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

Navigating the landscape of enzyme design: from molecular simulations to machine learning

Global environmental issues and sustainable development call for new technologies for fine chemical synthesis and waste valorization. Biocatalysis has attracted great attention as the alternative to the traditional organic synthesis. However, it is challenging to navigate the vast sequence space to identify those proteins with admirable biocatalytic functions. The recent development of deep-learning based structure prediction methods such as AlphaFold2 reinforced by different computational simulations or multiscale calculations has largely expanded the 3D structure databases and enabled structure-based design. While structure-based approaches shed light on site-specific enzyme engineering, they are not suitable for large-scale screening of potential biocatalysts. Effective utilization of big data using machine learning techniques opens up a new era for accelerated predictions. Here, we review the approaches and applications of structure-based and machine-learning guided enzyme design. We also provide our view on the challenges and perspectives on effectively employing enzyme design approaches integrating traditional molecular simulations and machine learning, and the importance of database construction and algorithm development in attaining predictive ML models to explore the sequence fitness landscape for the design of admirable biocatalysts.

Software Infrastructure for Next-Generation QM/MM-ΔMLP Force Fields

We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM-ΔMLP) force fields for a wide range of applications. The software integrates Amber's molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM-ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein-ligand binding.

Unlocking the potential of enzyme engineering via rational computational design strategies

Enzymes play a pivotal role in various industries by enabling efficient, eco-friendly, and sustainable chemical processes. However, the low turnover rates and poor substrate selectivity of enzymes limit their large-scale applications. Rational computational enzyme design, facilitated by computational algorithms, offers a more targeted and less labor-intensive approach. There has been notable advancement in employing rational computational protein engineering strategies to overcome these issues, it has not been comprehensively reviewed so far. This article reviews recent developments in rational computational enzyme design, categorizing them into three types: structure-based, sequence-based, and data-driven machine learning computational design. Case studies are presented to demonstrate successful enhancements in catalytic activity, stability, and substrate selectivity. Lastly, the article provides a thorough analysis of these approaches, highlights existing challenges and potential solutions, and offers insights into future development directions.

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Amber free energy tools: Interoperable software for free energy simulations using generalized quantum mechanical/molecular mechanical and machine learning potentials

We report the development and testing of new integrated cyberinfrastructure for performing free energy simulations with generalized hybrid quantum mechanical/molecular mechanical (QM/MM) and machine learning potentials (MLPs) in Amber. The Sander molecular dynamics program has been extended to leverage fast, density-functional tight-binding models implemented in the DFTB+ and xTB packages, and an interface to the DeePMD-kit software enables the use of MLPs. The software is integrated through application program interfaces that circumvent the need to perform "system calls" and enable the incorporation of long-range Ewald electrostatics into the external software's self-consistent field procedure. The infrastructure provides access to QM/MM models that may serve as the foundation for QM/MM-ΔMLP potentials, which supplement the semiempirical QM/MM model with a MLP correction trained to reproduce ab initio QM/MM energies and forces. Efficient optimization of minimum free energy pathways is enabled through a new surface-accelerated finite-temperature string method implemented in the FE-ToolKit package. Furthermore, we interfaced Sander with the i-PI software by implementing the socket communication protocol used in the i-PI client-server model. The new interface with i-PI allows for the treatment of nuclear quantum effects with semiempirical QM/MM-ΔMLP models. The modular interoperable software is demonstrated on proton transfer reactions in guanine-thymine mispairs in a B-form deoxyribonucleic acid helix. The current work represents a considerable advance in the development of modular software for performing free energy simulations of chemical reactions that are important in a wide range of applications.

emle-engine: A Flexible Electrostatic Machine Learning Embedding Package for Multiscale Molecular Dynamics Simulations

We present in this work the emle-engine package (https://github.com/chemle/emle-engine)─the implementation of a new machine learning embedding scheme for hybrid machine learning potential/molecular-mechanics (ML/MM) dynamics simulations. The package is based on an embedding scheme that uses a physics-based model of the electronic density and induction with a handful of tunable parameters derived from in vacuo properties of the subsystem to be embedded. This scheme is completely independent of the in vacuo potential and requires only the positions of the atoms of the machine learning subsystem and the positions and partial charges of the molecular mechanics environment. These characteristics allow emle-engine to be employed in existing QM/MM software. We demonstrate that the implemented electrostatic machine learning embedding scheme (named EMLE) is stable in enhanced sampling molecular dynamics simulations. Through the calculation of free energy surfaces of alanine dipeptide in water with two different ML options for the in vacuo potential and three embedding models, we test the performance of EMLE. When compared to the reference DFT/MM surface, the EMLE embedding is clearly superior to the MM one based on fixed partial charges. The configurational dependence of the electronic density and the inclusion of the induction energy introduced by the EMLE model leads to a systematic reduction in the average error of the free energy surface when compared to MM embedding. By enabling the usage of EMLE embedding in practical ML/MM simulations, emle-engine will make it possible to accurately model systems and processes that feature significant variations in the charge distribution of the ML subsystem and/or the interacting environment.

Learning QM/MM potential using equivariant multiscale model

The machine learning (ML) method emerges as an efficient and precise surrogate model for high-level electronic structure theory. Its application has been limited to closed chemical systems without considering external potentials from the surrounding environment. To address this limitation and incorporate the influence of external potentials, polarization effects, and long-range interactions between a chemical system and its environment, the first two terms of the Taylor expansion of an electrostatic operator have been used as extra input to the existing ML model to represent the electrostatic environments. However, high-order electrostatic interaction is often essential to account for external potentials from the environment. The existing models based only on invariant features cannot capture significant distribution patterns of the external potentials. Here, we propose a novel ML model that includes high-order terms of the Taylor expansion of an electrostatic operator and uses an equivariant model, which can generate a high-order tensor covariant with rotations as a base model. Therefore, we can use the multipole-expansion equation to derive a useful representation by accounting for polarization and intermolecular interaction. Moreover, to deal with long-range interactions, we follow the same strategy adopted to derive long-range interactions between a target system and its environment media. Our model achieves higher prediction accuracy and transferability among various environment media with these modifications.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine-Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials

Rare tautomeric forms of nucleobases can lead to Watson-Crick-like (WC-like) mispairs in DNA, but the process of proton transfer is fast and difficult to detect experimentally. NMR studies show evidence for the existence of short-time WC-like guanine-thymine (G-T) mispairs; however, the mechanism of proton transfer and the degree to which nuclear quantum effects play a role are unclear. We use a B-DNA helix exhibiting a wGT mispair as a model system to study tautomerization reactions. We perform ab initio (PBE0/6-31G*) quantum mechanical/molecular mechanical (QM/MM) simulations to examine the free energy surface for tautomerization. We demonstrate that while the ab initio QM/MM simulations are accurate, considerable sampling is required to achieve high precision in the free energy barriers. To address this problem, we develop a QM/MM machine learning potential correction (QM/MM-ΔMLP) that is able to improve the computational efficiency, greatly extend the accessible time scales of the simulations, and enable practical application of path integral molecular dynamics to examine nuclear quantum effects. We find that the inclusion of nuclear quantum effects has only a modest effect on the mechanistic pathway but leads to a considerable lowering of the free energy barrier for the GT*⇌G*T equilibrium. Our results enable a rationalization of observed experimental data and the prediction of populations of rare tautomeric forms of nucleobases and rates of their interconversion in B-DNA.

Machine Learning of Reactive Potentials

In the past two decades, machine learning potentials (MLPs) have driven significant developments in chemical, biological, and material sciences. The construction and training of MLPs enable fast and accurate simulations and analysis of thermodynamic and kinetic properties. This review focuses on the application of MLPs to reaction systems with consideration of bond breaking and formation. We review the development of MLP models, primarily with neural network and kernel-based algorithms, and recent applications of reactive MLPs (RMLPs) to systems at different scales. We show how RMLPs are constructed, how they speed up the calculation of reactive dynamics, and how they facilitate the study of reaction trajectories, reaction rates, free energy calculations, and many other calculations. Different data sampling strategies applied in building RMLPs are also discussed with a focus on how to collect structures for rare events and how to further improve their performance with active learning.

Assessment of Embedding Schemes in a Hybrid Machine Learning/Classical Potentials (ML/MM) Approach

Machine learning (ML) methods have reached high accuracy levels for the prediction of in vacuo molecular properties. However, the simulation of large systems solely through ML methods (such as those based on neural network potentials) is still a challenge. In this context, one of the most promising frameworks for integrating ML schemes in the simulation of complex molecular systems are the so-called ML/MM methods. These multiscale approaches combine ML methods with classical force fields (MM), in the same spirit as the successful hybrid quantum mechanics-molecular mechanics methods (QM/MM). The key issue for such ML/MM methods is an adequate description of the coupling between the region of the system described by ML and the region described at the MM level. In the context of QM/MM schemes, the main ingredient of the interaction is electrostatic, and the state of the art is the so-called electrostatic-embedding. In this study, we analyze the quality of simpler mechanical embedding-based approaches, specifically focusing on their application within a ML/MM framework utilizing atomic partial charges derived in vacuo. Taking as reference electrostatic embedding calculations performed at a QM(DFT)/MM level, we explore different atomic charges schemes, as well as a polarization correction computed using atomic polarizabilites. Our benchmark data set comprises a set of about 80k small organic structures from the ANI-1x and ANI-2x databases, solvated in water. The results suggest that the minimal basis iterative stockholder (MBIS) atomic charges yield the best agreement with the reference coupling energy. Remarkable enhancements are achieved by including a simple polarization correction.

Accelerating reliable multiscale quantum refinement of protein-drug systems enabled by machine learning

Biomacromolecule structures are essential for drug development and biocatalysis. Quantum refinement (QR) methods, which employ reliable quantum mechanics (QM) methods in crystallographic refinement, showed promise in improving the structural quality or even correcting the structure of biomacromolecules. However, vast computational costs and complex quantum mechanics/molecular mechanics (QM/MM) setups limit QR applications. Here we incorporate robust machine learning potentials (MLPs) in multiscale ONIOM(QM:MM) schemes to describe the core parts (e.g., drugs/inhibitors), replacing the expensive QM method. Additionally, two levels of MLPs are combined for the first time to overcome MLP limitations. Our unique MLPs+ONIOM-based QR methods achieve QM-level accuracy with significantly higher efficiency. Furthermore, our refinements provide computational evidence for the existence of bonded and nonbonded forms of the Food and Drug Administration (FDA)-approved drug nirmatrelvir in one SARS-CoV-2 main protease structure. This study highlights that powerful MLPs accelerate QRs for reliable protein-drug complexes, promote broader QR applications and provide more atomistic insights into drug development.

Long-range proton and hydroxide ion transfer dynamics at the water/CeO2 interface in the nanosecond regime: reactive molecular dynamics simulations and kinetic analysis

The structural properties, dynamical behaviors, and ion transport phenomena at the interface between water and cerium oxide are investigated by reactive molecular dynamics (MD) simulations employing neural network potentials (NNPs). The NNPs are trained to reproduce density functional theory (DFT) results, and DFT-based MD (DFT-MD) simulations with enhanced sampling techniques and refinement schemes are employed to efficiently and systematically acquire training data that include diverse hydrogen-bonding configurations caused by proton hopping events. The water interfaces with two low-index surfaces of (111) and (110) are explored with these NNPs, and the structure and long-range proton and hydroxide ion transfer dynamics are examined with unprecedented system sizes and long simulation times. Various types of proton hopping events at the interface are categorized and analyzed in detail. Furthermore, in order to decipher the proton and hydroxide ion transport phenomena along the surface, a counting analysis based on the semi-Markov process is formulated and applied to the MD trajectories to obtain reaction rates by considering the transport as stochastic jump processes. Through this model, the coupling between hopping events, vibrational motions, and hydrogen bond networks at the interface are quantitatively examined, and the high activity and ion transport phenomena at the water/CeO2 interface are unequivocally revealed in the nanosecond regime.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

Training machine learning potentials for reactive systems: A Colab tutorial on basic models

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Machine learning from quantum chemistry to predict experimental solvent effects on reaction rates

Fast and accurate prediction of solvent effects on reaction rates are crucial for kinetic modeling, chemical process design, and high-throughput solvent screening. Despite the recent advance in machine learning, a scarcity of reliable data has hindered the development of predictive models that are generalizable for diverse reactions and solvents. In this work, we generate a large set of data with the COSMO-RS method for over 28 000 neutral reactions and 295 solvents and train a machine learning model to predict the solvation free energy and solvation enthalpy of activation (ΔΔG‡solv, ΔΔH‡solv) for a solution phase reaction. On unseen reactions, the model achieves mean absolute errors of 0.71 and 1.03 kcal mol-1 for ΔΔG‡solv and ΔΔH‡solv, respectively, relative to the COSMO-RS calculations. The model also provides reliable predictions of relative rate constants within a factor of 4 when tested on experimental data. The presented model can provide nearly instantaneous predictions of kinetic solvent effects or relative rate constants for a broad range of neutral closed-shell or free radical reactions and solvents only based on atom-mapped reaction SMILES and solvent SMILES strings.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

DP/MM: A Hybrid Model for Zinc-Protein Interactions in Molecular Dynamics

Zinc-containing proteins are vital for many biological processes, yet accurately modeling them using classical force fields is hindered by complicated polarization and charge transfer effects. This study introduces DP/MM, a hybrid force field scheme that utilizes a deep potential model to correct the atomic forces of zinc ions and their coordinated atoms, elevating them from MM to QM levels of accuracy. Trained on the difference between MM and QM atomic forces across diverse zinc coordination groups, the DP/MM model faithfully reproduces structural characteristics of zinc coordination during simulations, such as the tetrahedral coordination of Cys4 and Cys3His1 groups. Furthermore, DP/MM allows water exchange in the zinc coordination environment. With its unique blend of accuracy, efficiency, flexibility, and transferability, DP/MM serves as a valuable tool for studying structures and dynamics of zinc-containing proteins and also represents a pioneering approach in the evolving landscape of machine learning potentials for molecular modeling.

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

Modern Alchemical Free Energy Methods for Drug Discovery Explained

This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.

Accurate and Efficient Multilevel Free Energy Simulations with Neural Network-Assisted Enhanced Sampling

Free energy differences (ΔF) are essential to quantitative characterization and understanding of chemical and biological processes. Their direct estimation with an accurate quantum mechanical potential is of great interest and yet impractical due to high computational cost and incompatibility with typical alchemical free energy protocols. One promising solution is the multilevel free energy simulation in which the estimate of ΔF at an inexpensive low level of theory is combined with the correction toward a higher level of theory. The poor configurational overlap generally expected between the two levels of theory, however, presents a major challenge. We overcome this challenge by using a deep neural network model and enhanced sampling simulations. An adversarial autoencoder is used to identify a low-dimensional (latent) space that compactly represents the degrees of freedom that encode the distinct distributions at the two levels of theory. Enhanced sampling in this latent space is then used to drive the sampling of configurations that predominantly contribute to the free energy correction. Results for both gas phase and condensed phase systems demonstrate that this data-driven approach offers high accuracy and efficiency with great potential for scalability to complex systems.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Unveiling the Excited State Dynamics of Indole in Solution

In this paper, we reconstruct in detail the dynamics of the emitting electronic excited state of aqueous indole, investigating its relaxation mechanism and kinetics to be related to the time-dependent fluorescence signal. Taking advantage of the results shown in a very recent paper, we were able to model the relaxation process in solution in terms of the transitions between two gas-phase singlet electronic states (¹L_a and ¹L_b), subsequently irreversibly relaxing to the gas-phase singlet dark state (¹πσ*). A comparison of the results with the available experimental data shows that the relaxation mechanism we obtain by our theoretical-computational model is reliable, reproducing rather accurately all the experimental observables.

Drug Design in the Exascale Era: A Perspective from Massively Parallel QM/MM Simulations

The initial phases of drug discovery - in silico drug design - could benefit from first principle Quantum Mechanics/Molecular Mechanics (QM/MM) molecular dynamics (MD) simulations in explicit solvent, yet many applications are currently limited by the short time scales that this approach can cover. Developing scalable first principle QM/MM MD interfaces fully exploiting current exascale machines - so far an unmet and crucial goal - will help overcome this problem, opening the way to the study of the thermodynamics and kinetics of ligand binding to protein with first principle accuracy. Here, taking two relevant case studies involving the interactions of ligands with rather large enzymes, we showcase the use of our recently developed massively scalable Multiscale Modeling in Computational Chemistry (MiMiC) QM/MM framework (currently using DFT to describe the QM region) to investigate reactions and ligand binding in enzymes of pharmacological relevance. We also demonstrate for the first time strong scaling of MiMiC-QM/MM MD simulations with parallel efficiency of ∼70% up to >80,000 cores. Thus, among many others, the MiMiC interface represents a promising candidate toward exascale applications by combining machine learning with statistical mechanics based algorithms tailored for exascale supercomputers.

The confluence of machine learning and multiscale simulations

Multiscale modeling has a long history of use in structural biology, as computational biologists strive to overcome the time- and length-scale limits of atomistic molecular dynamics. Contemporary machine learning techniques, such as deep learning, have promoted advances in virtually every field of science and engineering and are revitalizing the traditional notions of multiscale modeling. Deep learning has found success in various approaches for distilling information from fine-scale models, such as building surrogate models and guiding the development of coarse-grained potentials. However, perhaps its most powerful use in multiscale modeling is in defining latent spaces that enable efficient exploration of conformational space. This confluence of machine learning and multiscale simulation with modern high-performance computing promises a new era of discovery and innovation in structural biology.

Perspective: Reference-Potential Methods for the Study of Thermodynamic Properties in Chemical Processes: Theory, Applications, and Pitfalls

In silico investigations of enzymatic reactions and chemical reactions in condensed phases often suffer from formidable computational costs due to a large number of degrees of freedom and enormous important volume in phase space. Usually, accuracy must be compromised to trade for efficiency by lowering the reliability of the Hamiltonians employed or reducing the sampling time. Reference-potential methods (RPMs) offer an alternative approach to reaching high accuracy of simulation without much loss of efficiency. In this Perspective, we summarize the idea of RPMs and showcase some recent applications. Most importantly, the pitfalls of these methods are also discussed, and remedies to these pitfalls are presented.

Does a Machine-Learned Potential Perform Better Than an Optimally Tuned Traditional Force Field? A Case Study on Fluorohydrins

We present a comparative study that evaluates the performance of a machine learning potential (ANI-2x), a conventional force field (GAFF), and an optimally tuned GAFF-like force field in the modeling of a set of 10 γ-fluorohydrins that exhibit a complex interplay between intra- and intermolecular interactions in determining conformer stability. To benchmark the performance of each molecular model, we evaluated their energetic, geometric, and sampling accuracies relative to quantum-mechanical data. This benchmark involved conformational analysis both in the gas phase and chloroform solution. We also assessed the performance of the aforementioned molecular models in estimating nuclear spin-spin coupling constants by comparing their predictions to experimental data available in chloroform. The results and discussion presented in this study demonstrate that ANI-2x tends to predict stronger-than-expected hydrogen bonding and overstabilize global minima and shows problems related to inadequate description of dispersion interactions. Furthermore, while ANI-2x is a viable model for modeling in the gas phase, conventional force fields still play an important role, especially for condensed-phase simulations. Overall, this study highlights the strengths and weaknesses of each model, providing guidelines for the use and future development of force fields and machine learning potentials.

The application of QM/MM simulations in heterogeneous catalysis

The QM/MM simulation method is provenly efficient for the simulation of biological systems, where an interplay of extensive environment and delicate local interactions drives a process of interest through a funnel on a complex energy landscape. Recent advances in quantum chemistry and force-field methods present opportunities for the adoption of QM/MM to simulate heterogeneous catalytic processes, and their related systems, where similar intricacies exist on the energy landscape. Herein, the fundamental theoretical considerations for performing QM/MM simulations, and the practical considerations for setting up QM/MM simulations of catalytic systems, are introduced; then, areas of heterogeneous catalysis are explored where QM/MM methods have been most fruitfully applied. The discussion includes simulations performed for adsorption processes in solvent at metallic interfaces, reaction mechanisms within zeolitic systems, nanoparticles, and defect chemistry within ionic solids. We conclude with a perspective on the current state of the field and areas where future opportunities for development and application exist.

QDπ: A Quantum Deep Potential Interaction Model for Drug Discovery

We report QDπ-v1.0 for modeling the internal energy of drug molecules containing H, C, N, and O atoms. The QDπ model is in the form of a quantum mechanical/machine learning potential correction (QM/Δ-MLP) that uses a fast third-order self-consistent density-functional tight-binding (DFTB3/3OB) model that is corrected to a quantitatively high-level of accuracy through a deep-learning potential (DeepPot-SE). The model has the advantage that it is able to properly treat electrostatic interactions and handle changes in charge/protonation states. The model is trained against reference data computed at the ωB97X/6-31G* level (as in the ANI-1x data set) and compared to several other approximate semiempirical and machine learning potentials (ANI-1x, ANI-2x, DFTB3, MNDO/d, AM1, PM6, GFN1-xTB, and GFN2-xTB). The QDπ model is demonstrated to be accurate for a wide range of intra- and intermolecular interactions (despite its intended use as an internal energy model) and has shown to perform exceptionally well for relative protonation/deprotonation energies and tautomers. An example application to model reactions involved in RNA strand cleavage catalyzed by protein and nucleic acid enzymes illustrates QDπ has average errors less than 0.5 kcal/mol, whereas the other models compared have errors over an order of magnitude greater. Taken together, this makes QDπ highly attractive as a potential force field model for drug discovery.

Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme

A powerful tool to study the mechanism of reactions in solutions or enzymes is to perform the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. However, the computational cost is too high due to the explicit electronic structure calculations at every time step of the simulation. A neural network (NN) method can accelerate the QM/MM-MD simulations, but it has long been a problem to accurately describe the QM/MM electrostatic coupling by NN in the electrostatic embedding (EE) scheme. In this work, we developed a new method to accelerate QM/MM calculations in the mechanic embedding (ME) scheme. The potentials and partial point charges of QM atoms are first learned in vacuo by the embedded atom neural networks (EANN) approach. MD simulations are then performed on this EANN/MM potential energy surface (PES) to obtain free energy (FE) profiles for reactions, in which the QM/MM electrostatic coupling is treated in the mechanic embedding (ME) scheme. Finally, a weighted thermodynamic perturbation (wTP) corrects the FE profiles in the ME scheme to the EE scheme. For two reactions in water and one in methanol, our simulations reproduced the B3LYP/MM free energy profiles within 0.5 kcal/mol with a speed-up of 30-60-fold. The results show that the strategy of combining EANN potential in the ME scheme with the wTP correction is efficient and reliable for chemical reaction simulations in liquid. Another advantage of our method is that the QM PES is independent of the MM subsystem, so it can be applied to various MM environments as demonstrated by an S_N2 reaction studied in water and methanol individually, which used the same EANN PES. The free energy profiles are in excellent accordance with the results obtained from B3LYP/MM-MD simulations. In future, this method will be applied to the reactions of enzymes and their variants.

Electrostatic Embedding of Machine Learning Potentials

This work presents a variant of an electrostatic embedding scheme that allows the embedding of arbitrary machine learned potentials trained on molecular systems in vacuo. The scheme is based on physically motivated models of electronic density and polarizability, resulting in a generic model without relying on an exhaustive training set. The scheme only requires in vacuo single point QM calculations to provide training densities and molecular dipolar polarizabilities. As an example, the scheme is applied to create an embedding model for the QM7 data set using Gaussian Process Regression with only 445 reference atomic environments. The model was tested on the SARS-CoV-2 protease complex with PF-00835231, resulting in a predicted embedding energy RMSE of 2 kcal/mol, compared to explicit DFT/MM calculations.

Data science techniques in biomolecular force field development

Recent advances in data science are impacting the development of classical force fields. Here we review some ideas and techniques from data science that have been used in force field development, including database construction, atom typing, and machine learning potentials. We highlight how new tools such as active learning and automatic differentiation are facilitating the generation of target data and the direct fitting with macroscopic observables. Philosophical changes on how force field models should be built and used are also discussed. It's inspiring that more accurate biomolecular force fields can be developed with the aid of data science techniques.

Machine learning based implicit solvent model for aqueous-solution alanine dipeptide molecular dynamics simulations

Inspired by the recent work from Noé and coworkers on the development of machine learning based implicit solvent model for the simulation of solvated peptides [Chen et al., J. Chem. Phys., 2021, 155, 084101], here we report another investigation of the possibility of using machine learning (ML) techniques to "derive" an implicit solvent model directly from explicit solvent molecular dynamics (MD) simulations. For alanine dipeptide, a machine learning potential (MLP) based on the DeepPot-SE representation of the molecule was trained to capture its interactions with its average solvent environment configuration (ASEC). The predicted forces on the solute deviated only by an RMSD of 0.4 kcal mol-1 Å-1 from the reference values, and the MLP-based free energy surface differed from that obtained from explicit solvent MD simulations by an RMSD of less than 0.9 kcal mol-1. Our MLP training protocol could also accurately reproduce combined quantum mechanical molecular mechanical (QM/MM) forces on the quantum mechanical (QM) solute in ASEC environment, thus enabling the development of accurate ML-based implicit solvent models for ab initio-QM MD simulations. Such ML-based implicit solvent models for QM calculations are cost-effective in both the training stage, where the use of ASEC reduces the number of data points to be labelled, and the inference stage, where the MLP can be evaluated at a relatively small additional cost on top of the QM calculation of the solute.

Machine Learning Exciton Hamiltonians in Light-Harvesting Complexes

We propose a machine learning (ML)-based strategy for an inexpensive calculation of excitonic properties of light-harvesting complexes (LHCs). The strategy uses classical molecular dynamics simulations of LHCs in their natural environment in combination with ML prediction of the excitonic Hamiltonian of the embedded aggregate of pigments. The proposed ML model can reproduce the effects of geometrical fluctuations together with those due to electrostatic and polarization interactions between the pigments and the protein. The training is performed on the chlorophylls of the major LHC of plants, but we demonstrate that the model is able to extrapolate well beyond the initial training set. Moreover, the accuracy in predicting the effects of the environment is tested on the simulation of the small changes observed in the absorption spectra of the wild-type and a mutant of a minor LHC.

Data-driven enzyme engineering to identify function-enhancing enzymes

Identifying function-enhancing enzyme variants is a 'holy grail' challenge in protein science because it will allow researchers to expand the biocatalytic toolbox for late-stage functionalization of drug-like molecules, environmental degradation of plastics and other pollutants, and medical treatment of food allergies. Data-driven strategies, including statistical modeling, machine learning, and deep learning, have largely advanced the understanding of the sequence-structure-function relationships for enzymes. They have also enhanced the capability of predicting and designing new enzymes and enzyme variants for catalyzing the transformation of new-to-nature reactions. Here, we reviewed the recent progresses of data-driven models that were applied in identifying efficiency-enhancing mutants for catalytic reactions. We also discussed existing challenges and obstacles faced by the community. Although the review is by no means comprehensive, we hope that the discussion can inform the readers about the state-of-the-art in data-driven enzyme engineering, inspiring more joint experimental-computational efforts to develop and apply data-driven modeling to innovate biocatalysts for synthetic and pharmaceutical applications.

Protein dynamics: The future is bright and complicated!

Biological life depends on motion, and this manifests itself in proteins that display motion over a formidable range of time scales spanning from femtoseconds vibrations of atoms at enzymatic transition states, all the way to slow domain motions occurring on micro to milliseconds. An outstanding challenge in contemporary biophysics and structural biology is a quantitative understanding of the linkages among protein structure, dynamics, and function. These linkages are becoming increasingly explorable due to conceptual and methodological advances. In this Perspective article, we will point toward future directions of the field of protein dynamics with an emphasis on enzymes. Research questions in the field are becoming increasingly complex such as the mechanistic understanding of high-order interaction networks in allosteric signal propagation through a protein matrix, or the connection between local and collective motions. In analogy to the solution to the "protein folding problem," we argue that the way forward to understanding these and other important questions lies in the successful integration of experiment and computation, while utilizing the present rapid expansion of sequence and structure space. Looking forward, the future is bright, and we are in a period where we are on the doorstep to, at least in part, comprehend the importance of dynamics for biological function.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.

Predicting Solvent Effects on SN2 Reaction Rates: Comparison of QM/MM, Implicit, and MM Explicit Solvent Models

Solvents are one of the key variables in the optimization of a synthesis yield or properties of a synthesis product. In this paper, contemporary solvent models are applied to predict the rates of S_N2 reactions in a range of aqueous and non-aqueous solvents. High-level CCSD(T)/CBS//M06-2X/6-31+G(d) gas phase energies were combined with solvation free energies from SMD, SM12, and ADF-COSMO-RS continuum solvent models, as well as molecular mechanics (MM) explicit solvent models with different atomic charge schemes to predict the rate constants of three S_N2 reactions in eight protic and aprotic solvents. It is revealed that the prediction of rate constants in organic solvents is not necessarily less challenging than in water and popular solvent models struggle to predict their rate constants to within 3 log units of experimental values. Among the continuum solvent models, the ADF-COSMO-RS model performed the best in predicting absolute rate contants while the SM12 model was best at predicting relative rate constants with an average accuracy of about 1.5 and 0.8 log units, respectively. The use of computationally more demanding MM explicit solvent models did not translate to improvements in absolute rate constants but was quite effective at predicting relative rate constants due to systematic error cancellation. Free energy barriers obtained from umbrella sampling with explicit solvent QM/MM simulations led to excellent agreement with experimental values, provided that a validated level of theory is used to treat the QM region.

Facilitating ab initio QM/MM free energy simulations by Gaussian process regression with derivative observations

In combined quantum mechanical and molecular mechanical (QM/MM) free energy simulations, how to synthesize the accuracy of ab initio (AI) methods with the speed of semiempirical (SE) methods for a cost-effective QM treatment remains a long-standing challenge. In this work, we present a machine-learning-facilitated method for obtaining AI/MM-quality free energy profiles through efficient SE/MM simulations. In particular, we use Gaussian process regression (GPR) to learn the energy and force corrections needed for SE/MM to match with AI/MM results during molecular dynamics simulations. Force matching is enabled in our model by including energy derivatives into the observational targets through the extended-kernel formalism. We demonstrate the effectiveness of this method on the solution-phase SN2 Menshutkin reaction using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. Trained on only 80 configurations sampled along the minimum free energy path (MFEP), the resulting GPR model reduces the average energy error in AM1/MM from 18.2 to 5.8 kcal mol-1 for the 4000-sample testing set with the average force error on the QM atoms decreased from 14.6 to 3.7 kcal mol-1 Å-1. Free energy sampling with the GPR corrections applied (AM1-GPR/MM) produces a free energy barrier of 14.4 kcal mol-1 and a reaction free energy of -34.1 kcal mol-1, in closer agreement with the AI/MM benchmarks and experimental results.

Improving the Accuracy of Quantum Mechanics/Molecular Mechanics (QM/MM) Models with Polarized Fragment Charges

This paper introduces an economical approach for improving the accuracy and convergence of quantum mechanics/molecular mechanics (QM/MM) models. The approach is tested on a series of neutral and charged amino acids embedded in a 160-water cluster, where their intramolecular proton transfer energies (neutral amino acid → zwitterionic amino acid) were previously obtained at the ωB97X-D/6-31G(d) level of theory. When the charges on the MM atoms were replaced with those obtained at the same QM level of theory used to treat the QM atoms, this significantly improved the accuracy and convergence of the QM/MM models. In particular, the QM/MM model converged to within 1.4 kcal mol^-1 of directly calculated DFT energies for smaller (by as many as 20 waters) QM regions. The use of atomic charges obtained from the natural population analysis yielded the most significant improvement, while other charge schemes such as Mulliken, electrostatic potential, or CM5 led to poorer outcomes. It is further demonstrated that the QM atomic charges can be accurately estimated in a highly efficient manner using an iterative fragmentation approach based on the moving-domain QM/MM method. Similar observations were made when the approach was used to predict the barrier of an S_N2 reaction. Thus, the use of QM-quality atomic charges on MM atoms represents a simple and easy-to-implement strategy for improving the accuracy of QM/MM models.

Combining Machine Learning Approaches and Accurate Ab Initio Enhanced Sampling Methods for Prebiotic Chemical Reactions in Solution

The study of the thermodynamics, kinetics, and microscopic mechanisms of chemical reactions in solution requires the use of advanced free-energy methods for predictions to be quantitative. This task is however a formidable one for atomistic simulation methods, as the cost of quantum-based ab initio approaches, to obtain statistically meaningful samplings of the relevant chemical spaces and networks, becomes exceedingly heavy. In this work, we critically assess the optimal structure and minimal size of an ab initio training set able to lead to accurate free-energy profiles sampled with neural network potentials. The results allow one to propose an ab initio protocol where the ad hoc inclusion of a machine-learning (ML)-based task can significantly increase the computational efficiency, while keeping the ab initio accuracy and, at the same time, avoiding some of the notorious extrapolation risks in typical atomistic ML approaches. We focus on two representative, and computationally challenging, reaction steps of the classic Strecker-cyanohydrin mechanism for glycine synthesis in water solution, where the main precursors are formaldehyde and hydrogen cyanide. We demonstrate that indistinguishable ab initio quality results are obtained, thanks to the ML subprotocol, at about 1 order of magnitude less of computational load.

Combined fragment-based machine learning force field with classical force field and its application in the NMR calculations of macromolecules in solutions

We have developed a combined fragment-based machine learning (ML) force field and molecular mechanics (MM) force field for simulating the structures of macromolecules in solutions, and then compute its NMR chemical shifts with the generalized energy-based fragmentation (GEBF) approach at the level of density functional theory (DFT). In this work, we first construct Gaussian approximation potential based on GEBF subsystems of macromolecules for MD simulations and then a GEBF-based neural network (GEBF-NN) with deep potential model for the studied macromolecule. Then, we develop a GEBF-NN/MM force field for macromolecules in solutions by combining the GEBF-NN force field for the solute molecule and ff14SB force field for solvent molecules. Using the GEBF-NN/MM MD simulation to generate snapshot structures of solute/solvent clusters, we then perform the NMR calculations with the GEBF approach at the DFT level to calculate NMR chemical shifts of the solute molecule. Taking a heptamer of oligopyridine-dicarboxamides in chloroform solution as an example, our results show that the GEBF-NN force field is quite accurate for this heptamer by comparing with the reference DFT results. For this heptamer in chloroform solution, both the GEBF-NN/MM and classical MD simulations could lead to helical structures from the same initial extended structure. The GEBF-DFT NMR results indicate that the GEBF-NN/MM force field could lead to more accurate NMR chemical shifts on hydrogen atoms by comparing with the experimental NMR results. Therefore, the GEBF-NN/MM force field could be employed for predicting more accurate dynamical behaviors than the classical force field for complex systems in solutions.

Combined QM/MM, Machine Learning Path Integral Approach to Compute Free Energy Profiles and Kinetic Isotope Effects in RNA Cleavage Reactions

We present a fast, accurate, and robust approach for determination of free energy profiles and kinetic isotope effects for RNA 2'-O-transphosphorylation reactions with inclusion of nuclear quantum effects. We apply a deep potential range correction (DPRc) for combined quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in the condensed phase. The method uses the second-order density-functional tight-binding method (DFTB2) as a fast, approximate base QM model. The DPRc model modifies the DFTB2 QM interactions and applies short-range corrections to the QM/MM interactions to reproduce ab initio DFT (PBE0/6-31G*) QM/MM energies and forces. The DPRc thus enables both QM and QM/MM interactions to be tuned to high accuracy, and the QM/MM corrections are designed to smoothly vanish at a specified cutoff boundary (6 Å in the present work). The computational speed-up afforded by the QM/MM+DPRc model enables free energy profiles to be calculated that include rigorous long-range QM/MM interactions under periodic boundary conditions and nuclear quantum effects through a path integral approach using a new interface between the AMBER and i-PI software. The approach is demonstrated through the calculation of free energy profiles of a native RNA cleavage model reaction and reactions involving thio-substitutions, which are important experimental probes of the mechanism. The DFTB2+DPRc QM/MM free energy surfaces agree very closely with the PBE0/6-31G* QM/MM results, and it is vastly superior to the DFTB2 QM/MM surfaces with and without weighted thermodynamic perturbation corrections. 18O and 34S primary kinetic isotope effects are compared, and the influence of nuclear quantum effects on the free energy profiles is examined.

How Reproducible Are QM/MM Simulations? Lessons from Computational Studies of the Covalent Inhibition of the SARS-CoV-2 Main Protease by Carmofur

This work explores the level of transparency in reporting the details of computational protocols that is required for practical reproducibility of quantum mechanics/molecular mechanics (QM/MM) simulations. Using the reaction of an essential SARS-CoV-2 enzyme (the main protease) with a covalent inhibitor (carmofur) as a test case of chemical reactions in biomolecules, we carried out QM/MM calculations to determine the structures and energies of the reactants, the product, and the transition state/intermediate using analogous QM/MM models implemented in two software packages, NWChem and Q-Chem. Our main benchmarking goal was to reproduce the key energetics computed with the two packages. Our results indicate that quantitative agreement (within the numerical thresholds used in calculations) is difficult to achieve. We show that rather minor details of QM/MM simulations must be reported in order to ensure the reproducibility of the results and offer suggestions toward developing practical guidelines for reporting the results of biosimulations.

Computer-aided drug design, quantum-mechanical methods for biological problems

Quantum chemistry enables to study systems with chemical accuracy (<1 kcal/mol from experiment) but is restricted to a handful of atoms due to its computational expense. This has led to ongoing interest to optimize and simplify these methods while retaining accuracy. Implementing quantum mechanical (QM) methods on modern hardware such as multiple-GPUs is one example of how the field is optimizing performance. Multiscale approaches like the so-called QM/molecular mechanical method are gaining popularity in drug discovery because they focus the application of QM methods on the region of choice (e.g., the binding site), while using efficient MM models to represent less relevant areas. The creation of simplified QM methods is another example, including the use of machine learning to create ultra-fast and accurate QM models. Herein, we summarize recent advancements in the development of optimized QM methods that enhance our ability to use these methods in computer aided drug discovery.

Accelerating Ab Initio Quantum Mechanical and Molecular Mechanical (QM/MM) Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semiempirical QM/MM Hamiltonian

Molecular dynamics (MD) simulations employing ab initio quantum mechanical and molecular mechanical (ai-QM/MM) potentials are considered to be the state of the art, but the high computational cost associated with the ai-QM calculations remains a theoretical challenge for their routine application. Here, we present a modified protocol of the multiple time step (MTS) method for accelerating ai-QM/MM MD simulations of condensed-phase reactions. Within a previous MTS protocol [Nam J. Chem. Theory Comput. 2014, 10, 4175], reference forces are evaluated using a low-level (semiempirical QM/MM) Hamiltonian and employed at inner time steps to propagate the nuclear motions. Correction forces, which arise from the force differences between high-level (ai-QM/MM) and low-level Hamiltonians, are applied at outer time steps, where the MTS algorithm allows the time-reversible integration of the correction forces. To increase the outer step size, which is bound by the highest-frequency component in the correction forces, the semiempirical QM Hamiltonian is recalibrated in this work to minimize the magnitude of the correction forces. The remaining high-frequency modes, which are mainly bond stretches involving hydrogen atoms, are then removed from the correction forces. When combined with a Langevin or SIN(R) thermostat, the modified MTS-QM/MM scheme remains robust with an up to 8 (with Langevin) or 10 fs (with SIN(R)) outer time step (with 1 fs inner time steps) for the chorismate mutase system. This leads to an over 5-fold speedup over standard ai-QM/MM simulations, without sacrificing the accuracy in the predicted free energy profile of the reaction.

Mechanistic Insights into Enzyme Catalysis from Explaining Machine-Learned Quantum Mechanical and Molecular Mechanical Minimum Energy Pathways

With the increasing popularity of machine learning (ML) applications, the demand for explainable artificial intelligence techniques to explain ML models developed for computational chemistry has also emerged. In this study, we present the development of the Boltzmann-weighted cumulative integrated gradients (BCIG) approach for effective explanation of mechanistic insights into ML models trained on high-level quantum mechanical and molecular mechanical (QM/MM) minimum energy pathways. Using the acylation reactions of the Toho-1 β-lactamase and two antibiotics (ampicillin and cefalexin) as the model systems, we show that the BCIG approach could quantitatively attribute the energetic contribution in one system and the relative reactivity of individual steps across different systems to specific chemical processes such as the bond making/breaking and proton transfers. The proposed BCIG contribution attribution method quantifies chemistry-interpretable insights in terms of contributions from each elementary chemical process, which is in agreement with the validating QM/MM calculations and our intuitive mechanistic understandings of the model reactions.