Development of polarizable models for molecular mechanical calculations I: parameterization of atomic polarizability

Development of an anisotropic polarizable model for the all-atom AMOEBA force field

For planar and rigid π-conjugated molecular systems, electrostatic and inductive interactions are pivotal in governing molecular packing structures and electron polarization energies. These electrostatic interactions typically exhibit an anisotropic nature within π-conjugated systems. In this study, we utilize the atoms in molecules (AIM) theory in conjunction with linear response theory to decompose molecular polarizability into distributed atomic polarizability tensors. On the basis of atomic polarizability tensors, we extended an anisotropic polarizable model into the AMOEBA polarizable force field. Both anisotropic and isotropic polarizable models in combination with various density functional theory (DFT)-derived atomic multipoles were applied to optimize the experimental crystals of naphthalene and anthracene. Furthermore, these two types of electrostatic models, coupled with the evolutionary algorithm USPEX program, are utilized to predict the crystal structures of oligoacenes. Our findings demonstrate that the anisotropic polarizable model exhibits superior performance in crystal refinement and crystal structure prediction. This enriched anisotropic polarizable model is seamlessly integrated into the AMOEBA polarizable force field and readily applicable within our modified Tinker program.

The Open Force Field Initiative: Open Software and Open Science for Molecular Modeling

Force fields are a key component of physics-based molecular modeling, describing the energies and forces in a molecular system as a function of the positions of the atoms and molecules involved. Here, we provide a review and scientific status report on the work of the Open Force Field (OpenFF) Initiative, which focuses on the science, infrastructure and data required to build the next generation of biomolecular force fields. We introduce the OpenFF Initiative and the related OpenFF Consortium, describe its approach to force field development and software, and discuss accomplishments to date as well as future plans. OpenFF releases both software and data under open and permissive licensing agreements to enable rapid application, validation, extension, and modification of its force fields and software tools. We discuss lessons learned to date in this new approach to force field development. We also highlight ways that other force field researchers can get involved, as well as some recent successes of outside researchers taking advantage of OpenFF tools and data.

Raman Spectra of Amino Acids and Peptides from Machine Learning Polarizabilities

Raman spectroscopy is an important tool in the study of vibrational properties and composition of molecules, peptides, and even proteins. Raman spectra can be simulated based on the change of the electronic polarizability with vibrations, which can nowadays be efficiently obtained via machine learning models trained on first-principles data. However, the transferability of the models trained on small molecules to larger structures is unclear, and direct training on large structures is prohibitively expensive. In this work, we first train two machine learning models to predict the polarizabilities of all 20 amino acids. Both models are carefully benchmarked and compared to density functional theory (DFT) calculations, with the neural network method being found to offer better transferability. By combination of machine learning models with classical force field molecular dynamics, Raman spectra of all amino acids are also obtained and investigated, showing good agreement with experiments. The models are further extended to small peptides. We find that adding structures containing peptide bonds to the training set greatly improves predictions, even for peptides not included in training sets.

Tandem Catalysts Enabling Efficient C-N Coupling toward the Electrosynthesis of Urea

The development of a methodology for synthesizing value-added urea (CO(NH2)2) via a renewable electricity-driven C-N coupling reaction under mild conditions is highly anticipated. However, the complex catalytic active sites that act on the carbon and nitrogen species make the reaction mechanism unclear, resulting in a low efficiency of C-N coupling from the co-reduction of carbon dioxide (CO2) and nitrate (NO3 -). Herein, we propose a novel tandem catalyst of Mo-PCN-222(Co), in which the Mo sites serve to facilitate nitrate reduction to the *NH2 intermediate, while the Co sites enhance CO2 reduction to carbonic oxide (CO), thus synergistically promoting C-N coupling. The synthesized Mo-PCN-222(Co) catalyst exhibited a noteworthy urea yield rate of 844.11 mg h-1 g-1, alongside a corresponding Faradaic efficiency of 33.90 % at -0.4 V vs. reversible hydrogen electrode (RHE). By combining in situ spectroscopic techniques with density functional theory calculations, we demonstrate that efficient C-N coupling is attributed to a tandem system in which the *NH2 and *CO intermediates produced by the Mo and Co active sites of Mo-PCN-222(Co) stabilize the formation of the *CONH2 intermediate. This study provides an effective avenue for the design and synthesis of tandem catalysts for electrocatalytic urea synthesis.

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.

First-principles simulation of excitation energy transfer and transient absorption spectroscopy in the CP29 light-harvesting complex

The dynamics of delocalized excitons in light-harvesting complexes (LHCs) can be investigated using different experimental techniques, and transient absorption (TA) spectroscopy is one of the most valuable methods for this purpose. A careful interpretation of TA spectra is essential for the clarification of excitation energy transfer (EET) processes occurring during light-harvesting. However, even in the simplest LHCs, a physical model is needed to interpret transient spectra as the number of EET processes occurring at the same time is very large to be disentangled from measurements alone. Physical EET models are commonly built by fittings of the microscopic exciton Hamiltonians and exciton-vibrational parameters, an approach that can lead to biases. Here, we present a first-principles strategy to simulate EET and transient absorption spectra in LHCs, combining molecular dynamics and accurate multiscale quantum chemical calculations to obtain an independent estimate of the excitonic structure of the complex. The microscopic parameters thus obtained are then used in EET simulations to obtain the population dynamics and the related spectroscopic signature. We apply this approach to the CP29 minor antenna complex of plants for which we follow the EET dynamics and transient spectra after excitation in the chlorophyll b region. Our calculations reproduce all the main features observed in the transient absorption spectra and provide independent insight on the excited-state dynamics of CP29. The approach presented here lays the groundwork for the accurate simulation of EET and unbiased interpretation of transient spectra in multichromophoric systems.

Unraveling the role of thermal fluctuations on the exciton structure of the cryptophyte PC612 and PC645 photosynthetic antenna complexes

Protein scaffolds play a crucial role in tuning the light harvesting properties of photosynthetic pigment-protein complexes, influencing pigment-protein and pigment-pigment excitonic interactions. Here, we investigate the influence of thermal dynamic effects on the protein tuning mechanisms of phycocyanin PC645 and PC612 antenna complexes of cryptophyte algae, featuring closed or open quaternary structures. We employ a dual molecular dynamics (MD) strategy that combines extensive classical MD simulations with multiple short Born-Oppenheimer quantum/molecular mechanical (QM/MM) simulations to accurately account for both static and dynamic disorder effects. Additionally, we compare the results with an alternative protocol based on multiple QM/MM geometry optimizations of the pigments. Subsequently, we employ polarizable QM/MM calculations using time-dependent density functional theory (TD-DFT) to compute the excited states, and we adopt the full cumulant expansion (FCE) formalism to describe the absorption and circular dichroism spectra. Our findings indicate that thermal effects have only minor impacts on the energy ladder in PC612, despite its remarkable flexibility owing to an open quaternary structure. In striking contrast, thermal effects significantly influence the properties of PC645 due to the absence of a hydrogen bond controlling the twist of ring D in PCB β82 bilins, as well as the larger impact of fluctuations on the excited states of MBV pigments, which possess a higher conjugation length compared to other bilin types. Overall, the dual MD protocol combined with the FCE formalism yields excellent spectral properties for PC612 and PC645, and the resultant excitonic Hamiltonians pave the way for future investigations concerning the implications of open and closed quaternary structures on phycocyanin light harvesting properties.

Application of a Fluctuating Charge Polarization Model to Large Polyaromatic Hydrocarbons and Graphene Nanoflakes

We present a polarization model incorporating coupled fluctuating charges and point inducible dipoles that is able to accurately describe the dipole polarizabilities of small hydrocarbons and, for sufficiently large graphene nanoflakes, reproduce the classical image potential of an infinite conducting sheet. When our fluctuating charge model is applied to the hexagonal carbon nanoflake C60000 we attain excellent agreement with the image potential and induced charge distribution of a conducting sheet. With the inclusion of inducible dipole terms, the model predicts an image plane of zim = 1.3334 a0, which falls in line with prior estimates for graphene. We consider the case of two charges placed on opposite sides of C60000 and find that the fluctuating charge model reproduces classical electrostatics once again. By testing opposing and similar signs of the external charges, we conclude that an atomically thin molecule or extended system does not fully screen their interaction.

Quantum chemical elucidation of a sevenfold symmetric bacterial antenna complex

The light-harvesting complex 2 (LH2) of purple bacteria is one of the most studied photosynthetic antenna complexes. Its symmetric structure and ring-like bacteriochlorophyll arrangement make it an ideal system for theoreticians and spectroscopists. LH2 complexes from most bacterial species are thought to have eightfold or ninefold symmetry, but recently a sevenfold symmetric LH2 structure from the bacterium Mch. purpuratum was solved by Cryo-Electron microscopy. This LH2 also possesses unique near-infrared absorption and circular dichroism (CD) spectral properties. Here we use an atomistic strategy to elucidate the spectral properties of Mch. purpuratum LH2 and understand the differences with the most commonly studied LH2 from Rbl. acidophilus. Our strategy exploits a combination of molecular dynamics simulations, multiscale polarizable quantum mechanics/molecular mechanics calculations, and lineshape simulations. Our calculations reveal that the spectral properties of LH2 complexes are tuned by site energies and exciton couplings, which in turn depend on the structural fluctuations of the bacteriochlorophylls. Our strategy proves effective in reproducing the absorption and CD spectra of the two LH2 complexes, and in uncovering the origin of their differences. This work proves that it is possible to obtain insight into the spectral tuning strategies of purple bacteria by quantitatively simulating the spectral properties of their antenna complexes.

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Polarizabilities play significant roles in describing dispersive and inductive interactions of the atom and molecular systems. However, an accurate prediction of molecular polarizabilities from first principles is computationally prohibitive. Although physical models or statistical machine learning models have been proposed, either a lack of accurate description of local chemical environments or demanding a large number of samples for training has limited their practical applications. In this study, we combine a physically inspired dipole interaction model and an accurate neural network method for predicting the polarizability tensors of molecules. With the local chemical environment precisely described and the requirement of rotational covariance naturally fulfilled, this hybrid model is proven to give an accurate molecular polarizability prediction, essentially reducing the number of training samples. The atomic polarizabilities are physically interpretable and transferable to larger molecules unseen in the training set. This promising method may find its wide range of applications, such as spectroscopic simulations and the construction of polarizable force fields.

Molecular dynamics simulation studies of 1,3-dimethyl imidazolium nitrate ionic liquid with water

The fundamental understanding of intermolecular interactions of ionic liquids (ILs) with water is essential in predicting IL-water thermodynamic properties. In this study, intermolecular or noncovalent interactions were studied for 1,3-dimethyl imidazolium [DMIM]⁺ cation and nitrate [NO₃]^- anion with water, employing quantum mechanics and molecular dynamics simulations. Molecular dynamics simulations were performed using a revised multipolar polarizable force field. The effect of water on ionic liquids was evaluated in terms of thermodynamic and dynamic properties. Thermodynamic properties included liquid densities ρ, excess molar volumes ΔV^E, and liquid structures gr. Dynamic properties included self-diffusion coefficients D of mixture constituents as a function of water concentration. The density of ionic liquid-water mixtures monotonically decrease with increasing concentration of water. A negative excess volume was obtained for low and high water concentrations, demonstrating strong intermolecular interactions of water with ionic liquid components. Liquid structures of ionic liquid-water mixtures revealed a tendency for anions to interact with cations at shorter intermolecular distances when the water concentration is increased. Diffusion rates were found to increase for all mixture components with increase in the fraction of water. A significant change in the diffusion rate was found at ∼0.3 weight fraction of water. However, the water self-diffusion coefficient was dominant at all concentrations. The ratio of water/anion and anion/cation self-diffusion coefficients was found to decrease linearly with increasing concentration of water molecules.

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.

Machine Learning Exciton Hamiltonians in Light-Harvesting Complexes

We propose a machine learning (ML)-based strategy for an inexpensive calculation of excitonic properties of light-harvesting complexes (LHCs). The strategy uses classical molecular dynamics simulations of LHCs in their natural environment in combination with ML prediction of the excitonic Hamiltonian of the embedded aggregate of pigments. The proposed ML model can reproduce the effects of geometrical fluctuations together with those due to electrostatic and polarization interactions between the pigments and the protein. The training is performed on the chlorophylls of the major LHC of plants, but we demonstrate that the model is able to extrapolate well beyond the initial training set. Moreover, the accuracy in predicting the effects of the environment is tested on the simulation of the small changes observed in the absorption spectra of the wild-type and a mutant of a minor LHC.

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.

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.

A Unified Approach to Derive Atomic Partial Charges and Polarizabilities of Ionic Liquids

We propose a unified approach to fit simultaneously a set of atomic partial charges and polarizabilities of the polarizable model against the ab initio electrostatic potential (ESP) and polarizability. The polarizable model is represented with interactive atomic dipoles with distance-dependent attenuation. For the polarizable model employed in this study, the internal electric field on the polarization sites is fully turned on, and thus allows self-induced dipoles, which persist even for an isolated molecule/ion. By such treatment, the contribution of ESP stems not only from the partial charges but also from the self-induced dipoles, and the atomic partial charges and polarizabilities can be fitted simultaneously against ESP in a unified manner. The fitting with 1-ethyl-3-methylimidazolium (EMIM⁺) and nitrate (NO₃^-), a prototypical organic cation and inorganic anion, respectively, that can form ionic liquid, demonstrates that allowance of the self-induced dipoles gives much better fitness. Moreover, test on the total dipole of an EMIM⁺/NO₃^- ion pair shows that the agreement with the ab initio dipole is also much improved for the polarizable model, which highlights the importance of the polarization effects of ionic liquids.

A fast method for electronic couplings in embedded multichromophoric systems

Electronic couplings are key to understanding exciton delocalization and transport in natural and artificial light harvesting processes. We develop a method to compute couplings in multichromophoric aggregates embedded in complex environments without running expensive quantum chemical calculations. We use a transition charge approximation to represent the quantum mechanical transition densities of the chromophores and an atomistic and polarizable classical model to describe the environment atoms. We extend our framework to estimate transition charges directly from the chromophore geometry, i.e., bypassing completely the quantum mechanical calculations using a regression approach. The method allows to rapidly compute accurate couplings for a large number of geometries along molecular dynamics trajectories.

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.

Deep Neural Network Model to Predict the Electrostatic Parameters in the Polarizable Classical Drude Oscillator Force Field

The Drude polarizable force field (FF) captures electronic polarization effects via auxiliary Drude particles that are attached to non-hydrogen atoms, distinguishing it from commonly used additive FFs that rely on fixed charges. The Drude FF currently includes parameters for biomolecules such as proteins, nucleic acids, lipids, and carbohydrates and small-molecule representative of those classes of molecules as well as a range of atomic ions. Extension of the Drude FF to novel small druglike molecules is challenging as it requires the assignment of partial charges, atomic polarizabilities, and Thole scaling factors. In the present article, deep neural network (DNN) models are trained on quantum mechanical (QM)-based partial charges and atomic polarizabilities along with Thole scale factors trained to target QM molecular dipole moments and polarizabilities. Training of the DNN model used a collection of 39 421 molecules with molecular weights up to 200 Da and containing H, C, N, O, P, S, F, Cl, Br, or I atoms. The DNN model utilizes bond connectivity, including 1,2, 1,3, 1,4, and 1,5 terms and distances of Drude FF atom types as the feature vector to build the model, allowing it to capture both local and nonlocal effects in the molecules. Novel methods have been developed to determine restrained electrostatic potential (RESP) charges on atoms and external points representing lone pairs and to determine Thole scale factors, which have no QM analogue. A penalty scheme is devised as a performance predictor of the trained model. Validation studies show that these DNN models can precisely predict molecular dipole and polarizabilities of Food and Drug Administration (FDA)-approved drugs compared to reference MP2 calculations. The availability of the DNN model allowing for the rapid estimation of the Drude electrostatic parameters will facilitate its applicability to a wider range of molecular species.

Anti-glioblastoma effects of phenolic variants of benzoylphenoxyacetamide (BPA) with high potential for blood brain barrier penetration

Glioblastomas are the most aggressive brain tumors for which therapeutic options are limited. Current therapies against glioblastoma include surgical resection, followed by radiotherapy plus concomitant treatment and maintenance with temozolomide (TMZ), however, these standard therapies are often ineffective, and average survival time for glioblastoma patients is between 12 and 18 months. We have previously reported a strong anti-glioblastoma activity of several metabolic compounds, which were synthetized based compounds, which were synthetized based on the chemical structure of a common lipid-lowering drug, fenofibrate, and share a general molecular skeleton of benzoylphenoxyacetamide (BPA). Extensive computational analyses of phenol and naphthol moieties added to the BPA skeleton were performed in this study with the objective of selecting new BPA variants for subsequent compound preparation and anti-glioblastoma testing. Initially, 81 structural variations were considered and their physical properties such as solubility (logS), blood–brain partitioning (logBB), and probability of entering the CNS calculated by the Central Nervous System—Multiparameter Optimization (MPO-CNS) algorithm were evaluated. From this initial list, 18 compounds were further evaluated for anti-glioblastoma activity in vitro. Nine compounds demonstrated desirable glioblastoma cell toxicity in cell culture, and two of them, HR51, and HR59 demonstrated significantly improved capability of crossing the model blood–brain-barrier (BBB) composed of endothelial cells, astrocytes and pericytes.

Structure of the stress-related LHCSR1 complex determined by an integrated computational strategy

Light-harvesting complexes (LHCs) are pigment-protein complexes whose main function is to capture sunlight and transfer the energy to reaction centers of photosystems. In response to varying light conditions, LH complexes also play photoregulation and photoprotection roles. In algae and mosses, a sub-family of LHCs, light-harvesting complex stress-related (LHCSR), is responsible for photoprotective quenching. Despite their functional and evolutionary importance, no direct structural information on LHCSRs is available that can explain their unique properties. In this work, we propose a structural model of LHCSR1 from the moss P. patens, obtained through an integrated computational strategy that combines homology modeling, molecular dynamics, and multiscale quantum chemical calculations. The model is validated by reproducing the spectral properties of LHCSR1. Our model reveals the structural specificity of LHCSR1, as compared with the CP29 LH complex, and poses the basis for understanding photoprotective quenching in mosses.

The structure of the moss P. patens light-harvesting complex stress-related 1 (LHCSR1) is determined using a multi-scale computational approach for investigations of its photoprotective function.

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.

Validation of Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) approaches as alternatives to skin sensitization risk assessment

The aim of this study was conducted to validate the physicochemical properties of a total of 362 chemicals [305 skin sensitizers (212 in the previous study + 93 additional new chemicals), 57 non-skin sensitizers (38 in the previous study + 19 additional new chemicals)] for skin sensitization risk assessment using quantitative structure-activity relationship (QSAR)/quantitative structure-property relationship (QSPR) approaches. The average melting point (MP), surface tension (ST), and density (DS) of the 305 skin sensitizers and 57 non-sensitizers were used to determine the cutoff values distinguishing positive and negative sensitization, and correlation coefficients were employed to derive effective 3-fold concentration (EC3 (%)) values. QSAR models were also utilized to assess skin sensitization. The sensitivity, specificity, and accuracy were 80, 15, and 70%, respectively, for the Toxtree QSAR model; 88, 46, and 81%, respectively, for Vega; and 56, 61, and 56%, respectively, for Danish EPA QSAR. Surprisingly, the sensitivity, specificity, and accuracy were 60, 80, and 64%, respectively, when MP, ST, and DS (MP+ST+DS) were used in this study. Further, MP+ST+DS exhibited a sensitivity of 77%, specificity 57%, and accuracy 73% when the derived EC3 values were classified into local lymph node assay (LLNA) skin sensitizer and non-sensitizer categories. Thus, MP, ST, and DS may prove useful in predicting EC3 values as not only an alternative approach to animal testing but also for skin sensitization risk assessment.

From crystallographic data to the solution structure of photoreceptors: the case of the AppA BLUF domain

Photoreceptor proteins bind a chromophore, which, upon light absorption, modifies its geometry or its interactions with the protein, finally inducing the structural change needed to switch the protein from an inactive to an active or signaling state. In the Blue Light-Using Flavin (BLUF) family of photoreceptors, the chromophore is a flavin and the changes have been connected with a rearrangement of the hydrogen bond network around it on the basis of spectroscopic changes measured for the dark-to-light conversion. However, the exact conformational change triggered by the photoexcitation is still elusive mainly because a clear consensus on the identity not only of the light activated state but also of the dark one has not been achieved. Here, we present an integrated investigation that combines microsecond MD simulations starting from the two conflicting crystal structures available for the AppA BLUF domain with calculations of NMR, IR and UV-Vis spectra using a polarizable QM/MM approach. Thanks to such a combined analysis of the three different spectroscopic responses, a robust characterization of the structure of the dark state in solution is given together with the uncovering of important flaws of the most popular molecular mechanisms present in the literature for the dark-to-light activation.

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.

Computational Investigation of Structural and Spectroscopic Properties of LOV-Based Proteins with Improved Fluorescence

Flavin-based fluorescent proteins are a class of fluorescent reporters derived from light, oxygen, and voltage (LOV) sensing proteins. Through mutagenesis, natural LOV proteins have been engineered to obtain improved fluorescence properties. In this study, we combined extended classical Molecular Dynamics simulations and multiscale Quantum Mechanics/Molecular Mechanics methods to clarify the relationship between structural and dynamic changes induced by specific mutations and the spectroscopic response. To reach this goal we compared two LOV variants, one obtained by the single mutation needed to photochemically inactivate the natural system, and the other (iLOV) obtained through additional mutations and characterized by a significantly improved fluorescence. Our simulations confirmed the "flipping and crowding" effect induced in iLOV by the additional mutations and revealed its mechanism of action. We also showed that these mutations, and the resulting differences in the composition and flexibility of the binding pockets, are not reflected in significant shifts of the excitation and emission energies, in agreement with the similarity of the spectra measured for the two systems. However, a small but consistent reduction was found in the Stokes shift of iLOV, suggesting a reduction of the intermolecular reorganization experienced by the chromophore after excitation, which could slow down its internal conversion to the ground state and improve the fluorescence.

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.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

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).

Identification of Novel Chemical Entities for Adenosine Receptor Type 2A Using Molecular Modeling Approaches

Adenosine Receptor Type 2A (A_2AAR) plays a role in important processes, such as anti-inflammatory ones. In this way, the present work aimed to search for compounds by pharmacophore-based virtual screening. The pharmacokinetic/toxicological profiles of the compounds, as well as a robust QSAR, predicted the binding modes via molecular docking. Finally, we used molecular dynamics to investigate the stability of interactions from ligand-A_2AAR. For the search for A_2AAR agonists, the UK-432097 and a set of 20 compounds available in the BindingDB database were studied. These compounds were used to generate pharmacophore models. Molecular properties were used for construction of the QSAR model by multiple linear regression for the prediction of biological activity. The best pharmacophore model was used by searching for commercial compounds in databases and the resulting compounds from the pharmacophore-based virtual screening were applied to the QSAR. Two compounds had promising activity due to their satisfactory pharmacokinetic/toxicological profiles and predictions via QSAR (Diverset 10002403 pEC₅₀ = 7.54407; ZINC04257548 pEC₅₀ = 7.38310). Moreover, they had satisfactory docking and molecular dynamics results compared to those obtained for Regadenoson (Lexiscan^®), used as the positive control. These compounds can be used in biological assays (in vitro and in vivo) in order to confirm the potential activity agonist to A_2AAR.

Cost-Effective Potential for Accurate Polarizable Embedding Calculations in Protein Environments

The fragment-based polarizable embedding (PE) model combined with an appropriate electronic structure method constitutes a highly efficient and accurate multiscale approach for computing spectroscopic properties of a central moiety including effects from its molecular environment through an embedding potential. There is, however, a comparatively high computational overhead associated with the computation of the embedding potential, which is derived from first-principles calculations on individual fragments of the environment. To reduce the computational cost associated with the calculation of embedding potential parameters, we developed a set of amino acid-specific transferable parameters tailored for large-scale PE-based calculations that include proteins. The amino acid-based parameters are obtained by simultaneously fitting to a set of reference electric potentials based on structures derived from a backbone-dependent rotamer library. The developed cost-effective polarizable protein potential (CP³) consists of atom-centered charges and isotropic dipole-dipole polarizabilities of the standard amino acids. In terms of reproduction of electric potentials, the CP³ is shown to perform consistently and with acceptable accuracy across both small tripeptide test systems and larger proteins. We show, through applications on realistic protein systems, that acceptable accuracy can be obtained by using a pure CP³ representation of the protein environment, thus altogether omitting the cost associated with the calculation of embedding potential parameters. High accuracy comparable to that of the full fragment-based approach can be achieved through a mixed description where the CP³ is used only to describe amino acids beyond a threshold distance from the central quantum part.

Exploring anticancer activity of structurally modified benzylphenoxyacetamide (BPA); I: Synthesis strategies and computational analyses of substituted BPA variants with high anti-glioblastoma potential

Structural variations of the benzylphenoxyacetamide (BPA) molecular skeleton were explored as a viable starting point for designing new anti-glioblastoma drug candidates. Hand-to-hand computational evaluation, chemical modifications, and cell viability testing were performed to explore the importance of some of the structural properties in order to generate, retain, and improve desired anti-glioblastoma characteristics. It was demonstrated that several structural features are required to retain the anti-glioblastoma activity, including a carbonyl group of the benzophenone moiety, as well as 4′-chloro and 2,2-dimethy substituents. In addition, the structure of the amide moiety can be modified in such a way that desirable anti-glioblastoma and physical properties can be improved. Via these structural modifications, more than 50 compounds were prepared and tested for anti-glioblastoma activity. Four compounds were identified (HR28, HR32, HR37, and HR46) that in addition to HR40 (PP1) from our previous study, have been determined to have desirable physical and biological properties. These include high glioblastoma cytotoxicity at low μM concentrations, improved water solubility, and the ability to penetrate the blood brain barrier (BBB), which indicate a potential for becoming a new class of anti-glioblastoma drugs.

The molecular mechanisms of light adaption in light-harvesting complexes of purple bacteria revealed by a multiscale modeling

The light-harvesting in photosynthetic purple bacteria can be tuned in response to the light conditions during cell growth. One of the used strategies is to change the energy of the excitons in the major fight-harvesting complex, commonly known as LH2. In the present study we report the first systematic investigation of the microscopic origin of the exciton tuning using three complexes, namely the common (high-light) and the low-light forms of LH2 from Rps. acidophila plus a third complex analogous to the PucD complex from Rps. palustris. The study is based on the combination of classical molecular dynamics of each complex in a lipid membrane and excitonic calculations based on a multiscale quantum mechanics/molecular mechanics approach including a polarizable embedding. From the comparative analysis, it comes out that the mechanisms that govern the adaptation of the complex to different light conditions use the different H-bonding environment around the bacteriochlorophyll pigments to dynamically control both internal and inter-pigment degrees of freedom. While the former have a large effect on the site energies, the latter significantly change the electronic couplings, but only the combination of the two effects can fully reproduce the tuning of the final excitons and explain the observed spectroscopic differences.

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.

Coupled Cluster Theory with Induced Dipole Polarizable Embedding for Ground and Excited States

In this work, we present the theory and implementation of the coupled cluster single and double excitations (CCSD) method combined with a classical polarizable molecular mechanics force field (MMPol) based on the induced dipole model. The method is developed to compute electronic excitation energies within the state specific (SS) and linear response (LR) formalisms for the interaction of the quantum mechanical and classical regions. Furthermore, we consider an approximate expression of the correlation energy, originally developed for CCSD with implicit solvation models, where the interaction term is linear in the coupled cluster density. This approximation allows us to include the explicit contribution of the environment to the CC equations without increasing the computational effort. The test calculations on microsolvated systems, where the CCSD/MMPol method is compared to full CCSD calculations, demonstrates the reliability of this computational protocol for all interaction schemes (errors < 2%). We also show that it is important to include induced dipoles on all atom centers of the classical region and that too diffuse functions in the basis set may be problematic due to too strong interaction with the environment.

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.

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

A set of atomic polarizability parameters for a new polarizable Gaussian model (pGM) has been developed with the goal to accurately reproduce the polarizability anisotropy, taking advantage of its ability to attenuate all short-range electrostatic interactions, by fitting the ab initio molecular polarizability tensors ( A _pq) calculated at the B3LYP/aug-cc-pVTZ level. For comparison, we also rederived the parameters for three Thole models in which the 1-2 (bonded), 1-3 (separated by two bonds), and 1-4 (separated by three bonds) interactions are fully included. The average percent errors (APEs) of molecular polarizability tensors for 4842 molecules or dimers are 2.98, 3.76, 3.28, and 3.82% for the pGM, Thole linear, Thole exponential, and Thole Amoeba models, respectively, with atom-type independent, universal screening factors (USF). The APEs are reduced further to 2.30, 2.69, 2.25, and 2.48% for the four corresponding polarizable models with atom-type dependent, variable screening factors (VSF). It is encouraging that the pGM with variable screening factors achieved APEs of 1.83 for 1155 amino acid analogs, dipeptides, and tetrapeptides, 1.39 for 28 nucleic acid bases, 0.708 for 1464 water clusters, and 1.99 for 85 dimers of water and biological building blocks. Compared to the new set of models, the APEs of the old Thole models that were fitted to isotropic molecular polarizabilities are 8.7% for set A (without the 1-2 and 1-3 interactions) and 6.3% for set D (with the 1-2 and 1-3 interactions) models, respectively. MPAD, a metric of molecular polarization anisotropy difference based on the diagonal terms of molecular polarizability tensors was defined and applied to assess the polarizable models in reproducing the ab initio molecular polarization anisotropy. The MPADs are 3.71, 4.70, 4.11, and 4.77% for the pGM, Thole linear, Thole exponential, and Thole Amoeba USF models, respectively. The APEs are reduced further to 2.85, 3.58, 2.90, and 3.15% for the four corresponding VSF models. Thus, the new pGM and Thole models notably improve molecular polarization anisotropy. Since pGM attenuates all short-range electrostatic interactions, its application is expected to improve stability in charge fitting, energy, and force calculations and the accuracy of multibody polarization.

Decomposition of molecular properties

We review recent work on property decomposition techniques using quantum chemical methods and discuss some topical applications in terms of quantum mechanics-molecular mechanics calculations and the constructing of properties of large molecules and clusters. Starting out from the so-called LoProp decomposition scheme [Gagliardi et al., J. Chem. Phys., 2004, 121, 4994] for extracting atomic and inter-atomic contributions to molecular properties we show how this method can be generalized to localized frequency-dependent polarizabilities, to localized hyperpolarizabilities and to localized dispersion coefficients. Some applications of the generalized decomposition technique are reviewed - calculations of frequency-dependent polarizabilities, Rayleigh scattering of large clusters, and calculations of hyperpolarizabilities of proteins.