Accurate and Time-Efficient Condensed-Phase Free Energy Simulations with Reaction Specific Δ-Machine Learning Potentials in CHARMM

Abstract

The application of machine learning potentials (MLPs) to accurately simulate enzymatic reactions remains challenging. This is primarily due to the high dimensionality and structural heterogeneity of enzyme systems, as well as the need to incorporate off-equilibrium and transition state conformations into the training data. Integrating MLPs into a quantum mechanical/molecular mechanical (QM/MM) framework through either direct learning or Δ-learning, together with reaction-specific training strategies, can help overcome these limitations. In this work, we present an integrated workflow for MLP/ΔMLP-assisted QM/MM simulations that achieves ab initio (ai) or density functional theory (DFT)-level accuracy in predicting enzyme reaction thermodynamics. Developed within CHARMM and tightly integrated with the mlp_qmmm Python package, the workflow automates training-data generation, data sanitization, MLP/ΔMLP training, and deployment of trained models in QM/MM molecular dynamics (MD) simulations. In addition, a low-overhead interface implemented in CHARMM enables efficient model inference on both CPU and GPU during simulations. The workflow further incorporates an iterative model refinement strategy that systematically improves predictive performance through successive rounds of sampling, high-level labeling, and retraining. The capabilities of the approach are demonstrated using the hydride-transfer reaction catalyzed by four variants of dihydrofolate reductase (DHFR). Compared with conventional ai/DFT-QM/MM simulations, the ΔMLP-assisted approach achieves more than 500-fold acceleration while maintaining subkcal/mol accuracy in predicted reaction free energies and free energy barriers. Iterative refinement further improves the underlying energy and force predictions, leading to more accurate thermodynamic and structural properties obtained from QM/MM simulations with only a modest additional computational cost. Overall, this work establishes a scalable and extensible workflow for the systematic development and iterative refinement of reaction-specific MLP/ΔMLP models, enabling highly accurate and computationally efficient simulations of enzyme-catalyzed reactions.