Correction Terms for Calculating Binding Free Energy Using Rates from Nonequilibrium Simulations

The free energy of a process is the fundamental quantity that determines its spontaneity or propensity at a given temperature. Binding free energy of a drug candidate to its biomolecular target is used as an objective quantity in drug design. Binding kinetics -- rates of association (k_on) and dissociation (k_off) -- have also demonstrated utility for their ability to predict efficacy and in some cases have been shown to be more predictive than the binding free energy alone. Although challenging, some methods exist to calculate binding kinetics from molecular simulations. While the kinetics of the binding process are related to the free energy by the log of their ratio, it is not straightforward to account for common, practical details pertaining to the calculation of rates in molecular simulations, such as the finite simulation volume or the particular definition of the ``bound" and ``unbound" states. Here we derive a set of correction terms that can be applied to calculations of binding free energies using rates observed in simulations. One term accounts for the particular definitions of the bound and unbound states. The second term accounts for residual electrostatic interactions that might still be present between the molecules, which is especially useful if one or both of the molecules carry an explicit charge. The third term accounts for the volume of the unbound state in the simulation box, which is useful to keep the simulated volume as small as possible during rate calculations. We apply these correction terms to revisit the calculation of binding free energies from rate constants for a host-guest system that was part of a blind prediction challenge, where significant deviations were observed between free energies calculated with rate ratios and those calculated from alchemical perturbation. The correction terms combine to significantly decrease the error with respect to computational benchmarks, from 3.4 to 0.76 kcal/mol.