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 6 non-enzymatic 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 comparisons using the MNDO/d and DFTB2 semiempirical models because they 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 4 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 an 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.<br>

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

“…• In our current protocol, the samples from one or more iterations were all labelled using the high-level method. Active learning or concurrent learning 44,54 as well as a more robust data clustering algorithm can be adopted to reduce the cost of both data labelling and training.…”

“…A common strategy around this is to completely ignore the long-range electrostatics due to MM atoms beyond a cutoff distance. 44,45 In the context of DMLP-learning, this strategy means that the long-range electrostatics of DMLP is approximated at the low-level method. However, a systematic analysis has yet to be carried out to gauge the impact of solvent/enzyme atoms moving across the cutoff boundary during the simulation on the developed ML potentials, as it can contribute to a discontinuity on the potential energy surface.…”

“…Recently, Yang, [40][41][42] Gastegger, 43 York, 44 Riniker 45 and coworkers 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, referred to as the delta machine learning potential (DMLP).…”

“…These MLPs/DMLPs 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 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 (such as 6.0Å) from the QM region is included in the computation of ML descriptors. This approach was proposed by York and coworkers 44 for the QM/MM expansion to the embedding matrix within the DeePMD coding framework, 53,54 and also utilized by Riniker and coworkers 45 to extend the HDNNP descriptors to QM/MM calculations.…”