Torsional Energy Profiles Research Articles

Comparing ANI-2x, ANI-1ccx neural networks, force field, and DFT methods for predicting conformational potential energy of organic molecules

In this study, the conformational potential energy surfaces of Amylmetacresol, Benzocaine, Dopamine, Betazole, and Betahistine molecules were scanned and analyzed using the neural network architecture ANI-2 × and ANI-1ccx, the force field method OPLS, and density functional theory with the exchange-correlation functional B3LYP and the basis set 6-31G(d). The ANI-1ccx and ANI-2 × methods demonstrated the highest accuracy in predicting torsional energy profiles, effectively capturing the minimum and maximum values of these profiles. Conformational potential energy values calculated by B3LYP and the OPLS force field method differ from those calculated by ANI-1ccx and ANI-2x, which account for non-bonded intramolecular interactions, since the B3LYP functional and OPLS force field weakly consider van der Waals and other intramolecular forces in torsional energy profiles. For a more comprehensive analysis, electronic parameters such as dipole moment, HOMO, and LUMO energies for different torsional angles were calculated at two levels of theory, B3LYP/6-31G(d) and ωB97X/6-31G(d). These calculations confirmed that ANI predictions are more accurate than density functional theory calculations with B3LYP functional and OPLS force field for determining potential energy surfaces. This research successfully addressed the challenges in determining conformational potential energy levels and shows how machine learning and deep neural networks offer a more accurate, cost-effective, and rapid alternative for predicting torsional energy profiles.

Efficient Generation of Conformer Ensembles Using Internal Coordinates and a Generative Directional Graph Convolution Neural Network.

We present a neural-network-based high-throughput molecular conformer-generation algorithm. A chemical graph-convolutional network is trained to predict low-energy conformers in internal coordinate representation (bond lengths, bond, and torsion angles), starting from two-dimensional (2D) chemical topology. Generative neural network (NN) architecture performs denoising from torsion space, producing conformer ensembles with populations that are well correlated with torsion energy profiles. Short force-field-based energy minimization is applied to refine final conformers. All computation-intensive stages of the algorithm are GPU-optimized. The procedure (termed GINGER) is benchmarked on a commonly used test set of bioactive three-dimensional (3D) conformers from the PDB. We demonstrate highly competitive results in conformer recovery and throughput rates suitable for giga-scale compound library processing. A web server that allows interactive conformer ensemble generation by GINGER and their viewing is made freely available at https://www.molsoft.com/gingerdemo.html.

Graph-Convolutional Neural Net Model of the Statistical Torsion Profiles for Small Organic Molecules.

We present a graph-convolutional neural network (GCNN)-based method for learning and prediction of statistical torsional profiles (STP) in small organic molecules based on the experimental X-ray structure data. A specialized GCNN torsion profile model is trained using the structures in the Crystallography Open Database (COD). The GCNN-STP model captures torsional preferences over a wide range of torsion rotor chemotypes and correctly predicts a variety of effects from the vicinal atoms and moieties. GCNN-STP statistical profiles also show good agreement with quantum chemically (DFT) calculated torsion energy profiles. Furthermore, we demonstrate the application of the GCNN-STP statistical profiles for conformer generation. A web server that allows interactive profile prediction and viewing is made freely available at https://www.molsoft.com/tortool.html.

Transferable Neural Network Potential Energy Surfaces for Closed-Shell Organic Molecules: Extension to Ions.

Transferable high dimensional neural network potentials (HDNNPs) have shown great promise as an avenue to increase the accuracy and domain of applicability of existing atomistic force fields for organic systems relevant to life science. We have previously reported such a potential (Schrödinger-ANI) that has broad coverage of druglike molecules. We extend that work here to cover ionic and zwitterionic druglike molecules expected to be relevant to drug discovery research activities. We report a novel HDNNP architecture, which we call QRNN, that predicts atomic charges and uses these charges as descriptors in an energy model that delivers conformational energies within chemical accuracy when measured against the reference theory it is trained to. Further, we find that delta learning based on a semiempirical level of theory approximately halves the errors. We test the models on torsion energy profiles, relative conformational energies, geometric parameters, and relative tautomer errors.

TorsionNet: A Deep Neural Network to Rapidly Predict Small-Molecule Torsional Energy Profiles with the Accuracy of Quantum Mechanics.

Fast and accurate assessment of small-molecule dihedral energetics is crucial for molecular design and optimization in medicinal chemistry. Yet, accurate prediction of torsion energy profiles remains challenging as the current molecular mechanics (MM) methods are limited by insufficient coverage of drug-like chemical space and accurate quantum mechanical (QM) methods are too expensive. To address this limitation, we introduce TorsionNet, a deep neural network (DNN) model specifically developed to predict small-molecule torsion energy profiles with QM-level accuracy. We applied active learning to identify nearly 50k fragments (with elements H, C, N, O, F, S, and Cl) that maximized the coverage of our corporate compound library and leveraged massively parallel cloud computing resources for density functional theory (DFT) torsion scans of these fragments, generating a training data set of 1.2 million DFT energies. After training TorsionNet on this data set, we obtain a model that can rapidly predict the torsion energy profile of typical drug-like fragments with DFT-level accuracy. Importantly, our method also provides an uncertainty estimate for the predicted profiles without any additional calculations. In this report, we show that TorsionNet can accurately identify the preferred dihedral geometries observed in crystal structures. Our TorsionNet-based analysis of a diverse set of protein-ligand complexes with measured binding affinity shows a strong association between high ligand strain and low potency. We also present practical applications of TorsionNet that demonstrate how consideration of DNN-based strain energy leads to substantial improvement in existing lead discovery and design workflows. TorsionNet500, a benchmark data set comprising 500 chemically diverse fragments with DFT torsion profiles (12k MM- and DFT-optimized geometries and energies), has been created and is made publicly available.

A New Lipid Force Field (FUJI).

To explore inhomogeneous and anisotropic systems such as lipid bilayers, the Lennard-Jones particle mesh Ewald (LJ-PME) method has been applied without a conventional isotropic dispersion correction. As the popular AMBER and CHARMM lipid force fields were developed using a cutoff scheme, their lipid bilayers unacceptably shrink when using the LJ-PME method. In this study, a new all-atom lipid force field (FUJI) was developed on the basis of the AMBER force-field scheme including the Lipid14 van der Waals parameters. Point charges were calculated using the restrained electrostatic potentials of many lipid conformers. Further, torsion energy profiles were calculated using high-level ab initio molecular orbitals (LCCSD(T)/Aug-cc-pVTZ//LMP2/Aug-cc-pVTZ), following which the molecular mechanical dihedral parameters were derived through a fast Fourier transform. By incorporation of these parameters into a new lipid force field without fitting experimental data, the desired lipid characteristics such as the area per lipid and lateral diffusion coefficients were obtained through GROMACS molecular dynamics simulations using the LJ-PME method and virtual hydrogen sites. The calculated area per lipid and lateral diffusion coefficients showed satisfactory agreement with experimental data. Furthermore, the electron-density profiles along the membrane normal were calculated for pure lipid bilayers, and the resulting membrane thicknesses agreed well with the experimental values. As the new lipid force field is compatible with FUJI for protein and small molecules, the new FUJI force field will offer accurate modeling for complex systems consisting of various membrane proteins and lipids.

Force Field Parameter Development for the Thiolate/Defective Au(111) Interface.

A molecular-level understanding of the interplay between self-assembled monolayers (SAMs) of thiolates and gold surface is of great importance to a wide range of applications in surface science and nanotechnology. Despite theoretical research progress of the past decade, an atomistic model, capable of describing key features of SAMs at reconstructed gold surfaces, is still missing. In this work, periodic ab initio density functional theory (DFT) calculations were utilized to develop a new atomistic force field model for alkanethiolate (AT) SAMs on a reconstructed Au(111) surface. The new force field parameters were carefully trained to reproduce the key features, including vibrational spectra and torsion energy profiles of ethylthiolate (C2S) in the bridge or staple motif model on the Au(111) surface, wherein, the force constants of the bond and angle terms were trained by matching the vibrational spectra, while the torsion parameters of the dihedral angles were trained via fitting the torsion energy profiles from DFT calculations. To validate the developed force field parameters, we performed classical molecular dynamics (MD) simulations for both pristine and reconstructed Au-S interface models with a (2√3 × 3) unit cell, which includes four dodecanethiolate (C10S) molecules on the Au(111) surface. The simulation results showed that the geometrical features of the investigated Au-S interface models and structural properties of the C10S SAMs are in good agreement with the ab initio MD studies. The newly developed atomistic force field model provides new fundamental insights into AT SAMs on the reconstructed Au(111) surface and adds advancement to the existing interface research knowledge.

Torsional Energy Barriers of Biaryls Could Be Predicted by Electron Richness/Deficiency of Aromatic Rings; Advancement of Molecular Mechanics toward Atom-Type Independence.

Biaryl molecules are ubiquitous pharmacophores found in natural products and pharmaceuticals. In spite of this, existing molecular mechanics force fields are unable to accurately reproduce their torsional energy profiles, except for a few well-parametrized cases. This effectively limits the ability of structure-based drug design methods to correctly identify hits involving biaryls with confidence (e.g., during virtual screening, employing docking and/or molecular dynamics simulations). Continuing in our endeavor to quantify organic chemistry principles, we showed that the torsional energy profile of biaryl compounds could be computed on-the-fly based on the electron richness/deficiency of the aromatic rings. This method, called H-TEQ 4.0, was developed using a set of 131 biaryls. It was subsequently validated on a separate set of 100 diverse biaryls, including multisubstituted, bicyclic and tricyclic druglike molecules, and produced an average root-mean-square error (RMSE) of 0.95 kcal·mol-1. For comparison, GAFF2 produced an RMSE of 3.88 kcal·mol-1, owing to problems associated with the transferability of torsion parameters. The success of H-TEQ 4.0 provided further evidence that force fields could transition to become atom-type independent, providing that the correct chemical principles are used. Overall, this method solved the problem of transferability of biaryl torsion parameters, while simultaneously improving the overall accuracy of the force field.

Synthesis and conformational analysis of new arylated-diphenylurea derivatives related to sorafenib drug via Suzuki-Miyaura cross-coupling reaction

Sorafenib, is a relatively new cytostatic drug approved for the treatment of renal cell and hepatocellular carcinoma. The development of new sorafenib analogues offers the possibility of generating structures of increased potency. To this end, a series of arylated-diphenylurea analogues 17–31 were synthesized via Suzuki-Miyaura coupling reaction, related to sorafenib by treatment of three diarylureas 2–4 having 3-bromo, 4-chloro and 2-iodo groups with various arylboronic acids. Conformational analysis of the new arylated urea analogues has been investigated using MOPAC 2016 of semi empirical PM7 Hamiltonian computational method. Our results showed that all compounds preferred the trans-trans conformations. Compound 17 has been selected to calculate the torsional energy profiles for rotation around the urea bonds and found to be existed predominantly in the trans-trans conformation with only very minimal fluctuation in conformation.

Elucidating Hyperconjugation from Electronegativity to Predict Drug Conformational Energy in a High Throughput Manner.

Computational chemists use structure-based drug design and molecular dynamics of drug/protein complexes which require an accurate description of the conformational space of drugs. Organic chemists use qualitative chemical principles such as the effect of electronegativity on hyperconjugation, the impact of steric clashes on stereochemical outcome of reactions, and the consequence of resonance on the shape of molecules to rationalize experimental observations. While computational chemists speak about electron densities and molecular orbitals, organic chemists speak about partial charges and localized molecular orbitals. Attempts to reconcile these two parallel approaches such as programs for natural bond orbitals and intrinsic atomic orbitals computing Lewis structures-like orbitals and reaction mechanism have appeared. In the past, we have shown that encoding and quantifying chemistry knowledge and qualitative principles can lead to predictive methods. In the same vein, we thought to understand the conformational behaviors of molecules and to encode this knowledge back into a molecular mechanics tool computing conformational potential energy and to develop an alternative to atom types and training of force fields on large sets of molecules. Herein, we describe a conceptually new approach to model torsion energies based on fundamental chemistry principles. To demonstrate our approach, torsional energy parameters were derived on-the-fly from atomic properties. When the torsional energy terms implemented in GAFF, Parm@Frosst, and MMFF94 were substituted by our method, the accuracy of these force fields to reproduce MP2-derived torsional energy profiles and their transferability to a variety of functional groups and drug fragments were overall improved. In addition, our method did not rely on atom types and consequently did not suffer from poor automated atom type assignments.

Conformational Mobility in Monolayer-Protected Nanoparticles: From Torsional Free Energy Profiles to NMR Relaxation

In this work, we develop a self-consistent route to inspect the conformational mobility of single chains in gold nanoparticles passivated with a monolayer of decanethiols. The approach is based on the match between a theoretical modeling under a coarse-grained level (i.e., system definition, buildup of the free energy profiles along relevant coordinates, modeling/parametrization of the friction, production of stochastic trajectories) and experimental spectroscopic investigations. The agreement between calculated and experimental values of 13C NMR longitudinal relaxation times supports the theoretical assumptions and the model parametrization. On physical grounds, it emerges that the mobility of the single chains resembles that of an ideal chain made of connected n-butane-like bonds.

Atomistic insight into orthoborate-based ionic liquids: force field development and evaluation.

We have developed an all-atomistic force field for a new class of halogen-free chelated orthoborate-phosphonium ionic liquids. The force field is based on an AMBER framework with determination of force field parameters for phosphorus and boron atoms, as well as refinement of several available parameters. The bond and angle force constants were adjusted to fit vibration frequency data derived from both experimental measurements and ab initio calculations. The force field parameters for several dihedral angles were obtained by fitting torsion energy profiles deduced from ab initio calculations. To validate the proposed force field parameters, atomistic simulations were performed for 12 ionic liquids consisting of tetraalkylphosphonium cations and chelated orthoborate anions. The predicted densities for neat ionic liquids and the [P6,6,6,14][BOB] sample, with a water content of approximately 2.3-2.5 wt %, are in excellent agreement with available experimental data. The potential energy components of 12 ionic liquids were discussed in detail. The radial distribution functions and spatial distribution functions were analyzed and visualized to probe the microscopic ionic structures of these ionic liquids. There are mainly four high-probability regions of chelated orthoborate anions distributed around tetraalkylphosphonium cations in the first solvation shell, and such probability distribution functions are strongly influenced by the size of anions.

High performance computing for drug development on K computer

Massively parallel computations (MP-CAFEE) ware developed to calculate absolute binding free energies of small molecules bound to a protein by all-atom molecular dynamics. It uses the nonequilibrium work measurement and Bennett acceptance ratio methods to calculate the free energy difference between the bound and unbound states. The FUJI force field was developed in order to assign force field parameters to arbitrary organic molecules in a unified manner including proteins and nucleic acids. Its dihedral parameters agree with the torsion energy profiles calculated by high-level ab initio molecular orbital theory for the model systems of protein backbone. Comparing with various force fields it agrees well with recent observations by vibrational spectroscopy on Ramachandran angle's population of alanine dipeptide in water. MP-CAFEE with FUJI force field has an efficient parallel algorithm and enough accuracy for computer aided drug design.

Characterization of Biaryl Torsional Energetics and its Treatment in OPLS All-Atom Force Fields

The frequency of biaryl substructures in a database of approved oral drugs has been analyzed. This led to designation of 20 prototypical biaryls plus 10 arylpyridinones for parametrization in the OPLS all-atom force fields. Bond stretching, angle-bending, and torsional parameters were developed to reproduce the MP2 geometries and torsional energy profiles. The transferability of the new parameters was tested through their application to three additional biaryls. The torsional energetics for the 33 biaryl molecules are analyzed and factors leading to preferences for planar and nonplanar geometries are identified. For liquid biphenyl, the computed density and heat of vaporization at the boiling point (255 °C) are also reported.

Conformational preferences of furan- and thiophene-based arylamides: a combined computational and experimental study

We examine the conformational preferences of the furan- and thiophene-based arylamides, N-methylfuran-2-carboxamide (3) and N-methylthiophene-2-carboxamide (4), using a combination of computational methods and NMR experiments. The compound choice stems from their use as foldamer building blocks. We quantify the differences in the conformational rigidity of the two compounds, which governs corresponding foldamer conformations. Specifically, we demonstrate the effects of intramolecular hydrogen bonding (H-bonding), geometrical patterns and solvent polarity on arylamide conformations by comparing 3, 4 and previously studied ortho-methoxy N-methylbenzamide (1) and ortho-methylthio N-methylbenzamide (2). The study reveals that compound 3, despite its non-optimal S(5)-type H-bond geometry, retains a large portion of the H-bonded (eclipsed) conformation even in polar protic solvents. This behaviour is consistent with the quantum mechanical (QM) torsional energy profile. The percentages of H-bonded conformers that 3 retains are just slightly smaller than those of 1, which has a stronger S(6)-type H-bond. As for 2 and 4, the replacement of the O atom in 1 by an S atom in 2 results in a 70–90% loss of the H-bonded conformer in solution. However, the equivalent O to S replacement in 3 (leading to 4) causes only 15–30% loss of the eclipsed conformers in 4. Therefore, conformational preferences of 4 are very different from 2, in contrast to the similarity between 3 and 1. This study shows how the interplay of several forces modulates the conformational flexibility of arylamides. It also attests the strategy we are developing, which leads to accurate prediction of foldamer structure. The vital component of this strategy is the re-parameterization of critical force field parameters based on QM potential energy profiles, as well as validation of these parameters using experimental data in solution.

Force field parameter estimation of functional perfluoropolyether lubricants

The head disk interface in a hard disk drive can be considered to be one of the hierarchical multiscale systems, which require the hybridization of multiscale modeling methods with coarse-graining procedure. However, the fundamental force field parameters are required to enable the coarse-graining procedure from atomistic/molecular scale to mesoscale models. In this paper, we investigate beyond molecular level and perform ab initio calculations to obtain the force field parameters. Intramolecular force field parameters for Zdol and Ztetraol were evaluated with truncated PFPE molecules to allow for feasible quantum calculations while still maintaining the characteristic chemical structure of the end groups. Using the harmonic approximation to the bond and angle potentials, the parameters were derived from the Hessian matrix, and the dihedral force constants are fit to the torsional energy profiles generated by a series of constrained molecular geometry optimization.

Conformation and geometry of cyclopropane rings having π-acceptor substituents: a theoretical and database study

The 3e' orbitals of cyclopropane have the correct symmetry to interact with low-lying unoccupied orbitals of π-acceptor substituents and maximum overlap occurs when the two orbital systems are parallel, i.e. when the π-acceptor bisects the ring in projection down the substituent bond. Since the cyclopropyl group is a common component of active pharmaceutical and agrochemical ingredients, it is important that these strong conjugative interactions are well modelled by computational techniques, and clearly represented in experimental crystal structures. Here we show that torsion angle distributions derived from crystal structure data in the Cambridge Structural Database are in excellent correspondence with torsional energy profiles computed using density functional theory (DFT) for a range of substituents: -COOR, -CONR(2), -NO(2), vinyl and phenyl. We also show that crystal structure information is invaluable in modelling conformations of compounds that contain multiply substituted rings, where steric interactions require some substituents to adopt energetically disfavoured conformations. Further, conjugative interactions with π-acceptors lead to significant asymmetry in the cyclopropane ring bond lengths and again the experimental and computational results are in excellent agreement. Such asymmetry effects are additive, and this explains bond-length variations in cyclopropane rings bearing two or more π-acceptor substituents.

An Amber Force Field for S-Nitrosoethanethiol That Is Transferable to S-Nitrosocysteine

Protein S-nitrosation is common in cells under nitrosative stress. In order to model proteins with S-nitrosocysteine (CysSNO) residues, we first developed an Amber force field for S-nitrosoethanethiol (EtSNO) and then transferred it to CysSNO. Partial atomic charges for EtSNO and CysSNO were obtained by a restrained electrostatic potential approach to be compatible with the Amber-99 force field. The force field parameters for bonds and angles in EtSNO were obtained from a generalized Amber force field (GAFF) by running the Antechamber module of the Amber software package. The GAFF parameters for the CC-SN and CS-NO dihedrals were not accurate and thus determined anew. The CC-SN and CS-NO torsional energy profiles of EtSNO were calculated quantum mechanically at the level of B3LYP/cc-pVTZ//HF/6-31 G * . Torsional force constants were obtained by fitting the theoretical torsional energies with those obtained from molecular mechanics energy minimization. These parameters for EtSNO reproduced, to a reasonable accuracy, the corresponding torsional energy profiles of the capped tripeptide ACE-CysSNO-NLVIE as well as their structures obtained from quantum mechanical geometry optimization. A molecular dynamics simulation of myoglobin with a CysSNO residue produced a well-behaved trajectory demonstrating that the parameters may be used in modeling other S-nitrosated proteins.

Force Field Parameters for 3-Nitrotyrosine and 6-Nitrotryptophan

Nitration of tyrosine and tryptophan residues is common in cells under nitrative stress. However, physiological consequences of protein nitration are not well characterized on a molecular level due to limited availability of the 3D structures of nitrated proteins. Molecular dynamics (MD) simulation can be an alternative tool to probe the structural perturbations induced by nitration. In this study we developed molecular mechanics parameters for 3-nitrotyrosine (NIY) and 6-nitrotryptophan (NIW) that are compatible with the AMBER-99 force field. Partial atomic charges were derived by using a multi-conformational restrained electrostatic potential (RESP) methodology that included the geometry optimized structures of both <TEX>$\alpha$</TEX>- and <TEX>$\beta$</TEX>-conformers of a capped tripeptide ACE-NIY-NME or ACE-NIW-NME. Force constants for bonds and angles were adopted from the generalized AMBER force field. Torsional force constants for the proper dihedral C-C-N-O and improper dihedral C-O-N-O of the nitro group in NIY were determined by fitting the torsional energy profiles obtained from quantum mechanical (QM) geometry optimization with those from molecular mechanical (MM) energy minimization. Force field parameters obtained for NIY were transferable to NIW so that they reproduced the QM torsional energy profiles of ACE-NIW-NME accurately. Moreover, the QM optimized structures of the tripeptides containing NIY and NIW were almost identical to the corresponding structures obtained from MM energy minimization, attesting the validity of the current parameter set. Molecular dynamics simulations of thioredoxin nitrated at the single tyrosine and tryptophan yielded well-behaved trajectories suggesting that the parameters are suitable for molecular dynamics simulations of a nitrated protein.

Symmetry and polar-π effects on the dynamics of enshrouded aryl-alkyne molecular rotors

The central ring of a 1,4-bis(arylethynyl)arene (ditolan) can be viewed as a molecular rotor with an extremely low barrier to rotation in the gas phase or solution. The torsional energy profile of that ring is shown to be dependent on the relative conformation of the end capping arenes. When the capping arenes are sterically bulky m-terphenyl units, it is possible to rationalize the conformational dynamics of the central ring by a factorization analysis, involving perturbation of the basic torsional energy profile by polar-π, and dispersion interactions between the flanking rings of the cap and the central ring of the ditolan. The symmetry of the construct can modulate the effect of these interactions. These principles apply to the design of materials in which a steric shroud excludes packing distortions.