Polarization Effects for Hydrogen-Bonded Complexes of Substituted Phenols with Water and Chloride Ion

Refinement of the Drude Polarizable Force Field for Hexose Monosaccharides: Capturing Ring Conformational Dynamics with Enhanced Accuracy

We present a revised version of the Drude polarizable carbohydrate force field (FF), focusing on refining the ring and exocyclic torsional parameters for hexopyranose monosaccharides. This refinement addresses the previously observed discrepancies between calculated and experimental NMR 3J coupling values, particularly in describing ring dynamics and exocyclic rotamer populations within major hexose monosaccharides and their anomers. Specifically, α-MAN, β-MAN, α-GLC, β-GLC, α-GAL, β-GAL, α-ALT, β-ALT, α-IDO, and β-IDO were targeted for optimization. The optimization process involved potential energy scans (PES) of the ring and exocyclic dihedral angles computed using quantum mechanical (QM) methods. The target data for the reoptimization included PES of the inner ring dihedrals (C1-C2-C3-C4, C2-C3-C4-C5, C5-O5-C1-C2, C4-C5-O5-C1, O5-C1-C2-C3, C3-C4-C5-O5) and the exocyclic torsions, other than the pseudo ring dihedrals (O1-C1-O5-C5, O2-C2-C1-O5, and O4-C4-C5-O5) and hydroxyl torsions used in the previous parametrization efforts. These parameters, in conjunction with previously developed Drude parameters for hexopyranose monosaccharides, were validated against experimental observations, including NMR data and conformational energetics, in aqueous environments. The resulting polarizable model is shown to be in good agreement with a range of QM data, experimental NMR data, and conformational energetics of monosaccharides in aqueous solutions. This offers a significant improvement of the Drude carbohydrate force field, wherein the refinement enhances the accuracy of accessing the conformational dynamics of carbohydrates in biomolecular simulations.

Origin of Enantioselectivity in Engineered Cytochrome c-Catalyzed Carbon-Radical FePP Hydrolysis Revealed Using QM/MM (ABEEM Polarizable Force Field) and MD Simulations

The origin of highly efficient asymmetric aminohydroxylation of styrene catalyzed by engineered cytochrome c is investigated by the developed Atom-Bond Electronegativity Equalization Method polarizable force field (ABEEM PFF), which is a combined outcome of electronic and steric effects. Model molecules were used to establish the charge parameters of the ABEEM PFF, for which the bond-stretching and angle-bending parameters were obtained by using a combination of modified Seminario and scan methods. The interactions between carbon-radical Fe-porphyrin (FePP) and waters are simulated by molecular dynamics, which shows a clear preference for the pre-R over the pre-S. This preference is attributed to the hydrogen-bond between the mutated 100S and 101P residues as well as van der Waals interactions, enforcing a specific conformation of the carbon-radical FePP complex within the binding pocket. Meanwhile, the hydrogen-bond between water and the nitrogen atom in the active intermediate dictates the stereochemical outcome. Quantum mechanics/molecular mechanics (QM/MM (ABEEM PFF)) and free-energy perturbation calculations elucidate that the 3RTS is characterized by sandwich-like structure among adjacent amino acid residues, which exhibits greater stability than crowed arrangement in 3STS and enables the R enantiomer to form more favorably. Thus, this study provides mechanistic insight into the catalytic reaction of hemoproteins.

System-Specific Parameter Optimization for Nonpolarizable and Polarizable Force Fields

The accuracy of classical force fields (FFs) has been shown to be limited for the simulation of cation-protein systems despite their importance in understanding the processes of life. Improvements can result from optimizing the parameters of classical FFs or by extending the FF formulation by terms describing charge transfer (CT) and polarization (POL) effects. In this work, we introduce our implementation of the CTPOL model in OpenMM, which extends the classical additive FF formula by adding CT and POL. Furthermore, we present an open-source parametrization tool, called FFAFFURR, that enables the (system-specific) parametrization of OPLS-AA and CTPOL models. The performance of our workflow was evaluated by its ability to reproduce quantum chemistry energies and by molecular dynamics simulations of a zinc-finger protein.

A Fast, Convenient, Polarizable Electrostatic Model for Molecular Dynamics

We present an efficient polarizable electrostatic model, utilizing typed, atom-centered polarizabilities and the fast direct approximation, designed for efficient use in molecular dynamics (MD) simulations. The model provides two convenient approaches for assigning partial charges in the context of atomic polarizabilities. One is a generalization of RESP, called RESP-dPol, and the other, AM1-BCC-dPol, is an adaptation of the widely used AM1-BCC method. Both are designed to accurately replicate gas-phase quantum mechanical electrostatic potentials. Benchmarks of this polarizable electrostatic model against gas-phase dipole moments, molecular polarizabilities, bulk liquid densities, and static dielectric constants of organic liquids show good agreement with the reference values. Of note, the model yields markedly more accurate dielectric constants of organic liquids, relative to a matched nonpolarizable force field. MD simulations with this method, which is currently parametrized for molecules containing elements C, N, O, and H, run only about 3.6-fold slower than fixed charge force fields, while simulations with the self-consistent mutual polarization average 4.5-fold slower. Our results suggest that RESP-dPol and AM1-BCC-dPol afford improved accuracy relative to fixed charge force fields and are good starting points for developing general, affordable, and transferable polarizable force fields. The software implementing these approaches has been designed to utilize the force field fitting frameworks developed and maintained by the Open Force Field Initiative, setting the stage for further exploration of this approach to polarizable force field development.

Symmetrized Drude Oscillator Force Fields Improve Numerical Performance of Polarizable Molecular Dynamics

Drude oscillator potentials are a popular and computationally efficient class of polarizable models that represent each polarizable atom as a positively charged Drude core harmonically bound to a negatively charged Drude shell. We show that existing force fields that place all non-Coulomb forces on the Drude core and none on the shell inadvertently couple the dipole to non-Coulombic forces. This introduces errors where interactions with neutral particles can erroneously induce atomic polarization, leading to spurious polarizations in the absence of an electric field, exacerbating violations of equipartition in the employed Carr-Parinello scheme. A suitable symmetrization of the interaction potential that correctly splits the force between the Drude core and shell can correct this shortcoming, improving the stability and numerical performance of Drude oscillator-based simulations. The symmetrization procedure is straightforward and only requires the rescaling of a few force field parameters.

DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling

Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.

Development of a QM/MM(ABEEM) method combined with a polarizable force field to investigate the excision reaction mechanism of damaged thymine

This paper focuses on the development of a quantum mechanics/molecular mechanics method using the ABEEM polarizable force field (QM/MM(ABEEM) method) to investigate the excision reaction mechanism of damaged thymine. This method does not simply combine the QM method with the polarizable force field. A valence electronegativity piecewise function with the distance between atoms as a variable is introduced to describe the atomic partial charges, and changes greatly during the reaction process. At the same time, the charge transfer effect is treated using the condition of local charge conservation. Compared with the traditional QM/MM method, the QM/MM(ABEEM) method can more accurately simulate the polarization effect and charge transfer effect in the reaction process. Focusing on the controversial problems of the excision of damaged bases, six reaction pathways were designed for monofunctional and difunctional deglycosylation of neutral bases and protonated bases. The results show that the QM/MM(ABEEM) method accurately simulates the polarization effect, charge transfer effect, activation energy and other properties of the reaction process. The process in which the active residue Asp activates the nucleophile H₂O to attack the protonated base is the preferred path. The average activation energy and free activation energy of the protonated base are 7.00-14.00 kcal mol^-1 lower than that of the neutral base. The study in this paper is helpful to understand the mechanism of repair enzymes in repairing bases.

A new framework for frequency-dependent polarizable force fields

A frequency-dependent extension of the polarizable force field "Atom-Condensed Kohn-Sham density functional theory approximated to the second-order" (ACKS2) [Verstraelen et al., J. Chem. Phys. 141, 194114 (2014)] is proposed, referred to as ACKS2ω. The method enables theoretical predictions of dynamical response properties of finite systems after partitioning of the frequency-dependent molecular response function. Parameters in this model are computed simply as expectation values of an electronic wavefunction, and the hardness matrix is entirely reused from ACKS2 as an adiabatic approximation is used. A numerical validation shows that accurate models can already be obtained with atomic monopoles and dipoles. Absorption spectra of 42 organic and inorganic molecular monomers are evaluated using ACKS2ω, and our results agree well with the time-dependent DFT calculations. Also for the calculation of C₆ dispersion coefficients, ACKS2ω closely reproduces its TDDFT reference. When parameters for ACKS2ω are derived from a PBE/aug-cc-pVDZ ground state, it reproduces experimental values for 903 organic and inorganic intermolecular pairs with an MAPE of 3.84%. Our results confirm that ACKS2ω offers a solid connection between the quantum-mechanical description of frequency-dependent response and computationally efficient force-field models.

Development of QM/MM (ABEEM polarizable force field) method to simulate the excision reaction mechanism of damaged cytosine

DNA damages are regarded as having harmful effects on cell. The base excision repair mechanism combats these effects by removing damaged bases. The deglycosylation mechanism of excising damaged bases by DNA glycosylase and the state of the leaving base have been controversial. The enzymatic reaction of DNA glycosylase to remove the damaged bases involves not only the formation and breaking of chemical bonds, but also complex polarization effect and charge transfer, which cannot be accurately simulated by the QM/MM method combined with the fixed charge force field. This work has developed the ABEEM fluctuating polarizable force field combining with the QM method, that is (QM/MM[ABEEM]), to accurately simulate the proton transfer, charge transfer and the charge distribution. The piecewise function is used as the valence-state electronegativity in the QM/MM (ABEEM) to realize the accurate fitting of the charge distribution in reaction. And the charge transfer is accurately simulated by the local charge conservation conditions. Four deglycosylation mechanisms including the monofunctional and difunctional mechanisms of four neutral and protonated cytosine derivatives are explored. It is confirmed that the monofunctional mechanism of Asp-activated nucleophile water is a better deglycosylation mechanism and the base is protonated before the reaction occurs. Protonization of the base reduced the activation energy by 10.00-17.00 kcal/mol. Asp provides the necessary charge for the reaction, and DNA glycosylase preferentially cleaves ɛC. This work provides a theoretical basis for the research of excising damaged bases by DNA glycosylase.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

Water-Mediated Oxidation of Guanine by a Repair Enzyme: Simulation Using the ABEEM Polarizable Force Field

The recognition mechanism of oxidative damage in organisms has long been a research hotspot. Water is an important medium in the recognition process, but its specific role remains unknown. There is a need to develop a suitable force field that can adequately describe the electrostatic, hydrogen bond, and other interactions among the molecules in the complex system of the repair enzyme and oxidized base. The developing ABEEM polarizable force field (PFF) has been used to simulate the repaired enzyme hOGG1 and oxidized DNA (PDB ID: 1EBM) in a biological environment, and the corresponding results are better than those of the fixed-charge force fields OPLS/AA and AMBER OL15. 8-Oxo-G is recognized by Gln315 of hOGG1 mainly through hydrogen bonds mediated by continuous exchange of 2 water molecules. Phe319 and Cys253 are stacked on both sides of the π planes of bases to form sandwich structures. The charge polarization effect gives an important signal to drive the exchange of water molecules and maintains the recognition of oxidation bases by enzymes. The mediated main water molecule A and mediated auxiliary water molecule B together pull Gln315 to recognize 8-oxo-G by hydrogen bond interactions. Then, the charge polarization signal of solvent water molecule C with a large absolute charge causes the absolute charge of O atoms in water molecule A or B to increase by approximately 0.2 e, and water molecule A or B leaves Gln315 and 8-oxo-G. The other water molecule and water molecule C synergistically recognize 8-oxo-G with Gln315. Even though the water molecules between Gln315 and 8-oxo-G are removed, the MD simulation results show that water molecules appear between Gln315 and 8-oxo-G in a very short time (<2 ps). The dwell time of each water molecule is approximately 60 ps. The radial distribution function and dwell time support the correctness of the above mechanism. These polarization effects and hydrogen bonding interactions cannot be simulated by a fixed-charge force field.

Systematic Parameterization and Simulation of Boronic Acid-β-Lactamase Aqueous Solution in Developing the ABEEMσπ Polarizable Force Field

Boronic acid, an inhibitor of β-lactamase, has begun to be applied to the treatment of biological infections and tumors. Scientists are working to develop new and more effective boronic acid. Molecular dynamics (MD) simulation provides a powerful auxiliary tool for drug design. However, the current force fields have no boron-related parameters. In this work, an atom-bond electronegativity equalization method at the σπ level (ABEEMσπ) polarizable force field (ABEEMσπ PFF) of boronic acid and β-lactamase has been developed to determine the potential functions and parameters. The interaction between boron and serine in β-lactamase is regarded as a bonded mode. The interaction between them is simulated by the Morse potential energy function, which is close to the experimental change of the stretching potential energy in a large range. The potential energy surfaces of the bond length, bond angle, and dihedral angle of boronic acid-β-lactamase have the same stability point and change trend as M06-2X/6-311G**. For 47 boronic acid-β-lactamase training molecules, the linear correlation coefficient (R) of the charge distribution between the ABEEMσπ PFF and HF/STO-3G is greater than 0.96. Attributed to the fact that the charge distribution of the ABEEMσπ PFF can fluctuate with the change of geometry and environment, the polarization effect and charge-transfer effect are well reflected. The binding ability of different boronic acids with the same β-lactamase is different. A total of 10 boronic acid-β-lactamase model molecules and 10 boronic acid-β-lactamase and water complexes are simulated. The order of binding energy of five large model molecules calculated by the ABEEMσπ PFF is consistent with that of the MP2 method. The binding energies of boronic acid-β-lactamase and water complexes are close to those of the MP2 method. The results of MD simulation of five aqueous boronic acid-β-lactamase complexes in the NVT ensemble verify the rationality of boron-related parameters of the ABEEMσπ PFF, which have a good application prospect. This study lays a solid theoretical foundation for further study of the inhibition of boronic acid on β-lactamase.

ABEEM/MM OH- Models for OH-(H2O)n Clusters and Aqueous OH-: Structures, Charge Distributions, and Binding Energies

Based on the atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM), two fluctuating charge models of OH^--water system were proposed. The difference between these two models is whether there is charge transfer between OH^- and its first-shell water molecules. The structures, charge distributions, charge transfer, and binding energies of the OH^-(H₂O)_n (n = 1-8, 10, 15, 23) clusters were studied by these two ABEEM/MM models, the OPLS/AA force field, the OPLS-SMOOTH/AA force field, and the QM methods. The results demonstrate that two ABEEM/MM models can search out all stable structures just as the QM methods, and the structures and charge distributions agree well with those from the QM calculations. The structures, the charge transfer, and the strength of hydrogen bonds in the first hydration shell are closely related to the coordination number of OH^-. Molecular dynamics simulations on the aqueous OH^- solution are performed at 298 and 278 K using ABEEM/MM-I model. The MD results show that the populations of three-, four-, and five-coordinated OH^- are 29.6%, 67.1%, and 3.4% at 298 K, respectively, and those of two-, three-, four-, and five-coordinated OH^- are 10.8%, 44.9%, 39.2%, and 4.9% at 278 K, respectively; the average hydrogen bond lengths and the hydrogen bond angle in the first shell increase with the temperature decreasing.

Developing an effective polarizable bond method for small molecules with application to optimized molecular docking

Electrostatic interaction plays an essential role in protein-ligand binding. Due to the polarization effect, electrostatic interactions are largely impacted by their local environments. However, traditional force fields use fixed point charge-charge interactions to describe electrostatic interactions but is unable to include the polarization effect. The lack of the polarization effect in the force field representation can result in substantial error in biomolecular studies, such as molecular dynamics and molecular docking. Docking programs usually employ traditional force fields to estimate the binding energy between a ligand and a protein for pose selection or scoring. The intermolecular interaction energy mainly consists of van der Waals and electrostatic interaction in the force field representation. In the current study, we developed an Effective Polarizable Bond (EPB) method for small organic molecules and applied this EPB method to optimize protein-ligand docking in computational tests for a variety of protein-ligand systems. We tested the method on a set of 38 cocrystallized structures taken from the Protein Data Bank (PDB) and found that the maximum error was reduced from 7.98 Å to 2.03 Å when using EPB Dock, providing strong evidence that the use of EPB charges is important. We found that our optimized docking approach with EPB charges could improve the docking performance, sometimes dramatically, and the maximum error was reduced from 12.88 Å to 1.57 Å in Optimized Docking (in the case of 1fqx). The average RMSD decreased from 2.83 Å to 1.85 Å. Further investigations showed that the use of the EBP method could enhance intermolecular hydrogen bonding, which is a major contributing factor to improved docking performance. Developed tools for the calculation of the polarized ligand charge from a protein-ligand complex structure with the EPB method are freely available on GitHub (https://github.com/Xundrug/EPB).

A force consistent method for electrostatic energy calculation in fluctuating charge model

A practical approach to include the polarization effect in a molecular force field is the fluctuating charge method in which atomic charges vary as the configuration of the molecular system changes. However, the use of the Coulomb formula to evaluate energy in a fluctuating charge method is theoretically inconsistent with the forces given by the fluctuating method. In this work, we propose a force-consistent method to correctly calculate electrostatic energies of molecular systems using a fluctuating charge model (Effective Polarizable Bond or EPB). In this protocol, the electrostatic energy is obtained by numerical interaction of the atomic forces along the MD trajectory, rather than using the default Coulomb formula in the EPB model. Test study on the benchmark Barnase-Barstar protein-protein interaction system demonstrates that although the total electrostatic energy of the system shows little deviation due to the averaging effect, specific residue-residue electrostatic interaction energy is affected and the level of the effect depends on the charges of the interacting residues with charged residues showing pronounced differences in calculated energies between using the current protocol and the standard Coulomb formula. It is recommended that the proposed numerical interaction method should be preferred in the calculation of electrostatic energy in fluctuating charge models used in molecular dynamics simulations.

Drude Polarizable Force Field Parametrization of Carboxylate and N-Acetyl Amine Carbohydrate Derivatives

In this work, we report the development of Drude polarizable force field parameters for the carboxylate and N-acetyl amine derivatives, extending the functionality of the existing Drude polarizable carbohydrate force field. The force field parameters have been developed in a hierarchical manner, reproducing the quantum mechanical gas-phase properties of small model compounds representing the key functional group in the carbohydrate derivatives, including optimization of the electrostatic and bonded parameters. The optimized parameters were then used to generate the models for carboxylate and N-acetyl amine carbohydrate derivatives. The transferred parameters were further tested and optimized to reproduce crystal geometries and J-coupling data from nuclear magnetic resonance experiments. The parameter development resulted in the incorporation of d-glucuronate, l-iduronate, N-acetyl-d-glucosamine (GlcNAc), and N-acetyl-d-galactosamine (GalNAc) sugars into the Drude polarizable force field. The parameters developed in this study were then applied to study the conformational properties of glycosaminoglycan polymer hyaluronan, composed of d-glucuronate and N-acetyl-d-glucosamine, in aqueous solution. Upon comparing the results from the additive and polarizable simulations, it was found that the inclusion of polarization improved the description of the electrostatic interactions observed in hyaluronan, resulting in enhanced conformational flexibility. The developed Drude polarizable force field parameters in conjunction with the remainder of the Drude polarizable force field parameters can be used for future studies involving carbohydrates and their conjugates in complex, heterogeneous systems.

Development and Validation of the Quantum Mechanical Bespoke Protein Force Field

Molecular mechanics force field parameters for macromolecules, such as proteins, are traditionally fit to reproduce experimental properties of small molecules, and thus, they neglect system-specific polarization. In this paper, we introduce a complete protein force field that is designed to be compatible with the quantum mechanical bespoke (QUBE) force field by deriving nonbonded parameters directly from the electron density of the specific protein under study. The main backbone and sidechain protein torsional parameters are rederived in this work by fitting to quantum mechanical dihedral scans for compatibility with QUBE nonbonded parameters. Software is provided for the preparation of QUBE input files. The accuracy of the new force field, and the derived torsional parameters, is tested by comparing the conformational preferences of a range of peptides and proteins with experimental measurements. Accurate backbone and sidechain conformations are obtained in molecular dynamics simulations of dipeptides, with NMR J coupling errors comparable to the widely used OPLS force field. In simulations of five folded proteins, the secondary structure is generally retained, and the NMR J coupling errors are similar to standard transferable force fields, although some loss of the experimental structure is observed in certain regions of the proteins. With several avenues for further development, the use of system-specific nonbonded force field parameters is a promising approach for next-generation simulations of biological molecules.

New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 1. Theory and accuracy

Polarizabilities and London dispersion forces are important to many chemical processes. Force fields for classical atomistic simulations can be constructed using atom-in-material polarizabilities and C n (n = 6, 8, 9, 10…) dispersion coefficients. This article addresses the key question of how to efficiently assign these parameters to constituent atoms in a material so that properties of the whole material are better reproduced. We develop a new set of scaling laws and computational algorithms (called MCLF) to do this in an accurate and computationally efficient manner across diverse material types. We introduce a conduction limit upper bound and m-scaling to describe the different behaviors of surface and buried atoms. We validate MCLF by comparing results to high-level benchmarks for isolated neutral and charged atoms, diverse diatomic molecules, various polyatomic molecules (e.g., polyacenes, fullerenes, and small organic and inorganic molecules), and dense solids (including metallic, covalent, and ionic). We also present results for the HIV reverse transcriptase enzyme complexed with an inhibitor molecule. MCLF provides the non-directionally screened polarizabilities required to construct force fields, the directionally-screened static polarizability tensor components and eigenvalues, and environmentally screened C6 coefficients. Overall, MCLF has improved accuracy compared to the TS-SCS method. For TS-SCS, we compared charge partitioning methods and show DDEC6 partitioning yields more accurate results than Hirshfeld partitioning. MCLF also gives approximations for C8, C9, and C10 dispersion coefficients and quantum Drude oscillator parameters. This method should find widespread applications to parameterize classical force fields and density functional theory (DFT) + dispersion methods.

AMOEBA+ Classical Potential for Modeling Molecular Interactions

Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration, and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model based on the AMOEBA+ framework captures various liquid-phase properties in molecular dynamics simulations while remaining consistent with SAPT energy decompositions, utilizing both ab initio data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.

Combining Iteration-Free Polarization with Large Time Step Stochastic-Isokinetic Integration

In order to accelerate molecular dynamics simulations using polarizable force fields, we combine a new extended Lagrangian approach that eliminates the self-consistent field step (iEL/0-SCF) with a stochastic integration scheme that allows for a long time step using a multiple time scale algorithm (SIN(R)). We consider different algorithms for the combined scheme that places different components of the nonbonded forces into different time scales, as well as splitting individual nonbonded forces across time scales, to demonstrate that the combined method works well for bulk water as well as for a concentrated salt solution, aqueous peptide, and solvated protein. Depending on system and desired accuracy, the iEL/0-SCF and SIN(R) combination yields lower bound computational speed-ups of ∼6-8 relative to a molecular dynamics Verlet integration using a standard SCF solver implemented in the reference program TINKER 8.1. The combined approach embodies a significant advance for equilibrium simulations in the canonical ensemble of many-body potential energy surfaces for condensed phase systems with speed-ups that exceed what is possible by either method alone.

A New Method for Treating Drude Polarization in Classical Molecular Simulation

With polarization becoming an increasingly common feature in classical molecular simulation, it is important to develop methods that can efficiently and accurately evaluate the many-body polarization solution. In this work, we expand the theoretical framework of our inertial extended Langrangian, self-consistent field iteration-free method (iEL/0-SCF), introduced for point induced dipoles, to the polarization model of a Drude oscillator. When applied to the polarizable simple point charge model (PSPC) for water, our iEL/0-SCF method for Drude polarization is as stable as a well-converged SCF solution and more stable than traditional extended Lagrangian (EL) approaches or EL formulations based on two temperature ensembles where Drude particles are kept "colder" than the real degrees of freedom. We show that the iEL/0-SCF method eliminates the need for mass repartitioning from parent atoms onto Drude particles, obeys system conservation of linear and angular momentum, and permits the extension of the integration time step of a basic molecular dynamics simulation to 6.0 fs for PSPC water.

Improved Description of Sulfur Charge Anisotropy in OPLS Force Fields: Model Development and Parameterization

The atomic point-charge model used in most molecular mechanics force fields does not represent well the electronic anisotropy that is featured in many directional noncovalent interactions. Sulfur participates in several types of such interactions with its lone pairs and σ-holes. The current study develops a new model, via the addition of off-atom charged sites, for a variety of sulfur compounds in the OPLS-AA and OPLS/CM5 force fields to address the lack of charge anisotropy. Parameter optimization is carried out to reproduce liquid-state properties, torsional and noncovalent energetics from reliable quantum mechanical calculations, and electrostatic potentials. Significant improvements are obtained for computed free energies of hydration, reducing the mean unsigned errors from ca. 1.4 to 0.4-0.7 kcal/mol. Enhanced accuracy in directionality and energetics is also obtained for molecular complexes with sulfur-containing hydrogen and halogen bonds. Moreover, the new model reproduces the unusual conformational preferences of sulfur-containing compounds with 1,4-intramolecular chalcogen bonds. Transferability of the new force field parameters to cysteine and methionine is verified via molecular dynamic simulations of blocked dipeptides. The study demonstrates the effectiveness of using off-atom charge sites to address electronic anisotropy, and provides a parametrization methodology that can be applied to other systems.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Advanced Potential Energy Surfaces for Molecular Simulation

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

Prediction of cyclohexane-water distribution coefficients for the SAMPL5 data set using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics simulations were used to predict water-cyclohexane distribution coefficients [Formula: see text] of a range of small molecules as part of the SAMPL5 blind prediction challenge. Molecules were parameterized with the transferable all-atom OPLS-AA force field, which required the derivation of new parameters for sulfamides and heterocycles and validation of cyclohexane parameters as a solvent. The distribution coefficient was calculated from the solvation free energies of the compound in water and cyclohexane. Absolute solvation free energies were computed by an established protocol using windowed alchemical free energy perturbation with thermodynamic integration. This protocol resulted in an overall root mean square error in [Formula: see text] of almost 4 log units and an overall signed error of -3 compared to experimental data. There was no substantial overall difference in accuracy between simulating in NVT and NPT ensembles. The signed error suggests a systematic error but the experimental [Formula: see text] data on their own are insufficient to uncover the source of this error. Preliminary work suggests that the major source of error lies in the hydration free energy calculations.

An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications

Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena.

Biomolecular Force Field Parameterization via Atoms-in-Molecule Electron Density Partitioning

Molecular mechanics force fields, which are commonly used in biomolecular modeling and computer-aided drug design, typically treat nonbonded interactions using a limited library of empirical parameters that are developed for small molecules. This approach does not account for polarization in larger molecules or proteins, and the parametrization process is labor-intensive. Using linear-scaling density functional theory and atoms-in-molecule electron density partitioning, environment-specific charges and Lennard-Jones parameters are derived directly from quantum mechanical calculations for use in biomolecular modeling of organic and biomolecular systems. The proposed methods significantly reduce the number of empirical parameters needed to construct molecular mechanics force fields, naturally include polarization effects in charge and Lennard-Jones parameters, and scale well to systems comprised of thousands of atoms, including proteins. The feasibility and benefits of this approach are demonstrated by computing free energies of hydration, properties of pure liquids, and the relative binding free energies of indole and benzofuran to the L99A mutant of T4 lysozyme.

Numerical study on the partitioning of the molecular polarizability into fluctuating charge and induced atomic dipole contributions

In order to carry out a detailed analysis of the molecular static polarizability, which is the response of the molecule to a uniform external electric field, the molecular polarizability was computed using the finite-difference method for 21 small molecules, using density functional theory. Within nine charge population schemes (Löwdin, Mulliken, Becke, Hirshfeld, CM5, Hirshfeld-I, NPA, CHELPG, MK-ESP) in common use, the charge fluctuation contribution is found to dominate the molecular polarizability, with its ratio ranging from 59.9% with the Hirshfeld or CM5 scheme to 96.2% with the Mulliken scheme. The Hirshfeld-I scheme is also used to compute the other contribution to the molecular polarizability coming from the induced atomic dipoles, and the atomic polarizabilities in eight small molecules and water pentamer are found to be highly anisotropic for most atoms. Overall, the results suggest that (a) more emphasis probably should be placed on the charge fluctuation terms in future polarizable force field development and (b) an anisotropic polarizability might be more suitable than an isotropic one in polarizable force fields based entirely or partially on the induced atomic dipoles.

Implementation of extended Lagrangian dynamics in GROMACS for polarizable simulations using the classical Drude oscillator model

Explicit treatment of electronic polarization in empirical force fields used for molecular dynamics simulations represents an important advancement in simulation methodology. A straightforward means of treating electronic polarization in these simulations is the inclusion of Drude oscillators, which are auxiliary, charge-carrying particles bonded to the cores of atoms in the system. The additional degrees of freedom make these simulations more computationally expensive relative to simulations using traditional fixed-charge (additive) force fields. Thus, efficient tools are needed for conducting these simulations. Here, we present the implementation of highly scalable algorithms in the GROMACS simulation package that allow for the simulation of polarizable systems using extended Lagrangian dynamics with a dual Nosé-Hoover thermostat as well as simulations using a full self-consistent field treatment of polarization. The performance of systems of varying size is evaluated, showing that the present code parallelizes efficiently and is the fastest implementation of the extended Lagrangian methods currently available for simulations using the Drude polarizable force field.

Recent Advances in Polarizable Force Fields for Macromolecules: Microsecond Simulations of Proteins Using the Classical Drude Oscillator Model

In this Perspective, we summarize recent efforts to include the explicit treatment of induced electronic polarization in biomolecular force fields. Methods used to treat polarizability, including the induced dipole, fluctuating charge, and classical Drude oscillator models, are presented, including recent advances in force fields using those methods. This is followed by recent results obtained with the Drude model, including microsecond molecular dynamics (MD) simulations of multiple proteins in explicit solvent. Results show significant variability of backbone and side-chain dipole moments as a function of environment, including significant changes during individual simulations. Dipole moments of water in the vicinity of the proteins reveal small but systematic changes, with the direction of the changes dependent on the environment. Analyses of the full proteins show that the polarizable Drude model leads to larger values of the dielectric constant of the protein interior, especially in the case of hydrophobic regions. These results indicate that the inclusion of explicit electronic polarizability leads to significant differences in the physical forces affecting the structure and dynamics of proteins, which can be investigated in a computationally tractable fashion in the context of the Drude model.

Substituent effects in hydrogen bonding: DFT and QTAIM studies on acids and carboxylates complexes with formamide

Four series of hydrogen bonded complexes of formamide and substituted benzoic acids and benzoates were studied in the light of substituent effect on intermolecular interactions. The analysis based on energy of interaction, geometry, QTAIM-derived properties of hydrogen bond critical point and energy of hydrogen bonds were made and discussed. The opposite effect of the substituent on hydrogen bond donor and acceptor in acid series was found and analyzed. The isodesmic reactions were used to further study the interaction preferences.

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A Comparative Study of Transferable Aspherical Pseudoatom Databank and Classical Force Fields for Predicting Electrostatic Interactions in Molecular Dimers

Accurate and fast evaluation of electrostatic interactions in molecular systems is one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry and drug design. Electrostatic interactions are of crucial importance in biological systems. They are well represented by quantum mechanical methods; however, such calculations are computationally expensive. In this study, we have evaluated the University of Buffalo Pseudoatom Databank (UBDB)1,2 approach for approximation of electrostatic properties of macromolecules and their complexes. We selected the S663 and JSCH-20054 data sets (208 molecular complexes in total) for this study. These complexes represent a wide range of chemical and biological systems for which hydrogen bonding, electrostatic, and van der Waals interactions play important roles. Reference electrostatic energies were obtained directly from wave functions at the B3LYP/aug-cc-pVTZ level of theory using the SAPT (Symmetry-Adapted Perturbation Theory) scheme for calculation of electrostatic contributions to total intermolecular interaction energies. Electrostatic energies calculated on the basis of the UBDB were compared with corresponding reference results. Results were also compared with energies computed using a point charge model from popular force fields (AM1-BCC and RESP used in AMBER and CGenFF from CHARMM family). The energy trends are quite consistent (R2 ≈ 0.98) for the UBDB method as compared to the AMBER5 and CHARMM force field methods6(R2 ≈ 0.93 on average). The RSMEs do not exceed 3.2 kcal mol-1 for the UBDB and are in the range of 3.7-7.6 kcal mol-1 for the point charge models. We also investigated the discrepancies in electrostatic potentials and magnitudes of dipole moments among the tested methods. This study shows that estimation of electrostatic interaction energies using the UBDB databank is accurate and reasonably fast when compared to other known methods, which opens potential new applications to macromolecules.

Cooperative effects and optimal halogen bonding motifs for self-assembling systems

Halogen bonding, due to its directionality and tunable strength, is being increasingly utilized in self-assembling materials and crystal engineering. Using density functional theory (DFT) and molecular mechanics (OPLS/CM1Ax) calculations, multiply halogen bonded complexes of brominated imidazole and pyridine are investigated along with their potential in construction of self-assembling architectures. Dimers with 1–10 halogen bonds are considered and reveal maximal binding energies of 3–36 kcal/mol. Cooperative (nonadditive) effects are found in complexes that extend both along and perpendicular to the halogen bonding axes, with interaction energies depending on polarization, secondary interactions, and ring spacers. Four structural motifs were identified to yield optimal halogen bonding. For the largest systems, the excellent agreement found between the DFT and OPLS/CM1Ax results supports the utility of the latter approach for analysis and design of self-assembling supramolecular structures.

Prediction of hydration free energies for the SAMPL4 diverse set of compounds using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics computer simulations were used to blindly predict the hydration free energies of a range of small molecules as part of the SAMPL4 challenge. Compounds were parametrized on the basis of the OPLS-AA force field using three different protocols for deriving partial charges: (1) using existing OPLS-AA atom types and charges with minor adjustments of partial charges on equivalent connecting atoms and derivation of new parameters for a number of distinct chemical groups (N-alkyl imidazole, nitrate) that were not present in the published force field; (2) calculation of quantum mechanical charges via geometry optimization, followed by electrostatic potential (ESP) fitting, using Jaguar at the LMP2/cc-pVTZ(-F) level; and (3) via geometry optimization and CHelpG charges (Gaussian09 at the HF/6-31G* level), followed by two-stage RESP fitting. The absolute hydration free energy was computed by an established protocol including alchemical free energy perturbation with thermodynamic integration. The use of standard OPLS-AA charges (protocol 1) with a number of newly parametrized charges and the use of histidine derived parameters for imidazole yielded an overall root mean square deviation of the prediction from the experimental data of 1.75 kcal/mol. The precision of our results appears to be mainly limited by relatively poor reproducibility of the Lennard-Jones contribution towards the solvation free energy, for which we observed large variability that could be traced to a strong dependence on the initial system conditions.

Molecular mechanics

Molecular Mechanics (MM) force fields are the methods of choice for protein simulations, which are essential in the study of conformational flexibility. Given the importance of protein flexibility in drug binding, MM is involved in most if not all Computational Structure-Based Drug Discovery (CSBDD) projects. This paper introduces the reader to the fundamentals of MM, with a special emphasis on how the target data used in the parametrization of force fields determine their strengths and weaknesses. Variations and recent developments such as polarizable force fields are discussed. The paper ends with a brief overview of common force fields in CSBDD.

Advanced potential energy surfaces for condensed phase simulation

Computational modeling at the atomistic and mesoscopic levels has undergone dramatic development in the past 10 years to meet the challenge of adequately accounting for the many-body nature of intermolecular interactions. At the heart of this challenge is the ability to identify the strengths and specific limitations of pairwise-additive interactions, to improve classical models to explicitly account for many-body effects, and consequently to enhance their ability to describe a wider range of reference data and build confidence in their predictive capacity. However, the corresponding computational cost of these advanced classical models increases significantly enough that statistical convergence of condensed phase observables becomes more difficult to achieve. Here we review a hierarchy of potential energy surface models used in molecular simulations for systems with many degrees of freedom that best meet the trade-off between accuracy and computational speed in order to define a sweet spot for a given scientific problem of interest.