Machine Learning in QM/MM Molecular Dynamics Simulations of Condensed-Phase Systems

Potency Prediction of Covalent Inhibitors against SARS-CoV-2 3CL-like Protease and Multiple Mutants by Multiscale Simulations

3-Chymotrypsin-like protease (3CLpro) is a prominent target against pathogenic coronaviruses. Expert knowledge of the cysteine-targeted covalent reaction mechanism is crucial to predict the inhibitory potency of approved inhibitors against 3CLpros of SARS-CoV-2 variants and perform structure-based drug design against newly emerging coronaviruses. We carried out an extensive array of classical and hybrid QM/MM molecular dynamics simulations to explore covalent inhibition mechanisms of five well-characterized inhibitors toward SARS-CoV-2 3CLpro and its mutants. The calculated binding affinity and reactivity of the inhibitors are highly consistent with experimental data, and the predicted inhibitory potency of the inhibitors against 3CLpro with L167F, E166V, or T21I/E166V mutant is in full agreement with IC50s determined by the accompanying enzymatic assays. The explored mechanisms unveil the impact of residue mutagenesis on structural dynamics that communicates to change not only noncovalent binding strength but also covalent reaction free energy. Such a change is inhibitor dependent, corresponding to varied levels of drug resistance of these 3CLpro mutants against nirmatrelvir and simnotrelvir and no resistance to the 11a compound. These results together suggest that the present simulations with a suitable protocol can efficiently evaluate the reactivity and potency of covalent inhibitors along with the elucidated molecular mechanisms of covalent inhibition.

Searching for Protein Off-Targets of Prostate-Specific Membrane Antigen-Targeting Radioligands in the Salivary Glands

Background: Prostate specific membrane antigen (PSMA)-targeted radioligand therapies represent a highly effective treatment for metastatic prostate cancer. However, high and sustain uptake of PSMA-ligands in the salivary glands led to dose limiting dry mouth (xerostomia), especially with α-emitters. The expression of PSMA and histologic analysis couldn't directly explain the toxicity, suggesting a potential off-target mediator for uptake. In this study, we searched for possible off-target non-PSMA protein(s) in the salivary glands. Methods: A machine-learning based quantitative structure activity relationship (QSAR) model was built for seeking the possible off-target(s). The resulting target candidates from the model prediction were subjected to further analysis for salivary protein expression and structural homology at key regions required for PSMA-ligand binding. Furthermore, cellular binding assays were performed utilizing multiple cell lines with high expression of the candidate proteins and low expression of PSMA. Finally, PSMA knockout (PSMA-/-) mice were scanned by small animal PET/MR using [68Ga]Ga-PSMA-11 for in-vivo validation. Results: The screening of the trained QSAR model did not yield a solid off-target protein, which was corroborated in part by cellular binding assays. Imaging using PSMA-/- mice further demonstrated markedly reduced PSMA-radioligand uptake in the salivary glands. Conclusion: Uptake of the PSMA-targeted radioligands in the salivary glands remains primarily PSMA-mediated. Further investigations are needed to illustrate a seemingly different process of uptake and retention in the salivary glands than that in prostate cancer.

AI-Driven Discovery of Amorphous Fluorinated Polymer Electret with Improved Charge Stability for Energy Harvesting

Electret materials are promising dielectric materials with trapped charges for various applications such as vibration energy harvesters and acoustic transducers. In the present work, ionization potential is discovered as the descriptor to quantify the charging performance for amorphous fluorinated polymer electrets. Using this descriptor, high-throughput computations, and graph neural network models, 1 176 591 functional groups are screened on the cyclic transparent optical polymers (CYTOP), and 3 promising electrets are identified. The electrets are synthesized experimentally as 15 µm-thick films. The films are able to keep their both bipolar surface potentials above ±3.1 kV for over 1500 h and are estimated to have longevity of 146 years under 80 °C, achieving significant improvements on charging stability among CYTOP-based polymer electrets. The excellent bipolar charging performance can greatly enhance power generation capacity of electret-based vibration energy harvesters. This work also demonstrates the use of deep learning as a new paradigm for accelerating practical materials discovery.

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.

Nanoscale chemical reaction exploration with a quantum magnifying glass

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a "quantum magnifying glass" that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

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.

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.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

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.

Deciphering the Lexicon of Protein Targets: A Review on Multifaceted Drug Discovery in the Era of Artificial Intelligence

Understanding protein sequence and structure is essential for understanding protein-protein interactions (PPIs), which are essential for many biological processes and diseases. Targeting protein binding hot spots, which regulate signaling and growth, with rational drug design is promising. Rational drug design uses structural data and computational tools to study protein binding sites and protein interfaces to design inhibitors that can change these interactions, thereby potentially leading to therapeutic approaches. Artificial intelligence (AI), such as machine learning (ML) and deep learning (DL), has advanced drug discovery and design by providing computational resources and methods. Quantum chemistry is essential for drug reactivity, toxicology, drug screening, and quantitative structure-activity relationship (QSAR) properties. This review discusses the methodologies and challenges of identifying and characterizing hot spots and binding sites. It also explores the strategies and applications of artificial-intelligence-based rational drug design technologies that target proteins and protein-protein interaction (PPI) binding hot spots. It provides valuable insights for drug design with therapeutic implications. We have also demonstrated the pathological conditions of heat shock protein 27 (HSP27) and matrix metallopoproteinases (MMP2 and MMP9) and designed inhibitors of these proteins using the drug discovery paradigm in a case study on the discovery of drug molecules for cancer treatment. Additionally, the implications of benzothiazole derivatives for anticancer drug design and discovery are deliberated.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

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.

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.

NICE-FF: A non-empirical, intermolecular, consistent, and extensible force field for nucleic acids and beyond

A new non-empirical ab initio intermolecular force field (NICE-FF in buffered 14-7 potential form) has been developed for nucleic acids and beyond based on the dimer interaction energies (IEs) calculated at the spin component scaled-MI-second order Møller-Plesset perturbation theory. A fully automatic framework has been implemented for this purpose, capable of generating well-polished computational grids, performing the necessary ab initio calculations, conducting machine learning (ML) assisted force field (FF) parametrization, and extending existing FF parameters by incorporating new atom types. For the ML-assisted parametrization of NICE-FF, interaction energies of ∼18 000 dimer geometries (with IE < 0) were used, and the best fit gave a mean square deviation of about 0.46 kcal/mol. During this parametrization, atom types apparent in four deoxyribonucleic acid (DNA) bases have been first trained using the generated DNA base datasets. Both uracil and hypoxanthine, which contain the same atom types found in DNA bases, have been considered as test molecules. Three new atom types have been added to the DNA atom types by using IE datasets of both pyrazinamide and 9-methylhypoxanthine. Finally, the last test molecule, theophylline, has been selected, which contains already-fitted atom-type parameters. The performance of NICE-FF has been investigated on the S22 dataset, and it has been found that NICE-FF outperforms the well-known FFs by generating the most consistent IEs with the high-level ab initio ones. Moreover, NICE-FF has been integrated into our in-house developed crystal structure prediction (CSP) tool [called FFCASP (Fast and Flexible CrystAl Structure Predictor)], aiming to find the experimental crystal structures of all considered molecules. CSPs, which were performed up to 4 formula units (Z), resulted in NICE-FF being able to locate almost all the known experimental crystal structures with sufficiently low RMSD20 values to provide good starting points for density functional theory optimizations.

Structure-guided metagenome mining to tap microbial functional diversity

Scientists now have access to millions of accurate three-dimensional (3D) models of protein structures. How do we leverage 3D structural models to learn about microbial functions encoded in metagenomes? Here, we review recent developments using protein structural features to mine metagenomes from diverse environments ranging from the human gut to soil and ocean viromes. We compare 3D protein structural methods to characterize antibiotic resistance phenotypes, nutrient cycling, and host-drug-microbe interactions. Broadly, we encourage the scientific community to look beyond global sequence and structure alignments by considering fine-grained descriptors such as distance to ligand, active site, and tertiary interactions between amino acid residues scaling to microbiomes. Finally, we highlight structure-inspired approaches to chart new areas of microbial protein-coding sequence space.

Using machine learning to go beyond potential energy surface benchmarking for chemical reactivity

We train an equivariant machine learning (ML) model to predict energies and forces for hydrogen combustion under conditions of finite temperature and pressure. This challenging case for reactive chemistry illustrates that ML potential energy surfaces are difficult to make complete, due to overreliance on chemical intuition of what data are important for training. Instead, a 'negative design' data acquisition strategy using metadynamics as part of an active learning workflow helps to create a ML model that avoids unforeseen high-energy or unphysical energy configurations. This strategy more rapidly converges the potential energy surfaces such that it is now more efficient to make calls to the external ab initio source when query-by-committee models disagree to further molecular dynamics in time without need for ML retraining. With the hybrid ML-physics model we realize two orders of magnitude reduction in cost, allowing for prediction of the free-energy change in the transition-state mechanism for several hydrogen combustion reaction channels.

The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

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.

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.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

ONIOM meets : efficient, accurate, and robust multi-layer simulations across the periodic table

The computational treatment of large molecular structures is of increasing interest in fields of modern chemistry. Accordingly, efficient quantum chemical approaches are needed to perform sophisticated investigations on such systems. This engaged the development of the well-established "Our own N-layered integrated molecular orbital and molecular mechanics" (ONIOM) multi-layer scheme [L. W. Chung et al., Chem. Rev., 2015, 115, 5678-5796]. In this work, we present the specific implementation of the ONIOM scheme into the xtb semi-empirical extended tight-binding program package and its application to challenging transition-metal complexes. The efficient and broadly applicable GFNn-xTB and -FF methods are applied in the ONIOM framework to elucidate reaction energies, geometry optimizations, and explicit solvation effects for metal-organic systems with up to several hundreds of atoms. It is shown that an ONIOM-based combination of density functional theory, semi-empirical, and force-field methods can be used to drastically reduce the computational costs and thus enable the investigation of huge systems at almost no significant loss in accuracy.

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.

Unimolecular dissociation of C6H6-C6H5Cl, C6H6-C6H3Cl3, and C6H6-C6Cl6 complexes using machine learning approach

The application of Machine Learning (ML) algorithms in chemical sciences, particularly computational chemistry, is a vastly emerging area of modern research. While many applications of ML techniques have already been in place to use ML based potential energies in various dynamical simulation studies, specific applications are also being successfully tested. In this work, the ML algorithms are tested to calculate the unimolecular dissociation time of benzene-hexachlorobenzene, benzene-trichlorobenzene, and benzene-monochlorobenzene complexes. Three ML algorithms, namely, Decision-Tree-Regression (DTR), Multi-Layer Perceptron, and Support Vector Regression are considered. The algorithms are trained with simulated dissociation times as functions (attributes) of complexes' intramolecular and intermolecular vibrational energies. The simulation data are used for an excitation temperature of 1500 K. Considering that the converged result is obtained with 1500 trajectories, an ML algorithm trained with 700 simulation points provides the same dissociation rate constant within statistical uncertainty as obtained from the converged 1500 trajectory result. The DTR algorithm is also used to predict 1000 K simulation results using 1500 K simulation data.

Past, Present, and Future Perspectives on Computer-Aided Drug Design Methodologies

The application of computational approaches in drug discovery has been consolidated in the last decades. These families of techniques are usually grouped under the common name of "computer-aided drug design" (CADD), and they now constitute one of the pillars in the pharmaceutical discovery pipelines in many academic and industrial environments. Their implementation has been demonstrated to tremendously improve the speed of the early discovery steps, allowing for the proficient and rational choice of proper compounds for a desired therapeutic need among the extreme vastness of the drug-like chemical space. Moreover, the application of CADD approaches allows the rationalization of biochemical and interactive processes of pharmaceutical interest at the molecular level. Because of this, computational tools are now extensively used also in the field of rational 3D design and optimization of chemical entities starting from the structural information of the targets, which can be experimentally resolved or can also be obtained with other computer-based techniques. In this work, we revised the state-of-the-art computer-aided drug design methods, focusing on their application in different scenarios of pharmaceutical and biological interest, not only highlighting their great potential and their benefits, but also discussing their actual limitations and eventual weaknesses. This work can be considered a brief overview of computational methods for drug discovery.

Machine Learning Interatomic Potentials and Long-Range Physics

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

Accurate Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning

This work extends the electron deformation density-based descriptor, originally developed in the electron deformation density-based interaction energy machine learning (EDDIE-ML) algorithm to predict dimer interaction energies, to the prediction of three-body interactions in trimers. Using a sequential learning process to select the training data, the resulting Gaussian process regression (GPR) model predicts the three-body interaction energy within 0.2 kcal mol^-1 of the SRS-MP2/cc-pVTZ reference values for the 3B69 and S22-3 trimer data sets. A hybrid kernel function is introduced, which combines contributions from the average and individual atomic environments, allowing the total trimer interaction energy to be predicted in addition to the three-body contribution using the same descriptor. To extend the range and diversity of trimer interaction energies available in the literature, a new data set based on a protein-ligand crystal structure is introduced, consisting of 509 structures of a central ligand with two protein fragments. Benchmark calculations are provided for the new data set, which contains significantly larger molecular interactions than current databases in the literature in addition to charged fragments. Compared to density funtional theory (DFT)- and wavefunction-based methods for calculating the three-body interaction energy, our model makes predictions in a significantly shorter time frame by reducing the number of required SCF calculations from 7 to 4 performed at the PBE0 level of theory, showcasing the utility and efficiency of our Δ-ML method particularly when applied to larger systems.

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.

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.

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.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions

Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.

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.

Deep coarse-grained potentials via relative entropy minimization

Neural network (NN) potentials are a natural choice for coarse-grained (CG) models. Their many-body capacity allows highly accurate approximations of the potential of mean force, promising CG simulations of unprecedented accuracy. CG NN potentials trained bottom-up via force matching (FM), however, suffer from finite data effects: They rely on prior potentials for physically sound predictions outside the training data domain, and the corresponding free energy surface is sensitive to errors in the transition regions. The standard alternative to FM for classical potentials is relative entropy (RE) minimization, which has not yet been applied to NN potentials. In this work, we demonstrate, for benchmark problems of liquid water and alanine dipeptide, that RE training is more data efficient, due to accessing the CG distribution during training, resulting in improved free energy surfaces and reduced sensitivity to prior potentials. In addition, RE learns to correct time integration errors, allowing larger time steps in CG molecular dynamics simulation, while maintaining accuracy. Thus, our findings support the use of training objectives beyond FM, as a promising direction for improving CG NN potential's accuracy and reliability.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

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.

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.

Conformational Stability and Denaturation Processes of Proteins Investigated by Electrophoresis under Extreme Conditions

The functional structure of proteins results from marginally stable folded conformations. Reversible unfolding, irreversible denaturation, and deterioration can be caused by chemical and physical agents due to changes in the physicochemical conditions of pH, ionic strength, temperature, pressure, and electric field or due to the presence of a cosolvent that perturbs the delicate balance between stabilizing and destabilizing interactions and eventually induces chemical modifications. For most proteins, denaturation is a complex process involving transient intermediates in several reversible and eventually irreversible steps. Knowledge of protein stability and denaturation processes is mandatory for the development of enzymes as industrial catalysts, biopharmaceuticals, analytical and medical bioreagents, and safe industrial food. Electrophoresis techniques operating under extreme conditions are convenient tools for analyzing unfolding transitions, trapping transient intermediates, and gaining insight into the mechanisms of denaturation processes. Moreover, quantitative analysis of electrophoretic mobility transition curves allows the estimation of the conformational stability of proteins. These approaches include polyacrylamide gel electrophoresis and capillary zone electrophoresis under cold, heat, and hydrostatic pressure and in the presence of non-ionic denaturing agents or stabilizers such as polyols and heavy water. Lastly, after exposure to extremes of physical conditions, electrophoresis under standard conditions provides information on irreversible processes, slow conformational drifts, and slow renaturation processes. The impressive developments of enzyme technology with multiple applications in fine chemistry, biopharmaceutics, and nanomedicine prompted us to revisit the potentialities of these electrophoretic approaches. This feature review is illustrated with published and unpublished results obtained by the authors on cholinesterases and paraoxonase, two physiologically and toxicologically important enzymes.

Graph-convolutional neural networks for (QM)ML/MM molecular dynamics simulations

To accurately study the chemical reactions in the condensed phase or within enzymes, both quantum-mechanical description and sufficient configurational sampling are required to reach converged estimates. Here, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations play an important role, providing QM accuracy for the region of interest at a decreased computational cost. However, QM/MM simulations are still too expensive to study large systems on longer time scales. Recently, machine learning (ML) models have been proposed to replace the QM description. The main limitation of these models lies in the accurate description of long-range interactions present in condensed-phase systems. To overcome this issue, a recent workflow has been introduced combining a semi-empirical method (i.e. density functional tight binding (DFTB)) and a high-dimensional neural network potential (HDNNP) in a Δ-learning scheme. This approach has been shown to be capable of correctly incorporating long-range interactions within a cutoff of 1.4 nm. One of the promising alternative approaches to efficiently take long-range effects into account is the development of graph-convolutional neural networks (GCNNs) for the prediction of the potential-energy surface. In this work, we investigate the use of GCNN models - with and without a Δ-learning scheme - for (QM)ML/MM MD simulations. We show that the Δ-learning approach using a GCNN and DFTB as a baseline achieves competitive performance on our benchmarking set of solutes and chemical reactions in water. This method is additionally validated by performing prospective (QM)ML/MM MD simulations of retinoic acid in water and S-adenoslymethionine interacting with cytosine in water. The results indicate that the Δ-learning GCNN model is a valuable alternative for the (QM)ML/MM MD simulations of condensed-phase systems.

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.

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.

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Modelling and understanding properties of materials from first principles require knowledge of the underlyingatomistic structure. This entails knowing the individual chemical identity and position of all atoms involved.Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, andbulk phases of amorphous and solid materials represents a difficult high-dimensional global optimizationproblem. The rise of machine learning techniques in materials science has, however, led to many compellingdevelopments that may speed up structure searches. The complexity of such new methods has prompted aneed for an efficient way of assembling them into global optimization algorithms that can be experimentedwith. In this paper, we introduce the Atomistic Global Optimization X (AGOX) framework and code, asa customizable approach that enables efficient building and testing of global optimization algorithms. Amodular way of expressing global optimization algorithms is described and modern programming practicesare used to enable that modularity in the freely available AGOX python package. A number of examplesof global optimization approaches are implemented and analyzed. This ranges from random search andbasin-hopping to machine learning aided approaches with on-the-fly learnt surrogate energy landscapes. Themethods are show-cased on problems ranging from supported clusters over surface reconstructions to largecarbon clusters and metal-nitride clusters incorporated into graphene sheets.

Novel insights into the structural changes induced by disease-associated mutations in TDP-43: a computational approach

Over the last two decades, the pathogenic aggregation of TAR DNA-binding protein 43 (TDP-43) is found to be strongly associated with several fatal neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS) and frontotemporal lobar degeneration (FTD), etc. While the mutations and truncation in TDP-43 protein have been suggested to be responsible for TDP-43 pathogenesis by accelerating the aggregation process, the effects of these mutations on the bio-mechanism of pathological TDP-43 protein remained poorly understood. Investigating this at the molecular level, we formulized an integrated workflow of molecular dynamic simulation and machine learning models (MD-ML). By performing an extensive structural analysis of three disease-related mutations (i.e., I168A, D169G, and I168A-D169G) in the conserved RNA recognition motifs (RRM1) of TDP-43, we observed that the I168A-D169G double mutant delineates the highest packing of the protein inner core as compared to the other mutations, which may indicate more stability and higher chances of pathogenesis. Moreover, through our MD-ML workflow, we identified the biological descriptors of TDP-43 which includes the interacting residue pairs and individual protein residues that influence the stability of the protein and could be experimentally evaluated to develop potential therapeutic strategies.Communicated by Ramaswamy H. Sarma.

Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.

Double proton transfer in hydrated formic acid dimer: Interplay of spatial symmetry and solvent-generated force on reactivity

The double proton transfer (DPT) reaction in the hydrated formic acid dimer (FAD) is investigated at molecular-level detail. For this, a global and reactive machine learned (ML) potential energy surface (PES) is developed to run extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in explicit molecular mechanics (MM) solvent at MP2-quality for the solute. Simulations with fixed – as in a conventional empirical force field – and conformationally fluctuating – as available from the ML-based PES – charge models for FAD show a significant impact on the competition between DPT and dissociation of FAD into two formic acid monomers. With increasing temperature the barrier height for DPT in solution changes by about 10% (∼1 kcal mol⁻¹) between 300 K and 600 K. The rate for DPT is largest, ∼1 ns⁻¹, at 350 K and decreases for higher temperatures due to destabilisation and increased probability for dissociation of FAD. The water solvent is found to promote the first proton transfer by exerting a favourable solvent-induced Coulomb force along the O–H⋯O hydrogen bond whereas the second proton transfer is significantly controlled by the O–O separation and other conformational degrees of freedom. Double proton transfer in hydrated FAD is found to involve a subtle interplay and balance between structural and electrostatic factors.

Simulation of double proton transfer in formic acid dimer by reactive ML potential in explicit molecular mechanics water solvent.

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.