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.

Novel Lennard-Jones Parameters for Cysteine and Selenocysteine in the AMBER Force Field.

Cysteine is a common amino acid with a thiol group that plays a pivotal role in a variety of scenarios in redox biochemistry. In contrast, selenocysteine, the 21st amino acid, is only present in 25 human proteins. Classical force-field parameters for cysteine and selenocysteine are still scarce. In this context, we present a methodology to obtain Lennard-Jones parameters for cysteine and selenocysteine in different physiologically relevant oxidation and protonation states. The new force field parameters obtained in this work are available at https://github.com/MALBECC/AMBER-parameters-database. The parameters were adjusted to reproduce water radial distribution functions obtained by density functional theory ab initio molecular dynamics. We validated the results by evaluating the impact of the choice of parameters on the structure and dynamics in classical molecular dynamics simulations of representative proteins containing catalytic cysteine/selenocysteine residues. There are significant changes in protein structure and dynamics depending on the parameters choice, specifically affecting the residues close to the catalytic sites.

Elucidating the Protonation State of the γ-Secretase Catalytic Dyad.

γ-Secretase (GS) is an intramembrane aspartyl protease that participates in the sequential cleavage of C99 to generate different isoforms of the amyloid-ß (Aß) peptides that are associated with the development of Alzheimer's disease. Due to its importance in the proteolytic processing of C99 by GS, we performed pH replica exchange molecular dynamics (pH-REMD) simulations of GS in its apo and substrate-bound forms to sample the protonation states of the catalytic dyad. We found that the catalytic dyad is deprotonated at physiological pH in our apo form, but the presence of the substrate at the active site displaces its monoprotonated state toward physiological pH. Our results show that Asp257 acts as the general base and Asp385 as the general acid during the cleavage mechanism. We identified different amino acids such as Lys265, Arg269, and the PAL motif interacting with the catalytic dyad and promoting changes in its acid-base behavior. Finally, we also found a significant pKa shift of Glu280 related to the internalization of TM6-CT in the GS-apo form. Our study provides critical mechanistic insight into the GS mechanism and the basis for future research on the genesis of Aß peptides and the development of Alzheimer's disease.

Adiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation.

We present a method to link the Nonadiabatic EXcited-state Molecular Dynamics (NEXMD) package to the SANDER package supplied by AMBERTOOLS to provide excited-state adiabatic quantum mechanics/molecular mechanics (QM/MM) simulations. NEXMD is a computational package particularly developed to perform simulations of the photoexcitation and subsequent nonadiabatic electronic and vibrational energy relaxation in large multichromophoric conjugated molecules involving several coupled electronic excited states. The NEXMD-SANDER exchange has been optimized in order to achieve excited-state adiabatic dynamics simulations of large conjugated materials in a QM/MM environment, such as an explicit solvent. Dynamics of a substituted polyphenylene vinylene oligomer (PPV3-NO2) in vacuum and different explicit solvents has been used as a test case by performing comparative analysis of changes in its optical spectrum, state-dependent conformational changes, and quantum bond orderings. The method has been tested and compared with respect to previous implicit solvent implementations. Also, the impact on the expansion of the QM region by including a variable number of solvent molecules has been analyzed. Altogether, these results encourage future implementations of NEXMD simulations using the same combination of methods.

Anticancer Agents Derived from Cyclic Thiosulfonates: Structure-Reactivity and Structure-Activity Relationships.

Reported are structure-property-function relationships associated with a class of cyclic thiosulfonate molecules-disulfide-bond disrupting agents (DDAs)-with the ability to downregulate the Epidermal Growth Factor Receptor (HER) family in parallel and selectively induce apoptosis of EGFR+ or HER2+ breast cancer cells. Recent findings have revealed that the DDA mechanism of action involves covalent binding to the thiol(ate) from the active site cysteine residue of members of the protein disulfide isomerase (PDI) family. Reported is how structural modifications to the pharmacophore can alter the anticancer activity of cyclic thiosulfonates by tuning the dynamics of thiol-thiosulfonate exchange reactions, and the studies reveal a correlation between the biological potency and thiol-reactivity. Specificity of the cyclic thiosulfonate ring-opening reaction by a nucleophilic attack can be modulated by substituent addition to a parent scaffold. Lead compound optimization efforts are also reported, and have resulted in a considerable decrease of the IC50 /IC90 values toward HER-family overexpressing breast cancer cells.

Development and Evaluation of Geometry Optimization Algorithms in Conjunction with ANI Potentials.

An efficient yet accurate method for producing a large amount of energy data for molecular mechanical force field (MMFF) parameterization is on demand, especially for torsional angle parameters which are typically derived to reproduce ab initio rotational profiles or torsional potential energy surfaces (PESs). Recently, an active learning potential (ANI-1x) for organic molecules which can produce smooth and physically meaningful PESs has been developed. The high efficiency and accuracy make ANI-1x especially attractive for geometry optimization at low cost. To apply the ANI-1x potential in MMFF parameterization, one needs to perform constrained geometry optimization. In this work, we first developed a computational protocol to constrain rotatable torsional angles and other geometric parameters for a molecule whose geometry is described by Cartesian coordinates. The constraint is successfully achieved by force projection for the two conjugated gradient (CG) algorithms. We then conducted large-scale assessments on ANI-1x along with four different optimization algorithms in reproducing DFT energies and geometries for two CG algorithms, CG backtracking line search (CG-BS) and CG Wolfe line search (CG-WS), and two quasi-Newton algorithms, Broyden-Fletcher-Goldfarb-Shanno (BFGS) and low-memory BFGS (L-BFGS). Note that CG-BS is a new algorithm we developed in this work. All four algorithms take the ANI energies and forces to optimize a molecule geometry. Last, we conducted a large-scale assessment of applying ANI-1x in MMFF development in three aspects. First, we performed full optimizations for 100 drug molecules, each consisting of five distinct conformations. The average root-mean-square error (RMSE) between ANI-1x and DFT is about 1.3 kcal/mol, and the root-mean-square displacement (RMSD) of heavy atoms is about 0.35 Å. Second, we generated torsional PESs for 160 organic molecules, and constrained optimizations were performed for up to 18 conformations for each PES. We found that the RMSE of all the conformers is 1.23 kcal/mol. Last, we carried out constrained optimizations for alanine dipeptide with both ϕ and φ angles being frozen. The Ramachandran plots indicate that the two CG algorithms in conjunction with the ANI-1x potential could well reproduce the DFT-optimized geometries and torsional PESs. We concluded that CG-BS and CG-WS are good choices for generating PESs, while CG-WS or BFGS is ideal for performing full geometry optimization. With the continuously increased quality of ANI, it is expected that the computational algorithms and protocols presented in this work will have great applications in improving the quality of an existing small-molecule MMFF.

Exploring the concerted mechanistic pathway for HIV-1 PR-substrate revealed by umbrella sampling simulation.

HIV-1 protease (HIV-1 PR) is an essential enzyme for the replication process of its virus, and therefore considered an important target for the development of drugs against the acquired immunodeficiency syndrome (AIDS). Our previous study shows that the catalytic mechanism of subtype B/C-SA HIV-1 PR follows a one-step concerted acyclic hydrolysis reaction process using a two-layered ONIOM B3LYP/6-31++G(d,p) method. This present work is aimed at exploring the proposed mechanism of the proteolysis catalyzed by HIV-1 PR and to ensure our proposed mechanism is not an artefact of a single theoretical technique. Hence, we present umbrella sampling method that is suitable for calculating potential mean force (PMF) for non-covalent ligand/substrate-enzyme association/dissociation interactions which provide thermodynamic details for molecular recognition. The free activation energy results were computed in terms of PMF analysis within the hybrid QM(DFTB)/MM approach. The theoretical findings suggest that the proposed mechanism corresponds in principle with experimental data. Given our observations, we suggest that the QM/MM MD method can be used as a reliable computational technique to rationalize lead compounds against specific targets such as the HIV-1 protease.

pH Effects and Cooperativity among Key Titratable Residues for Escherichia coli Glycinamide Ribonucleotide Transformylase.

Human glycinamide ribonucleotide transformylase (GAR Tfase) is a regulatory enzyme in the de novo purine biosynthesis pathway that has been extensively studied as an anticancer target. To some extent, inhibition of GAR Tfase selectively targets cancer cells over normal cells and inhibits purine formation and DNA replication. In this study, we investigated E. coli GAR Tfase, which shares high sequence similarity with the human GAR Tfase, and most functional residues are conserved. Herein, we aim to predict the pH-activity curve through a computational approach. We carried out pH-replica exchange molecular dynamics (pH-REMD) simulations to investigate pH-dependent functions such as structural changes, ligand binding, and catalytic activity. To compute the pH-activity curve, we identified the catalytic residues in specific protonation states, referred to as the catalytic competent protonation states (CCPS), which maintain the structure, keep ligands bound, and facilitate catalysis. Our computed population of CCPS with respect to pH matches well with the experimental pH-activity curve. To compute the microscopic pKa values in the catalytically active conformation, we devised a thermodynamic model that considers the coupling between protonation states of CCPS residues and conformational states. These results allow us to correctly identify the general acid and base catalysts and interpret the pH-activity curve at an atomistic level.

pH-Dependent Conformational Changes Lead to a Highly Shifted pKa for a Buried Glutamic Acid Mutant of SNase.

Ionizable residues are rarely present in the hydrophobic interior of proteins, but when they are, they play important roles in biological processes such as energy transduction and enzyme catalysis. Internal ionizable residues have anomalous experimental pKa values with respect to their pKa in bulk water. This work investigates the atomistic cause of the highly shifted pKa of the internal Glu23 in the artificially mutated variant V23E of Staphylococcal Nuclease (SNase) using pH replica exchange molecular dynamics (pH-REMD) simulations. The pKa of Glu23 obtained from our calculations is 6.55, which is elevated with respect to the glutamate pKa of 4.40 in bulk water. The calculated value is close to the experimental pKa of 7.10. Our simulations show that the highly shifted pKa of Glu23 is the product of a pH-dependent conformational change, which has been observed experimentally and also seen in our simulations. We carry out an analysis of this pH-dependent conformational change in response to the protonation state change of Glu23. Using a four-state thermodynamic model, we estimate the two conformation-specific pKa values of Glu23 and describe the coupling between the conformational and ionization equilibria.

Steered molecular dynamic simulations reveal Marfan syndrome mutations disrupt fibrillin-1 cbEGF domain mechanosensitive calcium binding.

Marfan syndrome (MFS) is a highly variable genetic connective tissue disorder caused by mutations in the calcium binding extracellular matrix glycoprotein fibrillin-1. Patients with the most severe form of MFS (neonatal MFS; nMFS) tend to have mutations that cluster in an internal region of fibrillin-1 called the neonatal region. This region is predominantly composed of eight calcium-binding epidermal growth factor-like (cbEGF) domains, each of which binds one calcium ion and is stabilized by three highly conserved disulfide bonds. Crucially, calcium plays a fundamental role in stabilizing cbEGF domains. Perturbed calcium binding caused by cbEGF domain mutations is thus thought to be a central driver of MFS pathophysiology. Using steered molecular dynamics (SMD) simulations, we demonstrate that cbEGF domain calcium binding decreases under mechanical stress (i.e. cbEGF domains are mechanosensitive). We further demonstrate the disulfide bonds in cbEGF domains uniquely orchestrate protein unfolding by showing that MFS disulfide bond mutations markedly disrupt normal mechanosensitive calcium binding dynamics. These results point to a potential mechanosensitive mechanism for fibrillin-1 in regulating extracellular transforming growth factor beta (TGFB) bioavailability and microfibril integrity. Such mechanosensitive "smart" features may represent novel mechanisms for mechanical hemostasis regulation in extracellular matrix that are pathologically activated in MFS.

Selective ring-rearrangement or ring-closing metathesis of bicyclo[3.2.1]octenes.

Explored was the competitive ring-closing metathesis vs. ring-rearrangement metathesis of bicyclo[3.2.1]octenes prepared by a simple and convergent synthesis from bicyclic alkylidenemalono-nitriles and allylic electrophiles. It was uncovered that ring-closing metathesis occurs exclusively on the tetraene-variant, yielding unique, stereochemically and functionally rich polycyclic bridged frameworks, whereas the reduced version (a triene) undergoes ring-rearrangement metathesis to 5-6-5 fused ring systems resembling the isoryanodane core.

NEXMD Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present a versatile new code released for open community use, the nonadiabatic excited state molecular dynamics (NEXMD) package. This software aims to simulate nonadiabatic excited state molecular dynamics using several semiempirical Hamiltonian models. To model such dynamics of a molecular system, the NEXMD uses the fewest-switches surface hopping algorithm, where the probability of transition from one state to another depends on the strength of the derivative nonadiabatic coupling. In addition, there are a number of algorithmic improvements such as empirical decoherence corrections and tracking trivial crossings of electronic states. While the primary intent behind the NEXMD was to simulate nonadiabatic molecular dynamics, the code can also perform geometry optimizations, adiabatic excited state dynamics, and single-point calculations all in vacuum or in a simulated solvent. In this report, first, we lay out the basic theoretical framework underlying the code. Then we present the code's structure and workflow. To demonstrate the functionality of NEXMD in detail, we analyze the photoexcited dynamics of a polyphenylene ethynylene dendrimer (PPE, C30H18) in vacuum and in a continuum solvent. Furthermore, the PPE molecule example serves to highlight the utility of the getexcited.py helper script to form a streamlined workflow. This script, provided with the package, can both set up NEXMD calculations and analyze the results, including, but not limited to, collecting populations, generating an average optical spectrum, and restarting unfinished calculations.

TorchANI: A Free and Open Source PyTorch-Based Deep Learning Implementation of the ANI Neural Network Potentials.

This paper presents TorchANI, a PyTorch-based program for training/inference of ANI (ANAKIN-ME) deep learning models to obtain potential energy surfaces and other physical properties of molecular systems. ANI is an accurate neural network potential originally implemented using C++/CUDA in a program called NeuroChem. Compared with NeuroChem, TorchANI has a design emphasis on being lightweight, user friendly, cross platform, and easy to read and modify for fast prototyping, while allowing acceptable sacrifice on running performance. Because the computation of atomic environmental vectors and atomic neural networks are all implemented using PyTorch operators, TorchANI is able to use PyTorch's autograd engine to automatically compute analytical forces and Hessian matrices, as well as do force training without requiring any additional codes. TorchANI is open-source and freely available on GitHub: https://github.com/aiqm/torchani.

Extending the Applicability of the ANI Deep Learning Molecular Potential to Sulfur and Halogens.

Machine learning (ML) methods have become powerful, predictive tools in a wide range of applications, such as facial recognition and autonomous vehicles. In the sciences, computational chemists and physicists have been using ML for the prediction of physical phenomena, such as atomistic potential energy surfaces and reaction pathways. Transferable ML potentials, such as ANI-1x, have been developed with the goal of accurately simulating organic molecules containing the chemical elements H, C, N, and O. Here, we provide an extension of the ANI-1x model. The new model, dubbed ANI-2x, is trained to three additional chemical elements: S, F, and Cl. Additionally, ANI-2x underwent torsional refinement training to better predict molecular torsion profiles. These new features open a wide range of new applications within organic chemistry and drug development. These seven elements (H, C, N, O, F, Cl, and S) make up ∼90% of drug-like molecules. To show that these additions do not sacrifice accuracy, we have tested this model across a range of organic molecules and applications, including the COMP6 benchmark, dihedral rotations, conformer scoring, and nonbonded interactions. ANI-2x is shown to accurately predict molecular energies compared to density functional theory with a ∼106 factor speedup and a negligible slowdown compared to ANI-1x and shows subchemical accuracy across most of the COMP6 benchmark. The resulting model is a valuable tool for drug development which can potentially replace both quantum calculations and classical force fields for a myriad of applications.

The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules.

Maximum diversification of data is a central theme in building generalized and accurate machine learning (ML) models. In chemistry, ML has been used to develop models for predicting molecular properties, for example quantum mechanics (QM) calculated potential energy surfaces and atomic charge models. The ANI-1x and ANI-1ccx ML-based general-purpose potentials for organic molecules were developed through active learning; an automated data diversification process. Here, we describe the ANI-1x and ANI-1ccx data sets. To demonstrate data diversity, we visualize it with a dimensionality reduction scheme, and contrast against existing data sets. The ANI-1x data set contains multiple QM properties from 5 M density functional theory calculations, while the ANI-1ccx data set contains 500 k data points obtained with an accurate CCSD(T)/CBS extrapolation. Approximately 14 million CPU core-hours were expended to generate this data. Multiple QM calculated properties for the chemical elements C, H, N, and O are provided: energies, atomic forces, multipole moments, atomic charges, etc. We provide this data to the community to aid research and development of ML models for chemistry.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials.

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Exploring Coupled Redox and pH Processes with a Force-Field-Based Approach: Applications to Five Different Systems.

Coupled redox and pH-driven processes are at the core of many important biological mechanisms. As the distribution of protonation and redox states in a system is associated with the pH and redox potential of the solution, having efficient computational tools that can simulate under these conditions becomes very important. Such tools have the potential to provide information that complement and drive experiments. In previous publications we have presented the implementation of the constant pH and redox potential molecular dynamics (C(pH,E)MD) method in AMBER and we have shown how multidimensional replica exchange can be used to significantly enhance the convergence efficiency of our simulations. In the current work, after an improvement in our C(pH,E)MD approach that allows a given residue to be simultaneously pH- and redox-active, we have employed our methodologies to study five different systems of interest in the literature. We present results for capped tyrosine dipeptide, two maquette systems containing one pH- and redox-active tyrosine (α3Y and peptide A), and two proteins that contain multiple heme groups (diheme cytochrome c from Rhodobacter sphaeroides and Desulfovibrio vulgaris Hildenborough cytochrome c3). We show that our results can provide new insights into previous theoretical and experimental findings by using a fully force-field-based and GPU-accelerated approach, which allows the simulations to be executed with high computational performance.

The any particle molecular orbital/molecular mechanics approach.

A computational scheme is proposed to broaden the range of applications of multicomponent methodologies for the study of local properties of big molecular systems existing in the gas phase and in solvated environments. This scheme extends the any particle molecular orbital (APMO) approach in the quantum mechanics/molecular mechanics (QM/MM) framework. As a first assessment of the performance of the proposed approach, we estimate the proton affinities (PAs) of seventy amines in the gas phase and the proton binding energies (PBEs) in the gas phase and in an explicitly solvated environment of the sixty-one protons present in the chignolin protein. These calculations are performed with the QM/MM versions of the APMO second-order proton propagator (APMO-PP2) and the APMO extended Koopmans' theorem (APMO-KT) approaches. Calculated PAs and PBEs show significant reductions in the computational effort with a reduced loss in accuracy. These results suggest that the APMO/MM scheme might be used as a low-cost multi-component alternative for studies of local properties in big molecular systems. Graphical Abstract QMMM regions and CPU times for the APMO/MM approach.

Folding and Dynamics Are Strongly pH-Dependent in a Psychrophile Frataxin.

Protein dynamics, folding, and thermodynamics represent a central aspect of biophysical chemistry. pH, temperature, and denaturant perturbations inform our understanding of diverse contributors to stability and rates. In this work, we performed a thermodynamic analysis using a combined experimental and computational approach to gain insights into the role of electrostatics in the folding reaction of a psychrophile frataxin variant from Psychromonas ingrahamii. This folding reaction is strongly modulated by pH with a single, narrow, and well-defined transition state with ∼80% compactness, ∼70% electrostatic interactions, and ∼60% hydration shell compared to the native state (αD = 0.82, αH = 0.67, and αΔCp = 0.59). Our results are best explained by a two-proton/two-state model with very different pKa values of the native and denatured states (∼5.5 and ∼8.0, respectively). As a consequence, the stability strongly increases from pH 8.0 to 6.0 (|ΔΔG°| = 5.2 kcal mol-1), mainly because of a decrease in the TΔS°. Variation of ΔH° and ΔS° at pH below 7.0 is dominated by a change in ΔHf⧧ and ΔSf⧧, while at pH above 7.0, it is governed by ΔHu⧧ and ΔSu⧧. Molecular dynamics simulations showed that these pH modulations could be explained by the fluctuations of two regions, rich in electrostatic contacts, whose dynamics are pH-dependent and motions are strongly correlated. Results presented herein contribute to the understanding of the stability and dynamics of this frataxin variant, pointing to an intrinsic feature of the family topology to support different folding mechanisms.