained pulling. In contrast, for all tested restrained pulling protocols, significant differences arise between the two properties in both systems. We conclude that the non-equilibrium response of the solvent needs to be taken into account carefully when analyzing data from pulling simulations.