We present the design and implementation of a novel neural network potential (NNP) and its combination with an electrostatic embedding scheme, commonly used within the context of hybrid quantum-mechanical/molecular-mechanical (QM/MM) simulations. Substitution of a computationally expensive QM Hamiltonian by an NNP with the same accuracy largely reduces the computational cost and enables efficient sampling in prospective MD simulations, the main limitation faced by traditional QM/MM setups. The model relies on the recently introduced anisotropic message passing (AMP) formalism to compute atomic interactions and encode symmetries found in QM systems. AMP is shown to be highly efficient in terms of both data and computational costs and can be readily scaled to sample systems involving more than 350 solute and 40,000 solvent atoms for hundreds of nanoseconds using umbrella sampling. Most deviations of AMP predictions from the underlying DFT ground truth lie within chemical accuracy (4.184 kJ mol^-1). The performance and broad applicability of our approach are showcased by calculating the free-energy surface of alanine dipeptide, the preferred ligation states of nickel phosphine complexes, and dissociation free energies of charged pyridine and quinoline dimers. Results with this ML/MM approach show excellent agreement with experimental data and reach chemical accuracy in most cases. In contrast, free energies calculated with static DFT calculations paired with implicit solvent models or QM/MM MD simulations using cheaper semiempirical methods show up to ten times higher deviation from the experimental ground truth and sometimes even fail to reproduce qualitative trends.

The conformational ensemble of a molecule is strongly influenced by the surrounding environment. Correctly modeling the effect of any given environment is, hence, of pivotal importance in computational studies. Machine learning (ML) has been shown to be able to model these interactions probabilistically, with successful applications demonstrated for classical molecular dynamics. While first instances of ML implicit solvents for quantum-mechanical (QM) calculations exist, the high computational cost of QM reference calculations hinders the development of a generally applicable ML implicit solvent model for QM calculations. Here, we present a novel way of developing such a general machine-learned QM implicit solvent model by transferring knowledge obtained from classical interactions to QM, emulating a QM/MM setup with electrostatic embedding and a nonpolarizable MM solvent. This has the profound advantages that neither QM/MM reference calculations nor experimental data are required for training and that the obtained graph neural network (GNN)-based implicit solvent model (termed QM-GNNIS) is compatible with any functional and basis set. QM-GNNIS is currently applicable to small organic molecules and describes 39 different organic solvents. The performance of QM-GNNIS is validated on NMR and IR experiments, demonstrating that the approach can reproduce experimentally observed trends unattainable by state-of-the-art implicit-solvent models paired with static QM calculations.

We present the next generation of AMP, a neural network potential (NNP) with anisotropic message passing designed to study large biomolecular systems at DFT accuracy in the condensed phase using a multiscale approach similar to quantum-mechanics/molecular-mechanics (QM/MM) with electrostatic embedding. We trained AMPv3 on our recently published biomolecular multiscale simulation (BMS25) data set and demonstrated the model’s high efficiency, which enabled us to simulate proteins involving thousands of atoms at DFT accuracy in addition to explicit MM solvent for up to 100 ns, which presents a major leap for contemporary NNPs. We observe excellent scaling to large systems on a single GPU. AMPv3-BMS25 (or AMP-BMS for short) shows promising performance on benchmarks, and we demonstrate that the model can be used to accurately estimate experimental properties, including solvation free energies of small molecules and structural features of proteins. Finally, AMP-BMS/MM was employed to predict the free-energy profiles of reactions catalyzed by the enzymes chorismate mutase and fluoroacetate dehalogenase. In total, AMP-BMS/MM was used to simulate proteins in the condensed phase for a cumulative 23 μs simulation time or 48 billion integration steps. This work establishes AMP-BMS as a highly efficient and accurate model for multiscale simulations of biomolecules.