Polarizable empirical force field for nitrogen-containing heteroaromatic compounds based on the classical Drude oscillator

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Quantifying Induced Dipole Effects in Small Molecule Permeation in a Model Phospholipid Bilayer

The cell membrane functions as a semipermeable barrier that governs the transport of materials into and out of cells. The bilayer features a distinct dielectric gradient due to the amphiphilic nature of its lipid components. This gradient influences various aspects of small molecule permeation and the folding and functioning of membrane proteins. Here, we employ polarizable molecular dynamics simulations to elucidate the impact of the electronic environment on the permeation process. We simulated eight distinct amino-acid side chain analogs within a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer using the Drude polarizable force field (FF). Our approach includes both unbiased and umbrella sampling simulations. By using a polarizable FF, we sought to investigate explicit dipole responses in relation to local electric fields along the membrane normal. We evaluate molecular dipole moments, which exhibit variation based on their localization within the membrane, and compare the outcomes with analogous simulations using the nonpolarizable CHARMM36 FF. This comparative analysis aims to discern characteristic differences in the free energy surfaces of permeation for the various amino-acid analogs. Our results provide the first systematic quantification of the impact of employing an explicitly polarizable FF in this context compared to the fixed-charge convention inherent to nonpolarizable FFs, which may not fully capture the influence of the membrane dielectric gradient.

Harnessing Deep Learning for Optimization of Lennard-Jones Parameters for the Polarizable Classical Drude Oscillator Force Field

The outcomes of computational chemistry and biology research, including drug design, are significantly influenced by the underlying force field (FF) used in molecular simulations. While improved FF accuracy may be achieved via inclusion of explicit treatment of electronic polarization, such an extension must be accompanied by optimization of van der Waals (vdW) interactions, in the context of the Lennard-Jones (LJ) formalism in the present study. This is particularly challenging due to the extensive nature of chemical space combined with the correlated nature of LJ parameters. To address this challenge, a deep learning (DL)-based parametrization framework is developed, allowing for sampling of wide ranges of LJ parameters targeting experimental condensed phase thermodynamic properties. The present work utilizes this framework to develop the LJ parameters for atoms associated with four distinct groups covering 10 different atom types. Final parameter selection was facilitated by quantum mechanical data on rare-gas interactions with the training set molecules. The chosen parameters were then validated through experimental hydration free energies and condensed phase thermodynamic properties of validation set molecules to confirm transferability. The ultimate outcome of utilizing this framework is a set of LJ parameters in the context of the polarizable Drude FF, which demonstrated improvement in the reproduction of both experimental pure solvent and crystal properties and hydration free energies of the molecules compared to the additive CHARMM General FF (CGenFF) including the ability of the Drude FF to accurately reproduce both experimental pure solvent properties and hydration free energies. The study also shows how correlations between difference in the reproduction of condensed phase data between model compounds may be used to direct the selection of new atom types and training set molecules during FF development.

Development and application of quantum mechanics/molecular mechanics methods with advanced polarizable potentials

Quantum mechanics/molecular mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and biological systems. The combination of QM and MM methods to represent a system gives rise to several challenges that need to be addressed. The increase in computational speed has allowed the expanded use of more complicated and accurate methods for both QM and MM simulations. Here, we review some approaches that address several common challenges encountered in QM/MM simulations with advanced polarizable potentials, from methods to account for boundary across covalent bonds and long-range effects, to polarization and advanced embedding potentials.

Improved Modeling of Cation-π and Anion-Ring Interactions Using the Drude Polarizable Empirical Force Field for Proteins

Cation-π interactions are noncovalent interactions between a π-electron system and a positively charged ion that are regarded as a strong noncovalent interaction and are ubiquitous in biological systems. Similarly, though less studied, anion-ring interactions are present in proteins along with in-plane interactions of anions with aromatic rings. As these interactions are between a polarizing ion and a polarizable π system, the accuracy of the treatment of these interactions in molecular dynamics (MD) simulations using additive force fields (FFs) may be limited. In the present work, to allow for a better description of ion-π interactions in proteins in the Drude-2013 protein polarizable FF, we systematically optimized the parameters for these interactions targeting model compound quantum mechanical (QM) interaction energies with atom pair-specific Lennard-Jones parameters along with virtual particles as selected ring centroids introduced to target the QM interaction energies and geometries. Subsequently, MD simulations were performed on a series of protein structures where ion-π pairs occur to evaluate the optimized parameters in the context of the Drude-2013 FF. The resulting FF leads to a significant improvement in reproducing the ion-π pair distances observed in experimental protein structures, as well as a smaller root-mean-square differences and fluctuations of the overall protein structures from experimental structures. Accordingly, the optimized Drude-2013 protein polarizable FF is suggested for use in MD simulations of proteins where cation-π and anion-ring interactions are critical. © 2019 Wiley Periodicals, Inc.

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

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

Force Fields for Small Molecules

Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.

Improved Modeling of Halogenated Ligand-Protein Interactions Using the Drude Polarizable and CHARMM Additive Empirical Force Fields

Halogenated ligands can participate in nonbonding interactions with proteins via halogen bond (XB) or halogen-hydrogen bond donor (X-HBD) interactions. In the context of molecular dynamics (MD) simulations, the accuracy of the simulations depends strongly on the force field (FF) used. To ensure good reproduction of XB and X-HBD interactions with proteins, we optimized the previously developed additive CHARMM36/CHARMM General force field (CGenFF) and Drude polarizable force field by including atom pair-specific Lennard-Jones parameters for aromatic halogen-protein interactions. The optimization targeted quantum mechanical interaction energy surfaces with the developed parameters then examined for their ability to reproduce experimental halogen-containing ligand-protein interactions in MD simulations. The calculated halogenated ligand interaction geometries were in good overall agreement with the experimental crystal data for both the polarizable and additive FFs, showing that these models can accurately treat both XB and X-HBD interactions. Analysis of the ligand-protein interactions shows significant contributions of polarizability to binding occurring in the Drude FF, with self-polarization energy making both favorable and unfavorable contributions to binding. Further analysis of the dipole moments from aqueous solution to protein indicates the polarizable FF accounts for subtle changes of the environment of the ligands that can impact binding. The present work demonstrates the utility of the updated additive CHARMM36/CGenFF and polarizable Drude FFs for the study of halogenated ligand-protein interactions in computer-aided drug design.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

Folding free energy landscapes of β-sheets with non-polarizable and polarizable CHARMM force fields

Molecular dynamics (MD) simulations of peptides and proteins offer atomic-level detail into many biological processes, although the degree of insight depends on the accuracy of the force fields used to represent them. Protein folding is a key example in which the accurate reproduction of folded-state conformations of proteins and kinetics of the folding processes in simulation is a longstanding goal. Although there have been a number of recent successes, challenges remain in capturing the full complexity of folding for even secondary-structure elements. In the present work, we have used all-atom MD simulations to study the folding properties of one such element, the C-terminal β-hairpin of the B1 domain of streptococcal protein G (GB1). Using replica-exchange umbrella sampling simulations, we examined the folding free energy of two fixed-charge CHARMM force fields, CHARMM36 and CHARMM22^*, as well as a polarizable force field, the CHARMM Drude-2013 model, which has previously been shown to improve the folding properties of α-helical peptides. The CHARMM22^* and Drude-2013 models are in rough agreement with experimental studies of GB1 folding, while CHARMM36 overstabilizes the β-hairpin. Additional free-energy calculations show that small adjustments to the atomic polarizabilities in the Drude-2013 model can improve both the backbone solubility and folding properties of GB1 without significantly affecting the model's ability to properly fold α-helices. We also identify a non-native salt bridge in the β-turn region that overstabilizes the β-hairpin in the C36 model. Finally, we demonstrate that tryptophan fluorescence is insufficient for capturing the full β-hairpin folding pathway.

Development and Validation of Quantum Mechanically Derived Force-Fields: Thermodynamic, Structural, and Vibrational Properties of Aromatic Heterocycles

A selection of several aromatic molecules, representative of the important class of heterocyclic compounds, has been considered for testing and validating an automated Force Field (FF) parametrization protocol, based only on Quantum Mechanical data. The parametrization is carried out separately for the intra- and intermolecular contributions, employing respectively the Joyce and Picky software packages, previously implemented and refined in our research group. The whole approach is here automated and integrated with a computationally effective yet accurate method, devised very recently ( J. Chem.

THEORY

Comput., 2018, 14, 543-556) to evaluate a large number of dimer interaction energies. The resulting quantum mechanically derived FFs are then used in extensive molecular dynamics simulations, in order to evaluate a number of thermodynamic, structural, and dynamic properties of the heterocycle's gas and liquid phases. The comparison with the available experimental data is good and furnishes a validation of the presented approach, which can be confidently exploited for the design of novel and more complex materials.

Polarizable Force Field for Molecular Ions Based on the Classical Drude Oscillator

Development of accurate force field parameters for molecular ions in the context of a polarizable energy function based on the classical Drude oscillator is a crucial step toward an accurate polarizable model for modeling and simulations of biological macromolecules. Toward this goal we have undertaken a hierarchical approach in which force field parameter optimization is initially performed for small molecules for which experimental data exists that serve as building blocks of macromolecular systems. Small molecules representative of the ionic moieties of biological macromolecules include the cationic ammonium and methyl substituted ammonium derivatives, imidazolium, guanidinium and methylguanidinium, and the anionic acetate, phenolate, and alkanethiolates. In the present work, parameters for molecular ions in the context of the Drude polarizable force field are optimized and compared to results from the nonpolarizable additive CHARMM general force field (CGenFF). Electrostatic and Lennard-Jones parameters for the model compounds are developed in the context of the polarizable SWM4-NDP water model, with emphasis on assuring that the hydration free energies are consistent with previously reported parameters for atomic ions. The final parameters are shown to be in good agreement with the selected quantum mechanical (QM) and experimental target data. Analysis of the structure of water around the ions reveals substantial differences between the Drude and additive force fields indicating the important role of polarization in dictating the molecular details of aqueous solvation. The presented parameters represent the foundation for the charged functionalities in future generations of the Drude polarizable force field for biological macromolecules as well as for drug-like molecules.

Cation-π Interactions between Quaternary Ammonium Ions and Amino Acid Aromatic Groups in Aqueous Solution

Cation-π interactions play important roles in the stabilization of protein structures and protein-ligand complexes. They contribute to the binding of quaternary ammonium ligands (mainly RNH₃⁺ and RN(CH₃)₃⁺) to various protein receptors and are likely involved in the blockage of potassium channels by tetramethylammonium (TMA⁺) and tetraethylammonium (TEA⁺). Polarizable molecular models are calibrated for NH₄⁺, TMA⁺, and TEA⁺ interacting with benzene, toluene, 4-methylphenol, and 3-methylindole (representing aromatic amino acid side chains) based on the ab initio MP2(full)/6-311++G(d,p) properties of the complexes. Whereas the gas-phase affinity of the ions with a given aromatic follows the trend NH₄⁺ > TMA⁺ > TEA⁺, molecular dynamics simulations using the polarizable models show a reverse trend in water, likely due to a contribution from the hydrophobic effect. This reversed trend follows the solubility of aromatic hydrocarbons in quaternary ammonium salt solutions, which suggests a role for cation-π interactions in the salting-in of aromatic compounds in solution. Simulations in water show that the complexes possess binding free energies ranging from -1.3 to -3.3 kcal/mol (compared to gas-phase binding energies between -8.5 and -25.0 kcal/mol). Interestingly, whereas the most stable complexes involve TEA⁺ (the largest ion), the most stable solvent-separated complexes involve TMA⁺ (the intermediate-size ion).

Polarizable Empirical Force Field for Halogen-Containing Compounds Based on the Classical Drude Oscillator

The quality of the force field is crucial to ensure the accuracy of simulations used in molecular modeling, including computer-aided drug design (CADD). To perform more accurate modeling and simulations of halogenated molecules, in this study the polarizable force field based on the classical Drude oscillator model was extended to both aliphatic and aromatic systems using halogenated ethane and benzene model compounds for the halogens F, Cl, Br, and I. The force field parameters were optimized targeting quantum mechanical dipole moments, water interactions, and molecular polarizabilities as well as experimental observables, including enthalpies of vaporization, molecular volumes, hydration free energies, and dielectric constants. The developed halogenated polarizable force field is capable of reproducing QM relative energies and geometries of both halogen bonds and halogen-hydrogen bond donor interactions at an unprecedented level due to the inclusion of a virtual particle and anisotropic atomic polarizability on the halogen and, notably, the inclusion of Lennard-Jones parameters on the halogen Drude particle. The model was validated on the basis of its ability to accurately reproduce pure solvent properties for halogenated naphthalenes and alkanes, including species analogous to those used as refrigerants. Accordingly, it is anticipated that the model will be applicable for the study of halogenated derivatives in CADD as well as in other chemical and biophysical studies.

Proper balance of solvent-solute and solute-solute interactions in the treatment of the diffusion of glucose using the Drude polarizable force field

Motivated by underestimation of the diffusion constant of glucose in aqueous solution at high glucose concentrations we performed additional optimization of the Drude polarizable hexopyranose monosaccharide force field. This indicated aggregation of the glucose at higher concentrations, which is a concern for studies of complex glycan systems such as the HIV Envelope where high effective concentrations of sugars are present. High-level quantum mechanical calculations were undertaken on water monohydrate-glucose interactions, on water cluster-glucose interactions and on glucose-glucose dimers in stacked (parallel) and perpendicular orientations. Optimization of the nonbond and dihedral parameters targeting these data yielded a revised model that showed improved agreement with experimental aqueous diffusion data. However, limitations in the diffusion constants were still present. These were due to the SWM4-NDP inherently overestimating the diffusion constant of water, a problem that was validated by calculation of the aqueous diffusion constants using the SWM6-NDP water model. In addition, results show the water diffusion constant to be significantly overestimated at high glucose concentrations though the glucose diffusion is in satisfactory agreement with experiment. These results indicate the subtle balance of water-sugar, water-water and sugar-sugar interactions that needs to be properly modeled to account for the full range of aqueous behavior of sugars in aqueous solution.

Drude polarizable force field for aliphatic ketones and aldehydes, and their associated acyclic carbohydrates

The majority of computer simulations exploring biomolecular function employ Class I additive force fields (FF), which do not treat polarization explicitly. Accordingly, much effort has been made into developing models that go beyond the additive approximation. Development and optimization of the Drude polarizable FF has yielded parameters for selected lipids, proteins, DNA and a limited number of carbohydrates. The work presented here details parametrization of aliphatic aldehydes and ketones (viz. acetaldehyde, propionaldehyde, butaryaldehyde, isobutaryaldehyde, acetone, and butanone) as well as their associated acyclic sugars (D-allose and D-psicose). LJ parameters are optimized targeting experimental heats of vaporization and molecular volumes, while the electrostatic parameters are optimized targeting QM water interactions, dipole moments, and molecular polarizabilities. Bonded parameters are targeted to both QM and crystal survey values, with the models for ketones and aldehydes shown to be in good agreement with QM and experimental target data. The reported heats of vaporization and molecular volumes represent a compromise between the studied model compounds. Simulations of the model compounds show an increase in the magnitude and the fluctuations of the dipole moments in moving from gas phase to condensed phases, which is a phenomenon that the additive FF is intrinsically unable to reproduce. The result is a polarizable model for aliphatic ketones and aldehydes including the acyclic sugars D-allose and D-psicose, thereby extending the available biomolecules in the Drude polarizable FF.

Metal Ion Modeling Using Classical Mechanics

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

Evaluating Parametrization Protocols for Hydration Free Energy Calculations with the AMOEBA Polarizable Force Field

Hydration free energy (HFE) calculations are often used to assess the performance of biomolecular force fields and the quality of assigned parameters. The AMOEBA polarizable force field moves beyond traditional pairwise additive models of electrostatics and may be expected to improve upon predictions of thermodynamic quantities such as HFEs over and above fixed-point-charge models. The recent SAMPL4 challenge evaluated the AMOEBA polarizable force field in this regard but showed substantially worse results than those using the fixed-point-charge GAFF model. Starting with a set of automatically generated AMOEBA parameters for the SAMPL4 data set, we evaluate the cumulative effects of a series of incremental improvements in parametrization protocol, including both solute and solvent model changes. Ultimately, the optimized AMOEBA parameters give a set of results that are not statistically significantly different from those of GAFF in terms of signed and unsigned error metrics. This allows us to propose a number of guidelines for new molecule parameter derivation with AMOEBA, which we expect to have benefits for a range of biomolecular simulation applications such as protein-ligand binding studies.

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

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

CHARMM Drude Polarizable Force Field for Aldopentofuranoses and Methyl-aldopentofuranosides

An empirical all-atom CHARMM polarizable force filed for aldopentofuranoses and methyl-aldopentofuranosides based on the classical Drude oscillator is presented. A single electrostatic model is developed for eight different diastereoisomers of aldopentofuranoses by optimizing the existing electrostatic and bonded parameters as transferred from ethers, alcohols, and hexopyranoses to reproduce quantum mechanical (QM) dipole moments, furanose-water interaction energies and conformational energies. Optimization of selected electrostatic and dihedral parameters was performed to generate a model for methyl-aldopentofuranosides. Accuracy of the model was tested by reproducing experimental data for crystal intramolecular geometries and lattice unit cell parameters, aqueous phase densities, and ring pucker and exocyclic rotamer populations as obtained from NMR experiments. In most cases the model is found to reproduce both QM data and experimental observables in an excellent manner, whereas for the remainder the level of agreement is in the satisfactory regimen. In aqueous phase simulations the monosaccharides have significantly enhanced dipoles as compared to the gas phase. The final model from this study is transferrable for future studies on carbohydrates and can be used with the existing CHARMM Drude polarizable force field for biomolecules.

CHARMM additive and polarizable force fields for biophysics and computer-aided drug design

BACKGROUND

Molecular Mechanics (MM) is the method of choice for computational studies of biomolecular systems owing to its modest computational cost, which makes it possible to routinely perform molecular dynamics (MD) simulations on chemical systems of biophysical and biomedical relevance.

SCOPE OF REVIEW

As one of the main factors limiting the accuracy of MD results is the empirical force field used, the present paper offers a review of recent developments in the CHARMM additive force field, one of the most popular biomolecular force fields. Additionally, we present a detailed discussion of the CHARMM Drude polarizable force field, anticipating a growth in the importance and utilization of polarizable force fields in the near future. Throughout the discussion emphasis is placed on the force fields' parametrization philosophy and methodology.

MAJOR CONCLUSIONS

Recent improvements in the CHARMM additive force field are mostly related to newly found weaknesses in the previous generation of additive force fields. Beyond the additive approximation is the newly available CHARMM Drude polarizable force field, which allows for MD simulations of up to 1μs on proteins, DNA, lipids and carbohydrates.

GENERAL SIGNIFICANCE

Addressing the limitations ensures the reliability of the new CHARMM36 additive force field for the types of calculations that are presently coming into routine computational reach while the availability of the Drude polarizable force fields offers an inherently more accurate model of the underlying physical forces driving macromolecular structures and dynamics. This article is part of a Special Issue entitled "Recent developments of molecular dynamics".

Current status of protein force fields for molecular dynamics simulations

The current status of classical force fields for proteins is reviewed. These include additive force fields as well as the latest developments in the Drude and AMOEBA polarizable force fields. Parametrization strategies developed specifically for the Drude force field are described and compared with the additive CHARMM36 force field. Results from molecular simulations of proteins and small peptides are summarized to illustrate the performance of the Drude and AMOEBA force fields.

The CHARMM-TURBOMOLE interface for efficient and accurate QM/MM molecular dynamics, free energies, and excited state properties

The quantum mechanical (QM)/molecular mechanical (MM) interface between Chemistry at HARvard Molecular Mechanics (CHARMM) and TURBOMOLE is described. CHARMM provides an extensive set of simulation algorithms, like molecular dynamics (MD) and free energy perturbation, and support for mature nonpolarizable and Drude polarizable force fields. TURBOMOLE provides fast QM calculations using density functional theory or wave function methods and excited state properties. CHARMM-TURBOMOLE is well-suited for extended QM/MM MD simulations using first principles methods with large (triple-ζ) basis sets. We demonstrate these capabilities with a QM/MM simulation of Mg(2+) (aq), where the MM outer sphere water molecules are represented using the SWM4-NDP Drude polarizable force field and the ion and inner coordination sphere are represented using QM PBE, PBE0, and MP2 methods. The relative solvation free energies of Mg(2+) and Zn(2+) were calculated using thermodynamic integration. We also demonstrate the features for excited state properties. We calculate the time-averaged solution absorption spectrum of indole, the emission spectrum of the indole 1La excited state, and the electronic circular dichroism spectrum of an oxacepham.

All-atom polarizable force field for DNA based on the classical Drude oscillator model

Presented is a first generation atomistic force field (FF) for DNA in which electronic polarization is modeled based on the classical Drude oscillator formalism. The DNA model is based on parameters for small molecules representative of nucleic acids, including alkanes, ethers, dimethylphosphate, and the nucleic acid bases and empirical adjustment of key dihedral parameters associated with the phosphodiester backbone, glycosidic linkages, and sugar moiety of DNA. Our optimization strategy is based on achieving a compromise between satisfying the properties of the underlying model compounds in the gas phase targeting quantum mechanical (QM) data and reproducing a number of experimental properties of DNA duplexes in the condensed phase. The resulting Drude FF yields stable DNA duplexes on the 100-ns time scale and satisfactorily reproduce (1) the equilibrium between A and B forms of DNA and (2) transitions between the BI and BII substates of B form DNA. Consistency with the gas phase QM data for the model compounds is significantly better for the Drude model as compared to the CHARMM36 additive FF, which is suggested to be due to the improved response of the model to changes in the environment associated with the explicit inclusion of polarizability. Analysis of dipole moments associated with the nucleic acid bases shows the Drude model to have significantly larger values than those present in CHARMM36, with the dipoles of individual bases undergoing significant variations during the MD simulations. Additionally, the dipole moment of water was observed to be perturbed in the grooves of DNA.

Balancing the interactions of ions, water, and DNA in the Drude polarizable force field

Recently we presented a first-generation all-atom Drude polarizable force field for DNA based on the classical Drude oscillator model, focusing on optimization of key dihedral angles followed by extensive validation of the force field parameters. Presently, we describe the procedure for balancing the electrostatic interactions between ions, water, and DNA as required for development of the Drude force field for DNA. The proper balance of these interactions is shown to impact DNA stability and subtler conformational properties, including the conformational equilibrium between the BI and BII states, and the A and B forms of DNA. The parametrization efforts were simultaneously guided by gas-phase quantum mechanics (QM) data on small model compounds and condensed-phase experimental data on the hydration and osmotic properties of biologically relevant ions and their solutions, as well as theoretical predictions for ionic distribution around DNA oligomer. In addition, fine-tuning of the internal base parameters was performed to obtain the final DNA model. Notably, the Drude model is shown to more accurately reproduce counterion condensation theory predictions of DNA charge neutralization by the condensed ions as compared to the CHARMM36 additive DNA force field, indicating an improved physical description of the forces dictating the ionic solvation of DNA due to the explicit treatment of electronic polarizability. In combination with the polarizable DNA force field, the availability of Drude polarizable parameters for proteins, lipids, and carbohydrates will allow for simulation studies of heterogeneous biological systems.

Polarizable empirical force field for hexopyranose monosaccharides based on the classical Drude oscillator

A polarizable empirical force field based on the classical Drude oscillator is presented for the hexopyranose form of selected monosaccharides. Parameter optimization targeted quantum mechanical (QM) dipole moments, solute-water interaction energies, vibrational frequencies, and conformational energies. Validation of the model was based on experimental data on crystals, densities of aqueous-sugar solutions, diffusion constants of glucose, and rotational preferences of the exocylic hydroxymethyl of d-glucose and d-galactose in aqueous solution as well as additional QM data. Notably, the final model involves a single electrostatic model for all sixteen diastereomers of the monosaccharides, indicating the transferability of the polarizable model. The presented parameters are anticipated to lay the foundation for a comprehensive polarizable force field for saccharides that will be compatible with the polarizable Drude parameters for lipids and proteins, allowing for simulations of glycolipids and glycoproteins.

Molecular mechanics

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

Force Field for Peptides and Proteins based on the Classical Drude Oscillator

Presented is a polarizable force field based on a classical Drude oscillator framework, currently implemented in the programs CHARMM and NAMD, for modeling and molecular dynamics (MD) simulation studies of peptides and proteins. Building upon parameters for model compounds representative of the functional groups in proteins, the development of the force field focused on the optimization of the parameters for the polypeptide backbone and the connectivity between the backbone and side chains. Optimization of the backbone electrostatic parameters targeted quantum mechanical conformational energies, interactions with water, molecular dipole moments and polarizabilities and experimental condensed phase data for short polypeptides such as (Ala)₅. Additional optimization of the backbone φ, ψ conformational preferences included adjustments of the tabulated two-dimensional spline function through the CMAP term. Validation of the model included simulations of a collection of peptides and proteins. This 1^st generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns timescale in explicit solvent MD simulations. The Drude model typically yields larger RMS differences as compared to the additive CHARMM36 force field (C36) and shows additional flexibility as compared to the additive model. Comparison with NMR chemical shift data shows a small degradation of the polarizable model with respect to the additive, though the level of agreement may be considered satisfactory, while for residues shown to have significantly underestimated S² order parameters in the additive model, improvements are calculated with the polarizable model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have significantly larger values than those present in C36, with the dipole moments of the peptide backbone enhanced to a greater extent in sheets versus helices and the dipoles of individual moieties observed to undergo significant variations during the MD simulations. Although there are still some limitations, the presented model, termed Drude-2013, is anticipated to yield a molecular picture of peptide and protein structure and function that will be of increased physical validity and internal consistency in a computationally accessible fashion.

Polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator

A polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator is presented. The model is optimized with an emphasis on the transferability of the developed parameters among molecules of different sizes in this series and on the condensed-phase properties validated against experimental data. The importance of the explicit treatment of electronic polarizability in empirical force fields is demonstrated in the cases of this series of molecules with vicinal hydroxyl groups that can form cooperative intra- and intermolecular hydrogen bonds. Compared to the CHARMM additive force field, improved treatment of the electrostatic interactions avoids overestimation of the gas-phase dipole moments resulting in significant improvement in the treatment of the conformational energies and leads to the correct balance of intra- and intermolecular hydrogen bonding of glycerol as evidenced by calculated heat of vaporization being in excellent agreement with experiment. Computed condensed phase data, including crystal lattice parameters and volumes and densities of aqueous solutions are in better agreement with experimental data as compared to the corresponding additive model. Such improvements are anticipated to significantly improve the treatment of polymers in general, including biological macromolecules.

Kirkwood-Buff analysis of aqueous N-methylacetamide and acetamide solutions modeled by the CHARMM additive and Drude polarizable force fields

Kirkwood-Buff analysis was performed on aqueous solutions of N-methylacetamide and acetamide using the Chemistry at HARvard Molecular Mechanics additive and Drude polarizable all-atom force fields. Comparison of a range of properties with experimental results, including Kirkwood-Buff integrals, excess coordination numbers, solution densities, partial molar values, molar enthalpy of mixing, showed both models to be well behaved at higher solute concentrations with the Drude model showing systematic improvement at lower solution concentrations. However, both models showed difficulties reproducing experimental activity derivatives and the excess Gibbs energy, with the Drude model performing slightly better. At the molecular level, the improved agreement of the Drude model at low solute concentrations is due to increased structure in the solute-solute and solute-solvent interactions. The present results indicate that the explicit inclusion of electronic polarization leads to improved modeling of dilute solutions even when those properties are not included as target data during force field optimization.

CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side-chain amino- and methyl-containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ1 and χ2 dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs.

Matching of additive and polarizable force fields for multiscale condensed phase simulations

Inclusion of electronic polarization effects is one of the key aspects in which the accuracy of current biomolecular force fields may be improved. The principal drawback of such approaches is the computational cost, which typically ranges from 3 - 10 times that of the equivalent additive model, and may be greater for more sophisticated treatments of polarization or other many-body effects. Here, we present a multiscale approach which may be used to enhance the sampling in simulations with polarizable models, by using the additive model as a tool to explore configuration space. We use a method based on information theory to determine the charges for an additive model that has optimal overlap with the polarizable one, and we demonstrate the feasibility of enhancing sampling via a hybrid replica exchange scheme for several model systems. An additional advantage is that, in the process, we obtain a systematic method for deriving charges for an additive model that will be the natural complement to its polarizable parent. The additive charges are found by an effective coarse-graining of the polarizable force field, rather than by ad hoc procedures.

Charge sensitivity approach to mutual polarization of reactants: molecular mechanics perspective

Charge sensitivity analysis (CSA) in force-field atoms resolution was applied to describe the mutual polarization of reactants as well as charge-transfer (CT) effects. An inclusion complex of β-cyclodextrin with salicylic acid was used as a model system. Three CSA models were taken into account and verified on a Born–Oppenheimer molecular dynamics (BOMD) trajectory. The models differed in terms of the equilibrium conditions imposed on the system. It was demonstrated that mutual polarization is an important source of stabilization, in contrast to the results obtained from static charge calculations. The energy lowering induced by CT was small and comparable to the CT stabilization that occurs in hydrogen-bonded systems. All models correctly described the main topological features of the BOMD energy surface. CSA in force-field atoms resolution qualitatively reproduced the charge reorganization accompanying hydrogen-bond formation. It was shown that CSA parameters are very sensitive to the bond formation process, which suggests that they could be applied in reactive force fields as detectors of newly formed chemical bonds.

Figure

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first-order Fuzzy-Border continuum solvation model

We have computed pK(a) values for 11 substituted phenol compounds using the continuum Fuzzy-Border (FB) solvation model. Hydration energies for 40 other compounds, including alkanes, alkenes, alkynes, ketones, amines, alcohols, ethers, aromatics, amides, heterocycles, thiols, sulfides, and acids have been calculated. The overall average unsigned error in the calculated acidity constant values was equal to 0.41 pH units and the average error in the solvation energies was 0.076 kcal/mol. We have also reproduced pK(a) values of propanoic and butanoic acids within about 0.1 pH units from the experimental values by fitting the solvation parameters for carboxylate ion carbon and oxygen atoms. The FB model combines two distinguishing features. First, it limits the amount of noise which is common in numerical treatment of continuum solvation models by using fixed-position grid points. Second, it uses either second- or first-order approximation for the solvent polarization, depending on a particular implementation. These approximations are similar to those used for solute and explicit solvent fast polarization treatment which we developed previously. This article describes results of using the first-order technique. This approximation places the presented methodology between the Generalized Born and Poisson-Boltzmann continuum solvation models with respect to their accuracy of reproducing the many-body effects in modeling a continuum solvent.

Recent Developments and Applications of the CHARMM force fields

Empirical force fields commonly used to describe the condensed phase properties of complex systems such as biological macromolecules are continuously being updated. Improvements in quantum mechanical (QM) methods used to generate target data, availability of new experimental target data, incorporation of new classes of compounds and new theoretical developments (eg. polarizable methods) make force-field development a dynamic domain of research. Accordingly, a number of improvements and extensions of the CHARMM force fields have occurred over the years. The objective of the present review is to provide an up-to-date overview of the CHARMM force fields. A limited presentation on the historical aspects of force fields will be given, including underlying methodologies and principles, along with a brief description of the strategies used for parameter development. This is followed by information on the CHARMM additive and polarizable force fields, including examples of recent applications of those force fields.