Accurate Calculation of Relative Binding Free Energies between Ligands with Different Net Charges

In drug discovery programs, modifications that change the net charge of the ligands are often considered to improve the binding potency and solubility, or to address other ADME/Tox problems. Accurate calculation of the binding free-energy changes associated with charge-changing perturbations remains a great challenge of central importance in computational drug discovery. The finite size effects associated with periodic boundary condition and lattice summation employed in common molecular dynamics simulations introduce artifacts in the electrostatic potential energy calculations, which need to be carefully handled for accurate free-energy calculations between systems with different net charges. The salts in the buffer solution of experimental binding affinity assays also have a strong effect on the binding free energies between charged species, which further complicates the modeling of the charge-changing perturbations. Here, we extend our free-energy perturbation (FEP) algorithm, which has been extensively applied to many drug discovery programs for relative binding free-energy calculations between ligands with the same net charge (charge-conserving perturbation), to enable charge-changing perturbations. We have investigated three different approaches to correct the finite size effects and tested them on 10 protein targets and 31 charge-changing perturbations. We have found that all three methods are able to successfully eliminate the box-size dependence of calculated binding free energies associated with brute force FEP. Moreover, inclusion of salts matching the ionic strength of experimental buffer solution significantly improves the calculated binding free energies. For ligands with multiple possible protonation states, we applied the p K_a correction to account for the ionization equilibrium of the ligands and the results are significantly improved. Finally, the calculated binding free energies from these methods agree with each other, and also agree well with the experimental results. The root-mean-square error between the calculated binding free energies and experimental data is 1.1 kcal/mol, which is on par with the accuracy of charge-conserving perturbations. We anticipate that the outstanding accuracy demonstrated here across a broad range of target classes may have significant implications for drug discovery projects, where charge-changing modifications must be considered.