Probing the Binding Affinity by Jarzynski's Nonequilibrium Binding Free Energy and Rupture Time

Binding affinity of a small ligand to a receptor is the important quantity in drug design, and it might be characterized by different quantities. The most popular one is the binding free energy, which can be estimated by several methods in conventional molecular dynamics simulation. So far in steered molecular dynamics (SMD), one can use either the rupture force or nonequilibrium pulling work as a measure for binding affinity. In this paper, we have shown that the nonequilibrium binding free energy Δ G_neq^Jar, obtained by Jarzynski's equality at a finite pulling speed, has good correlation with experimental data on inhibition constants, implying that this quantity can be used as a good scoring function for binding affinity. A similar correlation has also been disclosed for binding and unbinding free energy barriers. Applying the SMD method to unbinding of 23 small compounds from the binding site of β-lactamase protein, a bacteria-produced enzyme, we have demonstrated that the rupture or unbinding time strongly correlates with experimental data with correlation level R ≈ 0.84. As follows from the Jarzynski's equality, the rupture time depends on the unbinding barrier exponentially. We show that Δ G_neq^Jar, the rupture time, and binding and unbinding free energy barriers are good descriptors for binding affinity. Our observation may be useful for fast screening of potential leads as the SMD simulation is not time-consuming. On the basis of nonequilibrium simulation, we disclosed that, in agreement with the experiment, the binding time is much longer than the unbinding one.