Polarizable force fields for molecular dynamics simulations of biomolecules

Methods for Theoretical Treatment of Local Fields in Proteins and Enzymes

Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

Simulating Ionized States in Realistic Chemical Environments with Algebraic Diagrammatic Construction Theory and Polarizable Embedding

Theoretical simulations of electron detachment processes are vital for understanding chemical redox reactions, semiconductor and electrochemical properties, and high-energy radiation damage. However, accurate calculations of ionized electronic states are very challenging due to their open-shell nature, importance of electron correlation effects, and strong interactions with chemical environment. In this work, we present an efficient approach based on algebraic diagrammatic construction theory with polarizable embedding that allows to accurately simulate ionized electronic states in condensed-phase or biochemical environments (PE-IP-ADC). We showcase the capabilities of PE-IP-ADC by computing the vertical ionization energy (VIE) of thymine molecule solvated in bulk water. Our results show that the second- and third-order PE-IP-ADC methods combined with the basis of set of triple-ζ quality yield a solvent-induced shift in VIE of -0.92 and -0.93 eV, respectively, in an excellent agreement with experimental estimate of -0.9 eV. This work demonstrates the power of PE-IP-ADC approach for simulating charged electronic states in realistic chemical environments and motivates its further development.

Grand canonical Monte Carlo and deep learning assisted enhanced sampling to characterize the distribution of Mg2+ and influence of the Drude polarizable force field on the stability of folded states of the twister ribozyme

Molecular dynamics simulations are crucial for understanding the structural and dynamical behavior of biomolecular systems, including the impact of their environment. However, there is a gap between the time scale of these simulations and that of real-world experiments. To address this problem, various enhanced simulation methods have been developed. In addition, there has been a significant advancement of the force fields used for simulations associated with the explicit treatment of electronic polarizability. In this study, we apply oscillating chemical potential grand canonical Monte Carlo and machine learning methods to determine reaction coordinates combined with metadynamics simulations to explore the role of Mg2+ distribution and electronic polarizability in the context of the classical Drude oscillator polarizable force field on the stability of the twister ribozyme. The introduction of electronic polarizability along with the details of the distribution of Mg2+ significantly stabilizes the simulations with respect to sampling the crystallographic conformation. The introduction of electronic polarizability leads to increased stability over that obtained with the additive CHARMM36 FF reported in a previous study, allowing for a distribution of a wider range of ions to stabilize twister. Specific interactions contributing to stabilization are identified, including both those observed in the crystal structures and additional experimentally unobserved interactions. Interactions of Mg2+ with the bases are indicated to make important contributions to stabilization. Notably, the presence of specific interactions between the Mg2+ ions and bases or the non-bridging phosphate oxygens (NBPOs) leads to enhanced dipole moments of all three moieties. Mg2+-NBPO interactions led to enhanced dipoles of the phosphates but, interestingly, not in all the participating ions. The present results further indicate the importance of electronic polarizability in stabilizing RNA in molecular simulations and the complicated nature of the relationship of Mg2+-RNA interactions with the polarization response of the bases and phosphates.

Evaluating Polarizable Biomembrane Simulations against Experiments

Owing to the increase of available computational capabilities and the potential for providing a more accurate description, polarizable molecular dynamics force fields are gaining popularity in modeling biomolecular systems. It is, however, crucial to evaluate how much precision is truly gained with increasing cost and complexity of the simulation. Here, we leverage the NMRlipids open collaboration and Databank to assess the performance of available polarizable lipid models─the CHARMM-Drude and the AMOEBA-based parameters─against high-fidelity experimental data and compare them to the top-performing nonpolarizable models. While some improvement in the description of ion binding to membranes is observed in the most recent CHARMM-Drude parameters, and the conformational dynamics of AMOEBA-based parameters are excellent, the best nonpolarizable models tend to outperform their polarizable counterparts for each property we explored. The identified shortcomings range from inaccuracies in describing the conformational space of lipids to excessively slow conformational dynamics. Our results provide valuable insights for the further refinement of polarizable lipid force fields and for selecting the best simulation parameters for specific applications.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

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

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

Deciphering the Lexicon of Protein Targets: A Review on Multifaceted Drug Discovery in the Era of Artificial Intelligence

Understanding protein sequence and structure is essential for understanding protein-protein interactions (PPIs), which are essential for many biological processes and diseases. Targeting protein binding hot spots, which regulate signaling and growth, with rational drug design is promising. Rational drug design uses structural data and computational tools to study protein binding sites and protein interfaces to design inhibitors that can change these interactions, thereby potentially leading to therapeutic approaches. Artificial intelligence (AI), such as machine learning (ML) and deep learning (DL), has advanced drug discovery and design by providing computational resources and methods. Quantum chemistry is essential for drug reactivity, toxicology, drug screening, and quantitative structure-activity relationship (QSAR) properties. This review discusses the methodologies and challenges of identifying and characterizing hot spots and binding sites. It also explores the strategies and applications of artificial-intelligence-based rational drug design technologies that target proteins and protein-protein interaction (PPI) binding hot spots. It provides valuable insights for drug design with therapeutic implications. We have also demonstrated the pathological conditions of heat shock protein 27 (HSP27) and matrix metallopoproteinases (MMP2 and MMP9) and designed inhibitors of these proteins using the drug discovery paradigm in a case study on the discovery of drug molecules for cancer treatment. Additionally, the implications of benzothiazole derivatives for anticancer drug design and discovery are deliberated.

Solvation of Model Biomolecules in Choline-Aminoate Ionic Liquids: A Computational Simulation Using Polarizable Force Fields

One can foresee a very near future where ionic liquids will be used in applications such as biomolecular chemistry or medicine. The molecular details of their interaction with biological matter, however, are difficult to investigate due to the vast number of combinations of both the biological systems and the variety of possible liquids. Here, we provide a computational study aimed at understanding the interaction of a special class of biocompatible ionic liquids (choline-aminoate) with two model biological systems: an oligopeptide and an oligonucleotide. We employed molecular dynamics with a polarizable force field. Our results are in line with previous experimental and computational evidence on analogous systems and show how these biocompatible ionic liquids, in their pure form, act as gentle solvents for protein structures while simultaneously destabilizing DNA structure.

Structural Insights and Influence of Terahertz Waves in Midinfrared Region on Kv1.2 Channel Selectivity Filter

Potassium ion channels are the structural basis for excitation transmission, heartbeat, and other biological processes. The selectivity filter is a critical structural component of potassium ion channels, whose structure is crucial to realizing their function. As biomolecules vibrate and rotate at frequencies in the terahertz band, potassium ion channels are sensitive to terahertz waves. Therefore, it is worthwhile to investigate how the terahertz wave influences the selectivity filter of the potassium channels. In this study, we investigate the structure of the selectivity filter of Kv1.2 potassium ion channels using molecular dynamics simulations. The effect of an electric field on the channel has been examined at four different resonant frequencies of the carbonyl group in SF: 36.75 37.06, 37.68, and 38.2 THz. As indicated by the results, 376GLY appears to be the critical residue in the selectivity filter of the Kv1.2 channel. Its dihedral angle torsion is detrimental to the channel structural stability and the transmembrane movement of potassium ions. 36.75 THz is the resonance frequency of the carbonyl group of 376GLY. Among all four frequencies explored, the applied terahertz electric field of this frequency has the most significant impact on the channel structure, negatively impacting the channel stability and reducing the ion permeability by 20.2% compared to the absence of fields. In this study, we simulate that terahertz waves in the mid-infrared frequency region can significantly alter the structure and function of potassium ion channels and that the effects of terahertz waves differ greatly based on frequency.

Thermodynamics of Metal-Acetate Interactions

Metal ions play crucial roles in protein- and ligand-mediated interactions. They not only act as catalysts to facilitate biological processes but are also important as protein structural elements. Accurately predicting metal ion interactions in computational studies has always been a challenge, and various methods have been suggested to improve these interactions. One such method is the 12-6-4 Lennard-Jones (LJ)-type nonbonded model. Using this model, it has been possible to successfully reproduce the experimental properties of metal ions in aqueous solution. The model includes induced dipole interactions typically ignored in the standard 12-6 LJ nonbonded model. In this we expand the applicability of this model to metal ion-carboxylate interactions. Using 12-6-4 parameters that reproduce the solvation free energies of the metal ions leads to an overestimation of metal ion-acetate interactions, thus, prompting us to fine-tune the model to specifically handle the latter. We also show that the standard 12-6 LJ model significantly falls short in reproducing the experimental binding free energy between acetate and 11 metal ions (Ni(II), Mg(II), Cu(II), Zn(II), Co(II), Cu(I), Fe(II), Mn(II), Cd(II), Ca(II), and Ag(I)). In this study, we describe optimized C4 parameters for the 12-6-4 LJ nonbonded model to be used with three widely employed water models (Transferable Intermolecular Potential with 3 Points (TIP3P), Simple Point Charge Extended (SPC/E), and Optimal Point Charge (OPC) water models). These parameters can accurately match the experimental binding free energy between 11 metal ions and acetate. These parameters can be applied to the study of metalloproteins and transition metal ion channels and transporters, as acetate serves as a representative of the negatively charged amino acid side chains from aspartate and glutamate.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Modeling Substrate Entry into the P-Glycoprotein Efflux Pump at the Blood-Brain Barrier

We report molecular dynamics simulations of rhodamine entry into the central binding cavity of P-gp in the inward open conformation. Rhodamine can enter the inner volume via passive transport across the luminal membrane or lateral diffusion in the lipid bilayer. Entry into the inner volume is determined by the aperture angle at the apex of the protein, with a critical angle of 27° for rhodamine. The central binding cavity has an aqueous phase with a few lipids, which significantly reduces substrate diffusion. Within the central binding cavity, we identified regions with relatively weak binding, suggesting that the combination of reduced mobility and weak substrate binding confines rhodamine to enable the completion of the efflux cycle. Tariquidar, a P-gp inhibitor, aggregates at the lower arms of the P-gp, suggesting that inhibition involves steric hindrance of entry into the inner volume and/or steric hindrance of access of ATP to the nucleotide-binding domains.

Perspectives on Ligand/Protein Binding Kinetics Simulations: Force Fields, Machine Learning, Sampling, and User-Friendliness

Computational techniques applied to drug discovery have gained considerable popularity for their ability to filter potentially active drugs from inactive ones, reducing the time scale and costs of preclinical investigations. The main focus of these studies has historically been the search for compounds endowed with high affinity for a specific molecular target to ensure the formation of stable and long-lasting complexes. Recent evidence has also correlated the in vivo drug efficacy with its binding kinetics, thus opening new fascinating scenarios for ligand/protein binding kinetic simulations in drug discovery. The present article examines the state of the art in the field, providing a brief summary of the most popular and advanced ligand/protein binding kinetics techniques and evaluating their current limitations and the potential solutions to reach more accurate kinetic models. Particular emphasis is put on the need for a paradigm change in the present methodologies toward ligand and protein parametrization, the force field problem, characterization of the transition states, the sampling issue, and algorithms' performance, user-friendliness, and data openness.

Toward a general neural network force field for protein simulations: Refining the intramolecular interaction in protein

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein-water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level.

Accurate Host-Guest Binding Free Energies Using the AMOEBA Polarizable Force Field

A grand challenge of computational biophysics is accurate prediction of interactions between molecules. Molecular dynamics (MD) simulations have recently gained much interest as a tool to directly compute rigorous intermolecular binding affinities. The choice of a fixed point-charge or polarizable multipole force field used in MD is a topic of ongoing discussion. To compare alternative methods, we participated in the SAMPL7 and SAMPL8 Gibb octaacid host-guest challenges to assess the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) polarizable multipole force field. Advantages of AMOEBA over fixed charge models include improved representation of molecular electrostatic potentials and better description of water occupying the unligated host cavity. Prospective predictions for 26 host-guest systems exhibit a mean unsigned error vs experiment of 0.848 kcal/mol across all absolute binding free energies, demonstrating excellent agreement between computational and experimental results. In addition, we explore two topics related to the inclusion of ions in MD simulations: use of a neutral co-alchemical protocol and the effect of salt concentration on binding affinity. Use of the co-alchemical method minimally affects computed energies, but salt concentration significantly perturbs our binding results. Higher salt concentration strengthens binding through classical charge screening. In particular, added Na+ ions screen negatively charged carboxylate groups near the binding cavity, thereby diminishing repulsive coulomb interactions with negatively charged guests. Overall, the AMOEBA results demonstrate the accuracy available through a force field providing a detailed energetic description of the four octaacid hosts and 13 charged organic guests. Use of the AMOEBA polarizable atomic multipole force field in conjunction with an alchemical free energy protocol can achieve chemical accuracy in application to realistic molecular systems.

Many-Body Effects in Aqueous Systems: Synergies Between Interaction Analysis Techniques and Force Field Development

Interaction analysis techniques, including the many-body expansion (MBE), symmetry-adapted perturbation theory, and energy decomposition analysis, allow for an intuitive understanding of complex molecular interactions. We review these methods by first providing a historical context for the study of many-body interactions and discussing how nonadditivities emerge from Hamiltonians containing strictly pairwise-additive interactions. We then elaborate on the synergy between these interaction analysis techniques and the development of advanced force fields aimed at accurately reproducing the Born-Oppenheimer potential energy surface. In particular, we focus on ab initio-based force fields that aim to explicitly reproduce many-body terms and are fitted to high-level electronic structure results. These force fields generally incorporate many-body effects through (a) parameterization of distributed multipoles, (b) explicit fitting of the MBE, (c) inclusion of many-atom features in a neural network, and (d) coarse-graining of many-body terms into an effective two-body term. We also discuss the emerging use of the MBE to improve the accuracy and speed of ab initio molecular dynamics.

Effects of temperature and microwave on the stability of the blast effector complex APikL2A/sHMA25 as determined by molecular dynamics analyses

Magnaporthe oryzae is the causal agent of rice blast, and understanding how abiotic stress affects the resistance of plants to this disease is useful for designing disease control strategies. In this paper, the effects of temperature and microwave irradiation on the effector complex comprising APikL2A from M. oryzae and sHMA25 from foxtail millet were investigated by molecular dynamics simulations using the GROMACS software package. While the structure of APikL2A/sHMA25 remained relatively stable in a temperature range of 290 K (16.85 °C) to 320 K (46.85 °C), the concave shape of the temperature-dependent binding free energy curve indicated that there was maximum binding affinity between APikL2A and sHMA25 at 300 K-310 K. This coincided with the optimum infectivity temperature, thus suggesting that coupling of the two polypeptides may play a role in the infection process. A strong oscillating electric field destroyed the structure of APikL2A/sHMA25, although it was stable and not susceptible to weak electric fields.

Benchmarking In Silico Tools for Cysteine pKa Prediction

Accurate estimation of the pK_a's of cysteine residues in proteins could inform targeted approaches in hit discovery. The pK_a of a targetable cysteine residue in a disease-related protein is an important physiochemical parameter in covalent drug discovery, as it influences the fraction of nucleophilic thiolate amenable to chemical protein modification. Traditional structure-based in silico tools are limited in their predictive accuracy of cysteine pK_a's relative to other titratable residues. Additionally, there are limited comprehensive benchmark assessments for cysteine pK_a predictive tools. This raises the need for extensive assessment and evaluation of methods for cysteine pK_a prediction. Here, we report the performance of several computational pK_a methods, including single-structure and ensemble-based approaches, on a diverse test set of experimental cysteine pK_a's retrieved from the PKAD database. The dataset consisted of 16 wildtype and 10 mutant proteins with experimentally measured cysteine pK_a values. Our results highlight that these methods are varied in their overall predictive accuracies. Among the test set of wildtype proteins evaluated, the best method (MOE) yielded a mean absolute error of 2.3 pK units, highlighting the need for improvement of existing pK_a methods for accurate cysteine pK_a estimation. Given the limited accuracy of these methods, further development is needed before these approaches can be routinely employed to drive design decisions in early drug discovery efforts.

A building-block database of distributed polarizabilities and dipole moments to estimate optical properties of biomacromolecules in isolation or in an explicitly solvated medium

Since atomic or functional-group properties in the bulk are generally not available from experimental methods, computational approaches based on partitioning schemes have emerged as a rapid yet accurate pathway to estimate the materials behavior from chemically meaningful building blocks. Among several applications, a comprehensive and systematically built database of atomic or group polarizabilities and related opto-electronic quantities would be very useful not only to envisage linear or non-linear optical properties of biomacromolecules but also to improve the accuracy of classical force fields devoted to simulate biochemical processes. In this work, we propose the first entries of such database that contains distributed polarizabilities and dipole moments extracted from fragments of peptides. Twenty three prototypical conformers of the dipeptides alanine-alanine and glycine-glycine were used to extract functional groups such as CH₂ , CHCH₃ , NH₂ , COOH, CONH, thus allowing construction of a diversity of chemically relevant environments. To evaluate the accuracy of our database, reconstructed properties of larger peptides containing up to six residues of alanine and glycine were tested against density functional theory calculations at the M06-HF/aug-cc-pVDZ level of theory. The procedure is particularly accurate for the diagonal components of the polarizability tensor with errors up to 15%. In order to include solvent effects explicitly, the peptides were also surrounded by a box of water molecules whose distribution was optimized using the CHARMM force field. Solvent effects introduced by a classical dipole-dipole interaction model were compared to those obtained from polarizable-continuum model calculations.

Gaussian Process Regression Models for Predicting Atomic Energies and Multipole Moments

Developing a force field is a difficult task because its design is typically pulled in opposite directions by speed and accuracy. FFLUX breaks this trend by utilizing Gaussian process regression (GPR) to predict, at ab initio accuracy, atomic energies and multipole moments as obtained from the quantum theory of atoms in molecules (QTAIM). This work demonstrates that the in-house FFLUX training pipeline can generate successful GPR models for six representative molecules: peptide-capped glycine and alanine, glucose, paracetamol, aspirin, and ibuprofen. The molecules were sufficiently distorted to represent configurations from an AMBER-GAFF2 molecular dynamics run. All internal degrees of freedom were covered corresponding to 93 dimensions in the case of the largest molecule ibuprofen (33 atoms). Benefiting from active learning, the GPR models contain only about 2000 training points and return largely sub-kcal mol^-1 prediction errors for the validation sets. A proof of concept has been reached for transferring the model produced through active learning on one atomic property to that of the remaining atomic properties. The prediction of electrostatic interaction can be assessed at the intermolecular level, and the vast majority of interactions have a root-mean-square error of less than 0.1 kJ mol^-1 with a maximum value of ∼1 kJ mol^-1 for a glycine and paracetamol dimer.

Conformational Features and Hydration Dynamics of Proteins in Cosolvents: A Perspective from Computational Approaches

The importance of solvent in stabilizing protein structures has long been recognized. Water is the common solvent for proteins, and hydration is elemental in governing protein stability, flexibility, and function through various interactions. The addition of small organic molecules known as cosolvents may deploy stabilization (folding) or destabilization (unfolding) effects on native protein conformations. Despite exhaustive literature, the molecular mechanism by which cosolvents regulate protein conformations and dynamics is controversial. Specifically, the cosolvent behavior has been unpredictable with the nature and concentrations that lead to protein stabilizing/destabilizing effects as it changes in water content near the vicinity of proteins. With the massive development of computational resources, advancement of computational methods, and the availability of numerous experimental techniques, various theoretical and computational studies of proteins in a mixture of solvents have been instigated. The growing interest in such studies has been to unravel the underlying mechanism of protein folding and cosolvent/solvent-protein interactions that have significant implications in biomedical and biotechnological applications. In this mini-review, apart from the brief overview of important theories and force-field model-based cosolvent effects on proteins, we present the current state of knowledge and recent advances in the field to describe cosolvent-guided conformational features of proteins and hydration dynamics from computational approaches. The mini-review further explains the mechanistic details of protein stability in various popularly used cosolvents, including limitations of present studies and future outlooks. The counteracting effects of cosolvent on the proteins in the mixture of stabilizing and destabilizing cosolvents are also presented and discussed.

Impact of Polarization on the Ring Puckering Dynamics of Hexose Monosaccharides

Analysis of crystal structures of hexose monosaccharides α-d-mannose (α-MAN), β-d-mannose (β-MAN), α-d-glucose (α-GLC), β-d-glucose (β-GLC), α-d-galactose (α-GAL), β-d-galactose (β-GAL), α-d-altrose (α-ALT), β-d-altrose (β-ALT), α-d-idose (α-IDO), and β-d-idose (β-IDO) reveals that the monosaccharide ring adopts multiple ring conformations. These ring conformations can be broadly classified as chair, half-chair, envelope, boat, and skew-boat conformations. The ability of the monosaccharide ring to adopt multiple conformations has been closely tied with their bioactivity. However, it has been difficult to capture the dynamic information of these conformations from experimental studies. Even from simulations, capturing these different conformations is challenging because of the energy barriers involved in the transitions between the stable ⁴C₁ and ¹C₄ chair forms. In this study, we analyze the influence of the polarizable force field on the ring dynamics of five major types of unsubstituted aldohexoses─glucose, mannose, galactose, altrose, and idose─and their anomers. We simulate microsecond trajectories to capture the influence of the CHARMM36 additive and polarizable carbohydrate force fields on the ring dynamics. The microsecond trajectories allow us to comment on the issues associated with equilibrium molecular dynamics simulations. Further, we use the extended system adaptive biasing force (eABF) method to compare the conformational sampling efficiencies of the additive and polarizable force fields. Our studies reveal that inclusion of polarization enhances the sampling of ring conformations and lowers the energy barriers between the ⁴C₁ and ¹C₄ conformations. Overall, the CHARMM36 additive force field is observed to be rigid and favor the ⁴C₁ conformations. Although the inclusion of polarizability results in enhancing ring flexibility, we observe sampling that does not agree with experimental results, warranting a revision of the polarizable Drude parameters.

Treating Polarization Effects in Charged and Polar Bio-Molecules Through Variable Electrostatic Parameters

Polarization plays important roles in charged and hydrogen bonding containing systems. Much effort ranging from the construction of physics-based models to quantum mechanism (QM)-based and machine learning (ML)-assisted models have been devoted to incorporating the polarization effect into the conventional force fields at different levels, such as atomic and coarse grained (CG). The application of polarizable force fields or polarization models was limited by two aspects, namely, computational cost and transferability. Different from physics-based models, no predetermining parameters were required in the QM-based approaches. Taking advantage of both the accuracy of QM calculations and efficiency of molecular mechanism (MM) and ML, polarization effects could be treated more efficiently while maintaining the QM accuracy. The computational cost could be reduced with variable electrostatic parameters, such as the charge, dipole, and electronic dielectric constant with the help of linear scaling fragmentation-based QM calculations and ML models. Polarization and entropy effects on the prediction of partition coefficient of druglike molecules are demonstrated by using both explicit or implicit all-atom molecular dynamics simulations and machine learning-assisted models. Directions and challenges for future development are also envisioned.

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.

Inclusion of High-Field Target Data in AMOEBA's Calibration Improves Predictions of Protein-Ion Interactions

The reliability of molecular mechanics simulations to predict effects of ion binding to proteins depends on their ability to simultaneously describe ion-protein, ion-water, and protein-water interactions. Force fields (FFs) to describe protein-water and ion-water interactions have been constructed carefully and have also been refined routinely to improve accuracy. Descriptions for ion-protein interactions have also been refined, although in an a posteriori manner through the use of "nonbonded-fix (NB-fix)" approaches in which parameters from default Lennard-Jones mixing rules are replaced with those optimized against some reference data. However, even after NB-fix corrections, there remains a significant need for improvement. This is also true for polarizable FFs that include self-consistent inducible moments. Our recent studies on the polarizable AMOEBA FF suggested that the problem associated with modeling ion-protein interactions could be alleviated by recalibrating polarization models of cation-coordinating functional groups so that they respond better to the high electric fields present near ions. Here, we present such a recalibration of carbonyls, carboxylates, and hydroxyls in the AMOEBA protein FF and report that it does improve predictions substantially─mean absolute errors in Na⁺-protein and K⁺-protein interaction energies decrease from 8.7 to 5.3 and 9.6 to 6.3 kcal/mol, respectively. Errors are computed with respect to estimates from van der Waals-inclusive density functional theory benchmarked against high-level quantum mechanical calculations and experiments. While recalibration does improve ion-protein interaction energies, they still remain underestimated, suggesting that further improvements can be made in a systematic manner through modifications in classical formalism. Nevertheless, we show that by applying our many-body NB-fix correction to Lennard-Jones components, these errors are further reduced to 2.7 and 2.6 kcal/mol, respectively, for Na⁺ and K⁺ ions. Finally, we show that the recalibrated AMOEBA protein FF retains its intrinsic reliability in predicting protein structure and dynamics in the condensed phase.

Classical Exchange Polarization: An Anisotropic Variable Polarizability Model

Polarizability, or the tendency of the electron distribution to distort under an electric field, often depends on the local chemical environment. For example, the polarizability of a chloride ion is larger in gas phase compared to a chloride ion solvated in water. This effect is due to the restriction the Pauli exclusion principle places on the allowed electron states. Because no two electrons can occupy the same state, when a highly polarizable atom comes in close contact with other atoms or molecules, the space of allowed states can dramatically decrease. This constraint suggests that an accurate molecular mechanics polarizability model should depend on the radial distance between neighboring atoms. This paper introduces a variable polarizability model within the framework of the HIPPO (Hydrogen-like Intermolecular Polarizable Potential) force field, by damping the polarizability as a function of the orbital overlap of two atoms. This effectively captures the quantum mechanical exchange polarization effects, without explicit utilization of antisymmetrized wave functions. We show that the variable polarizability model remarkably improves the two-body polarization energies and three-body energies of ion-ion and ion-water systems. Under this model, no manual tuning of atomic polarizabilities for monatomic ions is required; the gas-phase polarizability can be used because an appropriate damping function is able to correct the polarizability at short range.

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

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

Extension of the CHARMM Classical Drude Polarizable Force Field to N- and O-Linked Glycopeptides and Glycoproteins

Molecular dynamic simulations are an effective tool to study complex molecular systems and are contingent upon the availability of an accurate and reliable molecular mechanics force field. The Drude polarizable force field, which allows for the explicit treatment of electronic polarization in a computationally efficient fashion, has been shown to reproduce experimental properties that were difficult or impossible to reproduce with the CHARMM additive force field, including peptide folding cooperativity, RNA hairpin structures, and DNA base flipping. Glycoproteins are essential components of glycoconjugate vaccines, antibodies, and many pharmaceutically important molecules, and an accurate polarizable force field that includes compatibility between the protein and carbohydrate aspect of the force field is essential to study these types of systems. In this work, we present an extension of the Drude polarizable force field to glycoproteins, including both N- and O-linked species. Parameter optimization focused on the dihedral terms using a reweighting protocol targeting NMR solution J-coupling data for model glycopeptides. Validation of the model include eight model glycopeptides and four glycoproteins with multiple N- and O-linked glycosylations. The new glycoprotein carbohydrate force field can be used in conjunction with the remainder of Drude polarizable force field through a variety of MD simulation programs including GROMACS, OPENMM, NAMD, and CHARMM and may be accessed through the Drude Prepper module in the CHARMM-GUI.

Is an Inductive Effect Explicit Account Required for Atomic Charges Aimed at Use within the Force Fields?

Polarization and inductive effects are the concepts that have been widely used in qualitative and even quantitative descriptions of experimentally observed properties in chemistry. The polarization effect has proven to be important in cases of biomolecular modeling though still the vast majority of molecular simulations use the classical non-polarizable force fields. In the last few decades, a lot of effort has been put into promoting the polarization effect and incorporating it into modern force fields and charge calculation methods. In contrast, the inductive effect has not attracted such attention and is effectively absent in both classic and modern force fields. Thus, a question is whether this difference corresponds to the difference in the physical significance of the effects and their explicit account, or is an artifact that should be corrected in the next generation of force fields. The significance of the electronic effects is studied in this paper through the prism of performance of specific models for atomic charge calculation that take into explicit account a nested set of effects: the formal charge, the nearest neighbors, the inductive effect, and finally the model, which takes into account all effects, which are possible to account for using atomic charges. The specific choice for the methods is the following: formal charges, MMFF94 bond charge increments, Dynamic Electronegativity Relaxation (DENR), and RESP. We propose a special scheme for the separate estimation of each particular effect contribution. By pairwise comparing the residual molecular electrostatic potential (MEP) errors of those charge models (aimed at best reproducing the quantum chemical reference MEP), we sequentially revealed how the account of each effect contributes to the better-quality MEP reproduction. The following relative importance of effects was estimated; thus, the natural hierarchy of the effects was established. First, the account of formal charges is of primordial importance. Second, the nearest neighbors account is the next in significance. Third, the explicit account of inductive effect in empirical charge calculation schemes was shown to significantly─both qualitatively and quantitatively─improve the quality of MEP reproduction. Fourth, the contribution of polarization is indirectly assessed. Surprisingly, it is of the order of magnitude of the inductive effect even for the molecular systems, for which it is anticipated to be more significant. Finally, the relative importance of anisotropic effects in neutral molecules was additionally reviewed.

A Small Molecule Stabilizes the Disordered Native State of the Alzheimer's Aβ Peptide

The stabilization of native states of proteins is a powerful drug discovery strategy. It is still unclear, however, whether this approach can be applied to intrinsically disordered proteins. Here, we report a small molecule that stabilizes the native state of the Aβ42 peptide, an intrinsically disordered protein fragment associated with Alzheimer's disease. We show that this stabilization takes place by a disordered binding mechanism, in which both the small molecule and the Aβ42 peptide remain disordered. This disordered binding mechanism involves enthalpically favorable local π-stacking interactions coupled with entropically advantageous global effects. These results indicate that small molecules can stabilize disordered proteins in their native states through transient non-specific interactions that provide enthalpic gain while simultaneously increasing the conformational entropy of the proteins.

A Polarizable Cationic Dummy Metal Ion Model

A novel locally polarizable multisite model based on the original cation dummy atom (CDA) model is described for molecular dynamics simulations of ions in condensed phases. Polarization effects are introduced by the electronegativity equalization model (EEM) method where charges on the metal ion and its dummy atoms can fluctuate to respond to the environment. This model includes explicit polarization and ion-induced interactions and can be coupled with nonpolarizable or polarizable water models, making it more transferable to simpler force fields. This approach allows us to enhance the original fixed charge CDA model where the charge distribution cannot adapt to the local solvent structure. To illustrate the new CDApol model, we examined properties of the Zn2+, Al3+, and Zr4+ ions in aqueous solution. The polarizable model and Lennard-Jones parameters were refined for octahedrally coordinated Zn2+, Al3+, and Zr4+ CDAs to reproduce thermodynamic and geometrical properties. Using this locally polarizable model, we were able to obtain the experimental hydration free energy, ion-oxygen distance, and coordination number coupled with the standard 12-6 Lennard-Jones model. This model can be used in myriad additional applications where local polarization and charge transfer is important.

A multiscale approach to predict the binding mode of metallo beta-lactamase inhibitors

Antibiotic resistance is a major threat to global public health. β-lactamases, which catalyze breakdown of β-lactam antibiotics, are a principal cause. Metallo β-lactamases (MBLs) represent a particular challenge because they hydrolyze almost all β-lactams and to date no MBL inhibitor has been approved for clinical use. Molecular simulations can aid drug discovery, for example, predicting inhibitor complexes, but empirical molecular mechanics (MM) methods often perform poorly for metalloproteins. Here we present a multiscale approach to model thiol inhibitor binding to IMP-1, a clinically important MBL containing two catalytic zinc ions, and predict the binding mode of a 2-mercaptomethyl thiazolidine (MMTZ) inhibitor. Inhibitors were first docked into the IMP-1 active site, testing different docking programs and scoring functions on multiple crystal structures. Complexes were then subjected to molecular dynamics (MD) simulations and subsequently refined through QM/MM optimization with a density functional theory (DFT) method, B3LYP/6-31G(d), increasing the accuracy of the method with successive steps. This workflow was tested on two IMP-1:MMTZ complexes, for which it reproduced crystallographically observed binding, and applied to predict the binding mode of a third MMTZ inhibitor for which a complex structure was crystallographically intractable. We also tested a 12-6-4 nonbonded interaction model in MD simulations and optimization with a SCC-DFTB QM/MM approach. The results show the limitations of empirical models for treating these systems and indicate the need for higher level calculations, for example, DFT/MM, for reliable structural predictions. This study demonstrates a reliable computational pipeline that can be applied to inhibitor design for MBLs and other zinc-metalloenzyme systems.

Changes in the Local Conformational States Caused by Simple Na+ and K+ Ions in Polyelectrolyte Simulations: Comparison of Seven Force Fields with and without NBFIX and ECC Corrections

Electrostatic interactions have a determining role in the conformational and dynamic behavior of polyelectrolyte molecules. In this study, anionic polyelectrolyte molecules, poly(glutamic acid) (PGA) and poly(aspartic acid) (PASA), in a water solution with the most commonly used K+ or Na+ counterions, were investigated using atomistic molecular dynamics (MD) simulations. We performed a comparison of seven popular force fields, namely AMBER99SB-ILDN, AMBER14SB, AMBER-FB15, CHARMM22*, CHARMM27, CHARMM36m and OPLS-AA/L, both with their native parameters and using two common corrections for overbinding of ions, the non-bonded fix (NBFIX), and electronic continuum corrections (ECC). These corrections were originally introduced to correct for the often-reported problem concerning the overbinding of ions to the charged groups of polyelectrolytes. In this work, a comparison of the simulation results with existing experimental data revealed several differences between the investigated force fields. The data from these simulations and comparisons with previous experimental data were then used to determine the limitations and strengths of these force fields in the context of the structural and dynamic properties of anionic polyamino acids. Physical properties, such as molecular sizes, local structure, and dynamics, were studied using two types of common counterions, namely potassium and sodium. The results show that, in some cases, both the macroion size and dynamics depend strongly on the models (parameters) for the counterions due to strong overbinding of the ions and charged side chain groups. The local structures and dynamics are more sensitive to dihedral angle parameterization, resulting in a preference for defined monomer conformations and the type of correction used. We also provide recommendations based on the results.

Classical electronic and molecular dynamics simulation for optical response of metal system

An extended molecular dynamics simulation that incorporates classical free electron dynamics in the framework of the force-field model has been developed to enable us to describe the optical response of metal materials under the visible light electric field. In the simulation, dynamical atomic point charges follow equations of motion of classical free electrons that include Coulomb interactions with the oscillating field and surrounding atomic sites and collision effects from nearby electrons and ions. This scheme allows us to simulate an interacting system of metals with molecules using an ordinary polarizable force-field and preserves energy conservation in the case without applying an external electric field. As the first applications, we show that the presented simulation accurately reproduces (i) the classical image potential in a metal-charge interaction system and (ii) the dielectric function of bulk metal. We also demonstrate (iii) calculations of absorption spectra of metal nano-particles with and without a water solvent at room temperature, showing reasonable red-shift by the solvent effect, and (iv) plasmon resonant excitation of the metal nano-particle in solution under the visible light pulse and succeeding energy relaxation of the absorbed light energy from electrons to atoms on the metal and to the water solvent. Our attempt thus opens the possibility to expand the force-field based molecular dynamics simulation to an alternative tool for optical-related fields.

Polarizable and non-polarizable force fields: Protein folding, unfolding, and misfolding

Molecular dynamics simulations are an invaluable tool to characterize the dynamic motions of proteins in atomistic detail. However, the accuracy of models derived from simulations inevitably relies on the quality of the underlying force field. Here, we present an evaluation of current non-polarizable and polarizable force fields (AMBER ff14SB, CHARMM 36m, GROMOS 54A7, and Drude 2013) based on the long-standing biophysical challenge of protein folding. We quantify the thermodynamics and kinetics of the β-hairpin formation using Markov state models of the fast-folding mini-protein CLN025. Furthermore, we study the (partial) folding dynamics of two more complex systems, a villin headpiece variant and a WW domain. Surprisingly, the polarizable force field in our set, Drude 2013, consistently leads to destabilization of the native state, regardless of the secondary structure element present. All non-polarizable force fields, on the other hand, stably characterize the native state ensembles in most cases even when starting from a partially unfolded conformation. Focusing on CLN025, we find that the conformational space captured with AMBER ff14SB and CHARMM 36m is comparable, but the ensembles from CHARMM 36m simulations are clearly shifted toward disordered conformations. While the AMBER ff14SB ensemble overstabilizes the native fold, CHARMM 36m and GROMOS 54A7 ensembles both agree remarkably well with experimental state populations. In addition, GROMOS 54A7 also reproduces experimental folding times most accurately. Our results further indicate an over-stabilization of helical structures with AMBER ff14SB. Nevertheless, the presented investigations strongly imply that reliable (un)folding dynamics of small proteins can be captured in feasible computational time with current additive force fields.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Characterizing the Water Wire in the Gramicidin Channel Found by Monte Carlo Sampling Using Continuum Electrostatics and in Molecular Dynamics Trajectories with Conventional or Polarizable Force Fields

Water molecules play a key role in all biochemical processes. They help define the shape of proteins, and they are reactant or product in many reactions and are released as ligands are bound. They facilitate the transfer of protons through transmembrane proton channel, pump and transporter proteins. Continuum electrostatics (CE) force fields used by program Multiconformation CE (MCCE) capture electrostatic interactions in biomolecules with an implicit solvent, which captures the averaged solvent water equilibrium properties. Hybrid CE methods can use explicit water molecules within the protein surrounded by implicit solvent. These hybrid methods permit the study of explicit hydrogen bond networks within the protein and allow analysis of processes such as proton transfer reactions. Yet hybrid CE methods have not been rigorously tested. Here, we present an explicit treatment of water molecules in the Gramicidin A (gA) channel using MCCE and compare the resulting distributions of water molecules and key hydration features against those obtained with explicit solvent Molecular Dynamics (MD) simulations with the nonpolarizable CHARMM36 and polarizable Drude force fields. CHARMM36 leads to an aligned water wire in the channel characterized by a large absolute net water dipole moment; the MCCE and Drude analysis lead to a small net dipole moment as the water molecules change orientation within the channel. The correct orientation is not as yet known, so these calculations identify an open question.

Molecular Dynamics Simulations Based on Polarizable Models Show that Ion Permeation Interconverts between Different Mechanisms as a Function of Membrane Thickness

Different mechanisms have been proposed to explain the permeation of charged compounds through lipid membranes. Overall, it is expected that an ion-induced defect permeation mechanism, where substantial membrane deformations accompany ion movement, should be dominant in thin membranes but that a solubility-diffusion mechanism, where ions partition into the membrane core with large associated dehydration energy costs, becomes dominant in thicker membranes. However, while this physical picture is intuitively reasonable, capturing the interconversion between these two permeation mechanisms in molecular dynamics (MD) simulations based on atomic models is challenging. In particular, simulations relying on nonpolarizable force fields are artificially unfavorable to the solubility-diffusion mechanism, as induced polarization of the nonpolar hydrocarbon is ignored, causing overestimated free energy costs for charged molecules to enter into this region of the membrane. In this study, all-atom MD simulations based on nonpolarizable and polarizable force fields are used to quantitatively characterize the permeation process for the arginine side chain analog methyl-guanidinium through bilayer membranes of mono-unsaturated phosphatidylcholine lipids with and without cholesterol, resulting in thicknesses spanning from ∼24 to ∼42 Å. With simulations based on a nonpolarizable force field, ion translocation can take place solely through an ion-induced defect mechanism, with free energy barriers increasing linearly from 14 to 40 kcal/mol, depending on the thickness. However, with simulations based on a polarizable force field, ion translocation is predominantly dominated by an ion-induced defect mechanism in thin membranes, which progressively converts to a solubility-diffusion mechanism as the membranes get thicker. The transition between the two mechanisms occurs at a thickness of ∼29 Å, with lipid tails of 22 or more carbon atoms. This situation appears to represent the upper limit for ion-induced defect permeation within the current polarizable models. Beyond this thickness, it becomes energetically preferable for the ion to dehydrate and partition into the membrane core-a phenomenon that cannot be captured using the nonpolarizable models. Induced electronic polarizability therefore leads not just to a shift in permeation energetics but to an interconversion between two strikingly different physical mechanisms. The result highlights the importance of induced polarizability in modeling lipid membranes.

Accurate Description of Cation-π Interactions in Proteins with a Nonpolarizable Force Field at No Additional Cost

Cation-π interactions play a significant role in a host of processes eminently relevant to biology. However, polarization effects arising from the interaction of cations with aromatic moieties have long been recognized to be inadequately described by pairwise additive force fields. In the present work, we address this longstanding shortcoming through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field, modifying pair-specific Lennard-Jones (LJ) parameters, while circumventing the limitations of the Lorentz-Berthelot combination rules. The potentials of mean force (PMFs) characterizing prototypical cation-π interactions in aqueous solutions are first determined using a hybrid quantum mechanical/molecular mechanics (QM/MM) strategy in conjunction with an importance-sampling algorithm. The LJ parameters describing the cation-π pairs are then optimized to match the QM/MM PMFs. The standard binding free energies of nine cation-π complexes, i.e., toluene, para-cresol, and 3-methyl-indole interacting with either ammonium, guanidinium, or tetramethylammonium, determined with this new set of parameters agree well with the experimental measurements. Additional simulations were carried out on three different classes of biological objects featuring cation-π interactions, including five individual proteins, three protein-ligand complexes, and two protein-protein complexes. Our results indicate that the description of cation-π interactions is overall improved using NBFIX corrections, compared with the standard pairwise additive force field. Moreover, an accurate binding free energy calculation for a protein-ligand complex containing cation-π interactions (2BOK) shows that using the new parameters, the experimental binding affinity can be reproduced quantitatively. Put together, the present work suggests that the NBFIX parameters optimized here can be broadly utilized in the simulation of proteins in an aqueous solution to enhance the representation of cation-π interactions, at no additional computational cost.

Tautomer Standardization in Chemical Databases: Deriving Business Rules from Quantum Chemistry

Databases of small, potentially bioactive molecules are ubiquitous across the industry and academia. Designed such that each unique compound should appear only once, the multiplicity of ways in which many compounds can be represented means that these databases require methods for standardizing the representation of chemistry. This is commonly achieved through the use of "Chemistry Business Rules", sets of predefined rules that describe the "house style" of the database in question. At Syngenta, the historical approach to the design of chemistry business rules has been to focus on consistency of representation, with chemical relevance given secondary consideration. In this work, we overturn that convention. Through the use of quantum chemistry calculations, we define a set of chemistry business rules for tautomer standardization that reproduces gas-phase energetic preferences. We go on to show that, compared to our historic approach, this method yields tautomers that are in better agreement with those observed experimentally in condensed phases and that are better suited for use in predictive models.

Static Polarizabilities at the Basis Set Limit: A Benchmark of 124 Species

Benchmarking molecular properties with Gaussian-type orbital (GTO) basis sets can be challenging, because one has to assume that the computed property is at the complete basis set (CBS) limit, without a robust measure of the error. Multiwavelet (MW) bases can be systematically improved with a controllable error, which eliminates the need for such assumptions. In this work, we have used MWs within Kohn–Sham density functional theory to compute static polarizabilities for a set of 92 closed-shell and 32 open-shell species. The results are compared to recent benchmark calculations employing the GTO-type aug-pc4 basis set. We observe discrepancies between GTO and MW results for several species, with open-shell systems showing the largest deviations. Based on linear response calculations, we show that these discrepancies originate from artifacts caused by the field strength and that several polarizabilies from a previous study were contaminated by higher order responses (hyperpolarizabilities). Based on our MW benchmark results, we can affirm that aug-pc4 is able to provide results close to the CBS limit, as long as finite difference effects can be controlled. However, we suggest that a better approach is to use MWs, which are able to yield precise finite difference polarizabilities even with small field strengths.

A Simple Method for Including Polarization Effects in Solvation Free Energy Calculations When Using Fixed-Charge Force Fields: Alchemically Polarized Charges

The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed-charge force fields, which we call the alchemically polarized charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. APolQ can in principle be applied to any microscopically homogeneous system (e.g., pure or mixed solvents). We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database and compared results obtained using three different water models (SPC/E, TIP3P, and OPC3) and using minimal basis iterative Stockholder (MBIS) and restrained electrostatic potential (RESP) partial charge methodologies. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield absolute average deviations 1.5-1.9 kJ mol-1 lower than using AM1 bond charge correction (AM1-BCC). We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies.

Influence of Calcium Binding on Conformations and Motions of Anionic Polyamino Acids. Effect of Side Chain Length

Investigation of the effect of CaCl2 salt on conformations of two anionic poly(amino acids) with different side chain lengths, poly-(α-l glutamic acid) (PGA) and poly-(α-l aspartic acid) (PASA), was performed by atomistic molecular dynamics (MD) simulations. The simulations were performed using both unbiased MD and the Hamiltonian replica exchange (HRE) method. The results show that at low CaCl2 concentration adsorption of Ca2+ ions lead to a significant chain size reduction for both PGA and PASA. With the increase in concentration, the chains sizes partially recover due to electrostatic repulsion between the adsorbed Ca2+ ions. Here, the side chain length becomes important. Due to the longer side chain and its ability to distance the charged groups with adsorbed ions from both each other and the backbone, PGA remains longer in the collapsed state as the CaCl2 concentration is increased. The analysis of the distribution of the mineral ions suggests that both poly(amino acids) should induce the formation of mineral with the same structure of the crystal cell.

Balanced polarizable Drude force field parameters for molecular anions: phosphates, sulfates, sulfamates, and oxides

Polarizable force fields are emerging as a more accurate alternative to additive force fields in terms of modeling and simulations of a variety of chemicals including biomolecules. Explicit treatment of induced polarization in charged species such as phosphates and sulfates offers the potential for achieving an improved atomistic understanding of the physical forces driving their interactions with their environments. To help achieve this, in this study we present balanced Drude polarizable force field parameters for molecular ions including phosphates, sulfates, sulfamates, and oxides. Better balance was primarily achieved in the relative values of minimum interaction energies and distances of the anionic model compounds with water at the Drude and quantum mechanical (QM) model chemistries. Parametrization involved reoptimizing available parameters as well as extending the force field to new molecules with the goal of achieving self-consistency with respect to the Lennard-Jones and electrostatic parameters targeting QM and experimental hydration free energies. The resulting force field parameters achieve consistent treatment across the studied anions, facilitating more balanced simulations of biomolecules and small organic molecules in the context of the classical Drude polarizable force field. Graphical abstract.

Fine-Tuning of the AMBER RNA Force Field with a New Term Adjusting Interactions of Terminal Nucleotides

Determination of RNA structural-dynamic properties is challenging for experimental methods. Thus, atomistic molecular dynamics (MD) simulations represent a helpful technique complementary to experiments. However, contemporary MD methods still suffer from limitations of force fields (ffs), including imbalances in the nonbonded ff terms. We have recently demonstrated that some improvement of state-of-the-art AMBER RNA ff can be achieved by adding a new term for H-bonding called gHBfix, which increases tuning flexibility and reduces risk of side-effects. Still, the first gHBfix version did not fully correct simulations of short RNA tetranucleotides (TNs). TNs are key benchmark systems due to availability of unique NMR data, although giving too much weight on improving TN simulations can easily lead to overfitting to A-form RNA. Here we combine the gHBfix version with another term called tHBfix, which separately treats H-bond interactions formed by terminal nucleotides. This allows to refine simulations of RNA TNs without affecting simulations of other RNAs. The approach is in line with adopted strategy of current RNA ffs, where the terminal nucleotides possess different parameters for terminal atoms than the internal nucleotides. Combination of gHBfix with tHBfix significantly improves the behavior of RNA TNs during well-converged enhanced-sampling simulations using replica exchange with solute tempering. TNs mostly populate canonical A-form like states while spurious intercalated structures are largely suppressed. Still, simulations of r(AAAA) and r(UUUU) TNs show some residual discrepancies with primary NMR data which suggests that future tuning of some other ff terms might be useful. Nevertheless, the tHBfix has a clear potential to improve modeling of key biochemical processes, where interactions of RNA single stranded ends are involved.

Multiscale coupled Maxwell's equations and polarizable molecular dynamics simulation based on charge response kernel model

A computational scheme of coupled Maxwell's equations and polarizable molecular dynamics simulation has been developed based on a multi-scale model to describe the coupled dynamics of light electromagnetic waves and molecules in crystalline solids, where the charge response kernel model is employed to incorporate electronic polarization of the molecules. The method is applicable to electronically non-resonant light-matter interaction systems that involve atomic motions in spectroscopy and photonics. Since the scheme simultaneously traces the light propagation in a medium on a macroscopic scale and the microscopic molecular motion under the light electric field, this enables us to treat the experimental setup and mimic its measurement process. As the first applications, we demonstrate three numerical examples of basic spectroscopies of an ice crystalline solid: simulations of reflection and transmission of visible light, infrared absorption measurement, and stimulated Raman scattering measurement. These examples show the detailed behaviors of the interacting light fields and molecules in the spectroscopic processes.