Machine Learning Assisted Free Energy Simulation of Solution–Phase and Enzyme Reactions

Despite recent advances in the development of machine learning potentials (MLPs) for biomolecular simulations, there has been limited effort in developing stable and accurate MLPs for enzymatic reactions. Here, we report a protocol for performing machine learning assisted free energy simulation of solution-phase and enzyme reactions at an ab initio quantum mechanical and molecular mechanical (ai-QM/MM) level of accuracy. Within our protocol, the MLP is built to reproduce the ai-QM/MM energy as well as forces on both QM (reactive) and MM (solvent/enzyme) atoms. As an alternative strategy, a delta machine learning potential (DMLP) is trained to reproduce the differences between ai-QM/MM and semiempirical (se) QM/MM energy and forces. To account for the effect of the condensed–phase environment in both MLP and DMLP, the DeePMD representation of a molecular system is extended to incorporate external electrostatic potential and field on each QM atom. Using the Menshutkin and chorismate mutase reactions as examples, we show that the developed MLP and DMLP reproduce the ai-QM/MM energy and forces with an error on average less than 1.0 kcal/mol and 1.0 kcal/mol/Å for representative configurations along the reaction pathway. For both reactions, MLP/DMLP-based simulations yielded free energy profiles that differed by less than 1.0 kcal/mol from the reference ai-QM/MM results, but only at a fractional computational cost.