Development of Polarizable Gaussian Model for Molecular Mechanical Calculations I: Atomic Polarizability Parameterization To Reproduce ab Initio Anisotropy

Refinement of Atomic Polarizabilities for a Polarizable Gaussian Multipole Force Field with Simultaneous Considerations of Both Molecular Polarizability Tensors and In-Solution Electrostatic Potentials

Atomic polarizabilities are considered to be fundamental parameters in polarizable molecular mechanical force fields that play pivotal roles in determining model transferability across different electrostatic environments. In an earlier work, the atomic polarizabilities were obtained by fitting them to the B3LYP/aug-cc-pvtz molecular polarizability tensors of mainly small molecules. Taking advantage of the recent PCMRESPPOL method, we refine the atomic polarizabilities for condensed-phase simulations using a polarizable Gaussian Multipole (pGM) force field. Departing from earlier works, in this work, we incorporated polarizability tensors of a large number of dimers and electrostatic potentials (ESPs) in multiple solvents. We calculated 1565 × 4 ESPs of small molecule monomers and dimers of noble gas and small molecules and 4742 × 4 ESPs of small molecule dimers in four solvents (diethyl ether, ε = 4.24, dichloroethane, ε = 10.13, acetone, ε = 20.49, and water, ε = 78.36). For the gas-phase polarizability tensors, we supplemented the molecule set that was used in our earlier work by adding both the 4252 monomer and dimer sets studied by Shaw and co-workers and the 7211 small molecule monomers listed in the QM7b database to a combined total of 13,523 molecular polarizability tensors of monomers and dimers. The QM7b polarizability set was obtained from quantum-machine.org and was calculated at the LR-CCSD/d-aug-cc-pVDZ level of theory. All other polarizability tensors and all ESPs were calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The atomic polarizabilities were developed using all polarizability tensors and the 1565 × 4 ESPs of small molecule monomers and were then assessed by comparing them to the 4742 × 4 ab initio ESPs of small molecule dimers. The predicted dimer ESPs had an average relative root-mean-square error (RRMSE) of 9.30%, which was only slightly larger than the average fitting RRMSE of 9.15% of the monomer ESPs. The transferability of the polarizability set was further evaluated by comparing the ESPs calculated using parameters developed in another dielectric environment for both tetrapeptide and DES monomer data sets. It was observed that the polarizabilities of this work retained or slightly improved the transferability over the one discussed in earlier work even though the number of parameters in the present set is about half of that in the earlier set. Excluding the gas-phase data, for the DES monomer set, the average transfer RRMSEs were 16.25% and 10.83% for pGM-ind and pGM-perm methods, respectively, comparable to the average fitting RRMSEs of 16.03% and 10.54%; for tetrapeptides, the average transfer RRMSEs were 5.62% and 3.95% for pGM-ind and pGM-perm methods, respectively, slightly larger than 5.41% and 3.61% of the fitting RRMSEs. Therefore, we conclude that the pGM methods with updated polarizabilities achieved remarkable transferability from monomer to dimer and from one solvent to another.

PCMRESP: A Method for Polarizable Force Field Parameter Development and Transferability of the Polarizable Gaussian Multipole Models Across Multiple Solvents

The transferability of force field parameters is a crucial aspect of high-quality force fields. Previous investigations have affirmed the transferability of electrostatic parameters derived from polarizable Gaussian multipole models (pGMs) when applied to water oligomer clusters, polypeptides across various conformations, and different sequences. In this study, we introduce PCMRESP, a novel method for electrostatic parametrization in solution, intended for the development of polarizable force fields. We utilized this method to assess the transferability of three models: a fixed charge model and two variants of pGM models. Our analysis involved testing these models on 377 small molecules and 100 tetra-peptides in five representative dielectric environments: gas, diethyl ether, dichloroethane, acetone, and water. Our findings reveal that the inclusion of atomic polarization significantly enhances transferability and the incorporation of permanent atomic dipoles, in the form of covalent bond dipoles, leads to further improvements. Moreover, our tests on dual-solvent strategies demonstrate consistent transferability for all three models, underscoring the robustness of the dual-solvent approach. In contrast, an evaluation of the traditional HF/6-31G* method indicates poor transferability for the pGM-ind and pGM-perm models, suggesting the limitations of this conventional approach.

Assessment of Amino Acid Electrostatic Parametrizations of the Polarizable Gaussian Multipole Model

Accurate parametrization of amino acids is pivotal for the development of reliable force fields for molecular modeling of biomolecules such as proteins. This study aims to assess amino acid electrostatic parametrizations with the polarizable Gaussian Multipole (pGM) model by evaluating the performance of the pGM-perm (with atomic permanent dipoles) and pGM-ind (without atomic permanent dipoles) variants compared to the traditional RESP model. The 100-conf-combterm fitting strategy on tetrapeptides was adopted, in which (1) all peptide bond atoms (-CO-NH-) share identical set of parameters and (2) the total charges of the two terminal N-acetyl (ACE) and N-methylamide (NME) groups were set to neutral. The accuracy and transferability of electrostatic parameters across peptides with varying lengths and real-world examples were examined. The results demonstrate the enhanced performance of the pGM-perm model in accurately representing the electrostatic properties of amino acids. This insight underscores the potential of the pGM-perm model and the 100-conf-combterm strategy for the future development of the pGM force field.

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Streamlining and Optimizing Strategies of Electrostatic Parameterization

Accurate characterization of electrostatic interactions is crucial in molecular simulation. Various methods and programs have been developed to obtain electrostatic parameters for additive or polarizable models to replicate electrostatic properties obtained from experimental measurements or theoretical calculations. Electrostatic potentials (ESPs), a set of physically well-defined observables from quantum mechanical (QM) calculations, are well suited for optimization efforts due to the ease of collecting a large amount of conformation-dependent data. However, a reliable set of QM ESP computed at an appropriate level of theory and atomic basis set is necessary. In addition, despite the recent development of the PyRESP program for electrostatic parameterizations of induced dipole-polarizable models, the time-consuming and error-prone input file preparation process has limited the widespread use of these protocols. This work aims to comprehensively evaluate the quality of QM ESPs derived by eight methods, including wave function methods such as Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled cluster-singles and doubles (CCSD), as well as five hybrid density functional theory (DFT) methods, used in conjunction with 13 different basis sets. The highest theory levels CCSD/aug-cc-pV5Z (a5z) and MP2/aug-cc-pV5Z (a5z) were selected as benchmark data over two homemade data sets. The results show that the hybrid DFT method, ωB97X-D, combined with the aug-cc-pVTZ (a3z) basis set, performs well in reproducing ESPs while taking both accuracy and efficiency into consideration. Moreover, a flexible and user-friendly program called PyRESP_GEN was developed to streamline input file preparation. The restraining strengths, along with strategies for polarizable Gaussian multipole (pGM) model parameterizations, were also optimized. These findings and the program presented in this work facilitate the development and application of induced dipole-polarizable models, such as pGM models, for molecular simulations of both chemical and biological significance.

Assessment of an Electrostatic Energy-Based Charge Model for Modeling the Electrostatic Interactions in Water Solvent

The protein force field based on the restrained electrostatic potential (RESP) charges has limitations in accurately describing hydrogen bonding interactions in proteins. To address this issue, we propose an alternative approach called the electrostatic energy-based charges (EEC) model, which shows improved performance in describing electrostatic interactions (EIs) of hydrogen bonds in proteins. In this study, we further investigate the performance of the EEC model in modeling EIs in water solvent. Our findings demonstrate that the fixed EEC model can effectively reproduce the quantum mechanics/molecular mechanics (QM/MM)-calculated EIs between a water molecule and various water solvent environments. However, to achieve the same level of computational accuracy, the electrostatic potential (ESP) charge model needs to fluctuate according to the electrostatic environment. Our analysis indicates that the requirement for charge adjustments depends on the specific mathematical and physical representation of EIs as a function of the environment for deriving charges. By comparing with widely used empirical water models calibrated to reproduce experimental properties, we confirm that the performance of the EEC model in reproducing QM/MM EIs is similar to that of general purpose TIP4P-like water models such as TIP4P-Ew and TIP4P/2005. When comparing the computed 10,000 distinct EI values within the range of -40 to 0 kcal/mol with the QM/MM results calculated at the MP2/aug-cc-pVQZ/TIP3P level, we noticed that the mean unsigned error (MUE) for the EEC model is merely 0.487 kcal/mol, which is remarkably similar to the MUE values of the TIP4P-Ew (0.63 kcal/mol) and TIP4P/2005 (0.579 kcal/mol) models. However, both the RESP method and the TIP3P model exhibit a tendency to overestimate the EIs, as evidenced by their higher MUE values of 1.761 and 1.293 kcal/mol, respectively. EEC-based molecular dynamics simulations have demonstrated that, when combined with appropriate van der Waals parameters, the EEC model can closely reproduce oxygen-oxygen radial distribution function and density of water, showing a remarkable similarity to the well-established TIP4P-like empirical water models. Our results demonstrate that the EEC model has the potential to build force fields with comparable accuracy to more sophisticated empirical TIP4P-like water models.

Optimal Scheme to Achieve Energy Conservation in Induced Dipole Models

Induced dipole models have proven to be effective tools for simulating electronic polarization effects in biochemical processes, yet their potential has been constrained by energy conservation issue, particularly when historical data is utilized for dipole prediction. This study identifies error outliers as the primary factor causing this failure of energy conservation and proposes a comprehensive scheme to overcome this limitation. Leveraging maximum relative errors as a convergence metric, our data demonstrates that energy conservation can be upheld even when using historical information for dipole predictions. Our study introduces the multi-order extrapolation method to quicken induction iteration and optimize the use of historical data, while also developing the preconditioned conjugate gradient with local iterations to refine the iteration process and effectively remove error outliers. This scheme further incorporates a "peek" step via Jacobi under-relaxation for optimal performance. Simulation evidence suggests that our proposed scheme can achieve energy convergence akin to that of point-charge models within a limited number of iterations, thus promising significant improvements in efficiency and accuracy.

Transferability of the Electrostatic Parameters of the Polarizable Gaussian Multipole Model

Accuracy and transferability are the two highly desirable properties of molecular mechanical force fields. Compared with the extensively used point-charge additive force fields that apply fixed atom-centered point partial charges to model electrostatic interactions, polarizable force fields are thought to have the advantage of modeling the atomic polarization effects. Previous works have demonstrated the accuracy of the recently developed polarizable Gaussian multipole (pGM) models. In this work, we assessed the transferability of the electrostatic parameters of the pGM models with (pGM-perm) and without (pGM-ind) atomic permanent dipoles in terms of reproducing the electrostatic potentials surrounding molecules/oligomers absent from electrostatic parameterizations. Encouragingly, both the pGM-perm and pGM-ind models show significantly improved transferability than the additive model in the tests (1) from water monomer to water oligomer clusters; (2) across different conformations of amino acid dipeptides and tetrapeptides; (3) from amino acid tetrapeptides to longer polypeptides; and (4) from nucleobase monomers to Watson-Crick base pair dimers and tetramers. Furthermore, we demonstrated that the double-conformation fittings using amino acid tetrapeptides in the αR and β conformations can result in good transferability not only across different tetrapeptide conformations but also from tetrapeptides to polypeptides with lengths ranging from 1 to 20 repetitive residues for both the pGM-ind and pGM-perm models. In addition, the observation that the pGM-ind model has significantly better accuracy and transferability than the point-charge additive model, even though they have an identical number of parameters, strongly suggest the importance of intramolecular polarization effects. In summary, this and previous works together show that the pGM models possess both accuracy and transferability, which are expected to serve as foundations for the development of next-generation polarizable force fields for modeling various polarization-sensitive biological systems and processes.

Unexpected polarization properties of sub-nanosized magnesium clusters

The isotropic electrostatic polarizability (IEP) of sub-nanosized magnesium clusters Mg2-Mg32 was studied in an extensive set comprising 1237 structurally unique isomers. These isomers were found in the course of the global search for the potential energy surface minima of the magnesium clusters at the BP86/6-31G(d) level. The calculation of the polarizability at the same DFT level reveals an unexpected property of the IEP: the linear correlation between the polarizability of the most favorable isomers (and only them) and the cluster nuclearity n. Moreover, for each n, the most stable cluster isomer demonstrates nearly minimal IEP value among all found isomers of a given nuclearity. Surprisingly, these observed features are independent of the cluster structures which are quite different. We hypothesize that the energetic favorability of a cluster structure is related to their low polarizability. Apparently, the atoms forming the cluster tend to arrange themselves in such a way as to provide the most compact distribution of the cluster electron density. A possible explanation of the observed trends, their significance for cluster structure prediction, and the practical applications are discussed.

Polarizable Molecular Block Model: Toward the Development of an Induced Dipole Force Field for DNA

For flexible and highly ionized macromolecules such as DNA, it is important to correctly evaluate the intramolecular polarization in an induced dipole force field. In a proposed polarizable molecular block (PMB) model, a large molecule is divided into several molecular blocks. The atomic charges of the blocks are optimized by using the respective electrostatic potentials (ESPs) on the molecular surface. By using the capped hydrogen removal operation, the total charge of the blocks is controlled exactly to have an integer charge. The atomic polarizabilities of the blocks are optimized by using the respective polarized one-electron potentials that are the differences between ESPs with and without an external test charge. Induced dipole-charge interactions between the blocks are all included, but those interactions within the blocks are strictly excluded. All dipole-dipole interactions are included, but the damping functions are applied to the close dipole-dipole pairs. Several types of damping (simple scaling, exponential, linear, and Gaussian) are evaluated. The validity of the PMB model was verified by using trinucleotide duplexes which have A-, B-, and Z-DNA forms. The reference energies of trinucleotide duplexes including counterions (GGT3Na-ACC3Na, GAC3Na-GTC3Na, and GCG3Na-CGC3Na) are calculated using ωB97XD/aug-cc-pVDZ. All damping types reproduced well the reference interaction energies, dipole moments, and ESPs. Among them, the simple scaling with strong attenuation to 1-2 atomic pairs showed the highest stability against the polarization catastrophe. This study shows that it is possible to develop a high-quality polarizable force field by treating the intramolecular polarization on a block-by-block basis.

Accurate Reproduction of Quantum Mechanical Many-Body Interactions in Peptide Main-Chain Hydrogen-Bonding Oligomers by the Polarizable Gaussian Multipole Model

A key advantage of polarizable force fields is their ability to model the atomic polarization effects that play key roles in the atomic many-body interactions. In this work, we assessed the accuracy of the recently developed polarizable Gaussian Multipole (pGM) models in reproducing quantum mechanical (QM) interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, using glycine dipeptide oligomers as the model systems. Two types of pGM models were considered, including that with (pGM-perm) and without (pGM-ind) permanent atomic dipoles. The performances of the pGM models were compared with several widely used force fields, including two polarizable (Amoeba13 and ff12pol) and three additive (ff19SB, ff15ipq, and ff03) force fields. Encouragingly, the pGM models outperform all other force fields in terms of reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions, as measured by the root-mean-square errors (RMSEs) and mean absolute errors (MAEs). Furthermore, we tested the robustness of the pGM models against polarizability parameterization errors by employing alternative polarizabilities that are either scaled or obtained from other force fields. The results show that the pGM models with alternative polarizabilities exhibit improved accuracy in reproducing QM many-body interaction energies as well as the nonadditive and additive contributions compared with other polarizable force fields, suggesting that the pGM models are robust against the errors in polarizability parameterizations. This work shows that the pGM models are capable of accurately modeling polarization effects and have the potential to serve as templates for developing next-generation polarizable force fields for modeling various biological systems.

PyRESP: A Program for Electrostatic Parameterizations of Additive and Induced Dipole Polarizable Force Fields

Molecular modeling at the atomic level has been applied in a wide range of biological systems. The widely adopted additive force fields typically use fixed atom-centered partial charges to model electrostatic interactions. However, the additive force fields cannot accurately model polarization effects, leading to unrealistic simulations in polarization-sensitive processes. Numerous efforts have been invested in developing induced dipole-based polarizable force fields. Whether additive atomic charge models or polarizable induced dipole models are used, proper parameterization of the electrostatic term plays a key role in the force field developments. In this work, we present a Python program called PyRESP for performing atomic multipole parameterizations by reproducing ab initio electrostatic potential (ESP) around molecules. PyRESP provides parameterization schemes for several electrostatic models, including the RESP model with atomic charges for the additive force fields and the RESP-ind and RESP-perm models with additional induced and permanent dipole moments for the polarizable force fields. PyRESP is a flexible and user-friendly program that can accommodate various needs during force field parameterizations for molecular modeling of any organic molecules.

Stress tensor and constant pressure simulation for polarizable Gaussian multipole model

Our previous article has established the theory of molecular dynamics (MD) simulations for systems modeled with the polarizable Gaussian multipole (pGM) electrostatics [Wei et al., J. Chem. Phys. 153(11), 114116 (2020)]. Specifically, we proposed the covalent basis vector framework to define the permanent multipoles and derived closed-form energy and force expressions to facilitate an efficient implementation of pGM electrostatics. In this study, we move forward to derive the pGM internal stress tensor for constant pressure MD simulations with the pGM electrostatics. Three different formulations are presented for the flexible, rigid, and short-range screened systems, respectively. The analytical formulations were implemented in the SANDER program in the Amber package and were first validated with the finite-difference method for two different boxes of pGM water molecules. This is followed by a constant temperature and constant pressure MD simulation for a box of 512 pGM water molecules. Our results show that the simulation system stabilized at a physically reasonable state and maintained the balance with the externally applied pressure. In addition, several fundamental differences were observed between the pGM and classic point charge models in terms of the simulation behaviors, indicating more extensive parameterization is necessary to utilize the pGM electrostatics.

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

Atomic Polarizabilities for Interactive Dipole Induction Models

Thole-style mutual induction models for molecular polarization have been adopted by several popular polarizable force fields (FFs) for their simplicity and transferability. The atomic polarizability parameters of these models are typically derived by fitting to ab initio or/and experimental molecular polarizabilities. In this work, we improve upon Thole polarizability parameters by employing both high-level quantum mechanics molecular polarizabilities and electrostatic potential (ESP) responses on three-dimensional grids. Our results indicate that the two approaches to derive atomic polarizability parameters are both effective, while the ESP approaches can also capture the polarization for the atoms with lone pair electrons. The resulting polarizability parameters have been validated on a set of over 7200 molecules covering the most common elements found in organic molecules (C, H, O, N, P, S, F, Cl, Br, and I). These parameters have also been tested on the experimentally measured molecular polarizabilities of 422 molecules. The final set of parameters derived in this work show notable improvement over the current AMOEBA set. The result is a highly transferable, expanded set of atomic polarizabilities defined by the local chemical environment in the form of SMARTS patterns. These parameters can be used directly in molecular mechanics polarizable potential energy functions such as AMOEBA, AMOEBA+, and other Thole-style models.

Efficient formulation of polarizable Gaussian multipole electrostatics for biomolecular simulations

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

Estimating the Roles of Protonation and Electronic Polarization in Absolute Binding Affinity Simulations

Accurate prediction of binding free energies is critical to streamlining the drug development and protein design process. With the advent of GPU acceleration, absolute alchemical methods, which simulate the removal of ligand electrostatics and van der Waals interactions with the protein, have become routinely accessible and provide a physically rigorous approach that enables full consideration of flexibility and solvent interaction. However, standard explicit solvent simulations are unable to model protonation or electronic polarization changes upon ligand transfer from water to the protein interior, leading to inaccurate prediction of binding affinities for charged molecules. Here, we perform extensive simulation totaling ∼540 μs to benchmark the impact of modeling conditions on predictive accuracy for absolute alchemical simulations. Binding to urokinase plasminogen activator (UPA), a protein frequently overexpressed in metastatic tumors, is evaluated for a set of 10 inhibitors with extended flexibility, highly charged character, and titratable properties. We demonstrate that the alchemical simulations can be adapted to utilize the MBAR/PBSA method to improve the accuracy upon incorporating electronic polarization, highlighting the importance of polarization in alchemical simulations of binding affinities. Comparison of binding energy prediction at various protonation states indicates that proper electrostatic setup is also crucial in binding affinity prediction of charged systems, prompting us to propose an alternative binding mode with protonated ligand phenol and Hid-46 at the binding site, a testable hypothesis for future experimental validation.

Development of a Pantetheine Force Field Library for Molecular Modeling

Pantetheine is ubiquitous in nature in various forms of pantetheine-containing ligands (PCLs), including coenzyme A and phosphopantetheine. Lack of scalable force field libraries for PCLs has hampered the computational studies of biological macromolecules containing PCLs. We describe here the development of the first generation Pantetheine Force Field (PFF) library that is compatible with Amber force fields; parameterized using Gasteiger, AM1-BCC, or RESP charging methods combined with gaff2 and ff14SB parameter sets. In addition, a "plug-and-play" strategy was employed to enable the systematic charging of computationally expensive molecules sharing common substructural motifs. The validation studies performed on the PFF library showed promising performance where molecular dynamics (MD) simulations results were compared with experimental data of three representative systems. The PFF library represents the first force field library capable of modeling systems containing PCLs in silico and will aid in various applications including protein engineering and drug discovery.

Recent Force Field Strategies for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are widely distributed across eukaryotic cells, playing important roles in molecular recognition, molecular assembly, post-translational modification, and other biological processes. IDPs are also associated with many diseases such as cancers, cardiovascular diseases, and neurodegenerative diseases. Due to their structural flexibility, conventional experimental methods cannot reliably capture their heterogeneous structures. Molecular dynamics simulation becomes an important complementary tool to quantify IDP structures. This review covers recent force field strategies proposed for more accurate molecular dynamics simulations of IDPs. The strategies include adjusting dihedral parameters, adding grid-based energy correction map (CMAP) parameters, refining protein-water interactions, and others. Different force fields were found to perform well on specific observables of specific IDPs but also are limited in reproducing all available experimental observables consistently for all tested IDPs. We conclude the review with perspective areas for improvements for future force fields for IDPs.

Origin-Independent Decomposition of the Static Polarizability

Real-space analysis tools afford additive and transferable contributions of atoms to molecular properties. In the case of the molecular (hyper)polarizabilities, the atomic contributions that have been derived so far include a charge-transfer term that is origin-dependent. In this letter, we present the first genuinely origin-independent energy-based (OIEB) methodology for the decomposition of the static (hyper)polarizabilities that benefits from real-space molecular energy decomposition schemes, focusing on the static polarizability and showing that extension to static hyperpolarizabilities is straightforward. The numerical realization of the OIEB method shows the expected origin independence, atomic additivity, and transferability of atomic and functional group polarizability tensors. Furthermore, the OIEB atomic (fragment) polarizability tensors are symmetric by definition.

Relationship between Photoelasticity of Polyurethane and Dielectric Anisotropy of Diisocyanate, and Application of High-Photoelasticity Polyurethane to Tactile Sensor for Robot Hands

Eight types of polyurethane were synthesized using seven types of diisocyanate. It was found that the elasto-optical constant depends on the concentration of diisocyanate groups in a unit volume of a polymer and the magnitude of anisotropy of the dielectric constant of diisocyanate groups. It was also found that incident light scattered when bending stress was generated inside photoelastic polyurethanes. A high sensitive tactile sensor for robot hands was devised using one of the developed polyurethanes with high photoelasticity.

A fast and high-quality charge model for the next generation general AMBER force field

The General AMBER Force Field (GAFF) has been broadly used by researchers all over the world to perform in silico simulations and modelings on diverse scientific topics, especially in the field of computer-aided drug design whose primary task is to accurately predict the affinity and selectivity of receptor-ligand binding. The atomic partial charges in GAFF and the second generation of GAFF (GAFF2) were originally developed with the quantum mechanics derived restrained electrostatic potential charge, but in practice, users usually adopt an efficient charge method, Austin Model 1-bond charge corrections (AM1-BCC), based on which, without expensive ab initio calculations, the atomic charges could be efficiently and conveniently obtained with the ANTECHAMBER module implemented in the AMBER software package. In this work, we developed a new set of BCC parameters specifically for GAFF2 using 442 neutral organic solutes covering diverse functional groups in aqueous solution. Compared to the original BCC parameter set, the new parameter set significantly reduced the mean unsigned error (MUE) of hydration free energies from 1.03 kcal/mol to 0.37 kcal/mol. More excitingly, this new AM1-BCC model also showed excellent performance in the solvation free energy (SFE) calculation on diverse solutes in various organic solvents across a range of different dielectric constants. In this large-scale test with totally 895 neutral organic solvent-solute systems, the new parameter set led to accurate SFE predictions with the MUE and the root-mean-square-error of 0.51 kcal/mol and 0.65 kcal/mol, respectively. This newly developed charge model, ABCG2, paved a promising path for the next generation GAFF development.

Advances in Molecular Dynamics Simulations and Enhanced Sampling Methods for the Study of Protein Systems

Molecular dynamics (MD) simulation is a rigorous theoretical tool that when used efficiently could provide reliable answers to questions pertaining to the structure-function relationship of proteins. Data collated from protein dynamics can be translated into useful statistics that can be exploited to sieve thermodynamics and kinetics crucial for the elucidation of mechanisms responsible for the modulation of biological processes such as protein-ligand binding and protein-protein association. Continuous modernization of simulation tools enables accurate prediction and characterization of the aforementioned mechanisms and these qualities are highly beneficial for the expedition of drug development when effectively applied to structure-based drug design (SBDD). In this review, current all-atom MD simulation methods, with focus on enhanced sampling techniques, utilized to examine protein structure, dynamics, and functions are discussed. This review will pivot around computer calculations of protein-ligand and protein-protein systems with applications to SBDD. In addition, we will also be highlighting limitations faced by current simulation tools as well as the improvements that have been made to ameliorate their efficiency.

Data-Driven Mapping of Gas-Phase Quantum Calculations to General Force Field Lennard-Jones Parameters

Molecular dynamics simulations are helpful tools for a range of applications, ranging from drug discovery to protein structure determination. The successful use of this technology largely depends on the potential function, or force field, used to determine the potential energy at each configuration of the system. Most force fields encode all of the relevant parameters to be used in distinct atom types, each associated with parameters for all parts of the force field, typically bond stretches, angle bends, torsions, and nonbonded terms accounting for van der Waals and electrostatic interactions. Much attention has been paid to the nonbonded parameters and their derivation, which are important in particular due to their governance of noncovalent interactions, such as protein-ligand binding. Parametrization involves adjusting the nonbonded parameters to minimize the error between simulation results and experimental properties, such as heats of vaporization and densities of neat liquids. In this setting, determining the best set of atom types is far from trivial, and the large number of parameters to be fit for the atom types in a typical force field can make it difficult to approach a true optimum. Here, we utilize a previously described Minimal Basis Iterative Stockholder (MBIS) method to carry out an atoms-in-molecules partitioning of electron densities. Information from these atomic densities is then mapped to Lennard-Jones parameters using a set of mapping parameters much smaller than the typical number of atom types in a force field. This approach is advantageous in two ways: it eliminates atom types by allowing each atom to have unique Lennard-Jones parameters, and it greatly reduces the number of parameters to be optimized. We show that this approach yields results comparable to those obtained with the typed GAFF 1.7 force field, even when trained on a relatively small amount of experimental data.