Incorporating Polarization into ML/MM Endpoint Calculations for Protein–Ligand Affinity Ranking

Endpoint free-energy calculations combine low computational cost with reasonable accuracy and are widely used to rank protein–ligand affinities, yet describing charge polarization in these calculations remains a challenge. Here we introduce a machine learning/molecular mechanics (ML/MM) framework that incorporates polarizationcorrected mechanical embedding (PCME) and electrostatic embedding (EE) into endpoint calculations, using binding-state-and conformation-dependent ML charges in both the gas-phase energy and polar solvation terms. On a benchmark of 15 targets from the JACS and Merck sets, the PCME and EE routes of ML/MM-PBSA rank affinities better than classical MM-PBSA, raising the median Spearman ρ from 0.216 to 0.343 and 0.329, respectively, at an acceptable computational cost. A charge-source control and the analysis of a representative PTP1B complex show how conformationdependent ML charges resolve asymmetric local electrostatic environments and contribute to the improved ranking of ML/MM-PBSA(PCME) over MM-PBSA. By incorporating charge redistribution into both interaction and solvation energies, this work provides a practical ML/MM endpoint framework for protein–ligand affinity ranking and analysis of the underlying electrostatic contributions.