Development of Range-Corrected Deep Learning Potentials for Fast, Accurate Quantum Mechanical/Molecular Mechanical Simulations of Chemical Reactions in Solution

Abstract

We develop a new deep potentialrange correction (DPRc) machine learning potential for combined quantum mechanical/molecular mechanical (QM/MM) simulations of chemical reactions in the condensed phase. The new range correction enables short-ranged QM/MM interactions to be tuned for higher accuracy, and the correction smoothly vanishes within a specified cutoff. We further develop an active learning procedure for robust neural network training. We test the DPRc model and training procedure against a series of six nonenzymatic phosphoryl transfer reactions in solution that are important in mechanistic studies of RNA-cleaving enzymes. Specifically, we apply DPRc corrections to a base QM model and test its ability to reproduce free-energy profiles generated from a target QM model. We perform these comparisons using the MNDO/d and DFTB2 semiempirical models because they differ in the way they treat orbital orthogonalization and electrostatics and produce free-energy profiles which differ significantly from each other, thereby providing us a rigorous stress test for the DPRc model and training procedure. The comparisons show that accurate reproduction of the free-energy profiles requires correction of the QM/MM interactions out to 6 Å. We further find that the model’s initial training benefits from generating data from temperature replica exchange simulations and including high-temperature configurations into the fitting procedure, so the resulting models are trained to properly avoid high-energy regions. A single DPRc model was trained to reproduce four different reactions and yielded good agreement with the free-energy profiles made from the target QM/MM simulations. The DPRc model was further demonstrated to be transferable to 2D free-energy surfaces and 1D free-energy profiles that were not explicitly considered in the training. Examination of the computational performance of the DPRc model showed that it was fairly slow when run on CPUs but was sped up almost 100-fold when using NVIDIA V100 GPUs, resulting in almost negligible overhead. The new DPRc model and training procedure provide a potentially powerful new tool for the creation of next-generation QM/MM potentials for a wide spectrum of free-energy applications ranging from drug discovery to enzyme design.

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

“…In many cases, it is beneficial to reoptimize the se-QM/MM parameters 23,38 or directly modify the internal forces 39 to ensure a proper thermodynamic perturbation or interpolation correction or to maintain a stable multiple-time-step trajectory. Recently, Yang, 40−42 Gastegger, 43 York, 44 and Riniker 45 have proposed machine learning (ML) as a new strategy to address the computational cost of direct ai-QM/MM free energy simulations. Specifically, for configurations of interest, artificial neural network (ANN) models were designed and trained to reproduce either the ai-QM/MM potential, i.e., the machine learning potential (MLP), or the difference between the ai-QM/MM and se-QM/MM potentials, hereafter called the delta machine learning potential (ΔMLP).…”

“…These MLPs/ΔMLPs led to fairly accurate free energy barriers, with errors of around 1.0 kcal/mol, for several solution-phase reactions. [40][41][42]44 In these approaches, however, the effects of the solvent on the reacting system were rather homogeneous, and their applicability to reactions in a heterogeneous solvent environment, such as in enzyme, has not been fully explored.…”

“…The second is an "explicit" approach, in which any MM atom within a "cutoff" distance (e.g., 6.0 Å) from the QM region is included in the computation of ML descriptors. This approach was proposed by York and co-workers 44 for the QM/ MM expansion to the embedding matrix within the DeePMD coding framework 53,55 and also utilized by Riniker and coworkers 45 to extend the HDNNP descriptors to QM/MM calculations.…”

Affordable Ab Initio Path Integral for Thermodynamic Properties via Molecular Dynamics Simulations Using Semiempirical Reference Potential

“…If a larger QM region is necessary, for instance, when the solvent plays a more critical role than pure background charges polarizing the reaction center, more accurate reference potential is indispensable. Some recent studies have looked into this issue, and some practical solutions have been proposed, including optimizing the semiempirical methods and fitting the (delta) energy using machine learning techniques. ,,,− It is worth emphasizing that with the uncertainties in the free-energy profiles in the present study, it is difficult to quantitatively predict the magnitude of nuclear quantum effect (see Figure S4), and more extended simulations are required.…”

BuRNN: Buffer Region Neural Network Approach for Polarizable-Embedding Neural Network/Molecular Mechanics Simulations

“…The introduction of a cutoff, up to which the MM region is included, has emerged as a solution. 21 , 22 , 25 One example is FieldSchNet, 20 which circumvents this problem by sampling the environment while keeping the QM region fixed. This model has been shown to be powerful in predicting spectra and chemical reactions with neural networks (NNs) using electrostatic embedding but requires extended sampling.…”