Understanding the dielectric properties of liquid amides from a polarizable force field

Force fields optimized against experimental data for large compound families using CombiFF: Validation considering non-target properties and polyfunctional compounds

The CombiFF scheme is a workflow for the automated calibration of force-field parameters against condensed-phase experimental data considering simultaneously entire classes of organic molecules. The main steps of this scheme are: (i) selection of a molecule family; (ii) enumeration of all isomers; (iii) query for experimental data; (iv) automatic construction of the molecular topologies; (v) iterative refinement of the force-field parameters considering the entire family. In two recent articles, CombiFF was applied to the design of GROMOS-compatible united-atom force fields for the saturated acyclic haloalkanes and for saturated acyclic compounds involving eight common chemical functional groups of oxygen and nitrogen. This calibration and the subsequent initial validation involved two limitations: (i) the experimental data considered was restricted to values for the pure-liquid density ρ_liq and the vaporization enthalpy ΔH_vap of the compounds; (ii) beyond monofunctional compounds, the training set only involved homo-polyhaloalkanes (possibly mixing halogen types) in the first study, and homo-polyfunctional compounds of the considered oxygen or nitrogen functional groups (no mixing of different group types) in the second one. The goal of this article is to further test the accuracy of CombiFF-generated force fields by extending the validation to: (i) nine additional properties that were not used as optimization targets (pure-liquid thermodynamic, dielectric and transport properties, as well as solvation properties); (ii) hetero-polyfunctional molecules that were not included in the calibration and initial validation sets. The results for the nine additional properties show good agreement with experiment, except for the shear viscosity and the dielectric permittivity. There, larger discrepancies are observed, likely due to the united-atom representation adopted for the aliphatic groups and to the implicit treatment of electronic polarization effects. The results for the hetero-polyfunctional molecules also show reasonable agreement with experiment in terms of the monitored properties.

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.

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.

Integration of Experimental Data and Use of Automated Fitting Methods in Developing Protein Force Fields

The development of accurate protein force fields has been the cornerstone of molecular simulations for the past 50 years. During this period, many lessons have been learned regarding the use of experimental target data and parameter fitting procedures. Here, we review recent advances in protein force field development. We discuss the recent emergence of polarizable force fields and the role of electronic polarization and areas in which additive force fields fall short. The use of automated fitting methods and the inclusion of additional experimental solution data during parametrization is discussed as a means to highlight possible routes to improve the accuracy of force fields even further.

How the Choice of Force-Field Affects the Stability and Self-Assembly Process of Supramolecular CTA Fibers

In recent years, computational methods have become an essential element of studies focusing on the self-assembly process. Although they provide unique insights, they face challenges, from which two are the most often mentioned in the literature: the temporal and spatial scale of the self-assembly. A less often mentioned issue, but not less important, is the choice of the force-field. The repetitive nature of the supramolecular structure results in many similar interactions. Consequently, even a small deviation in these interactions can lead to significant energy differences in the whole structure. However, studies comparing different force-fields for self-assembling systems are scarce. In this article, we compare molecular dynamics simulations for trifold hydrogen-bonded fibers performed with different force-fields, namely GROMOS, CHARMM General Force Field (CGenFF), CHARMM Drude, General Amber Force-Field (GAFF), Martini, and polarized Martini. Briefly, we tested the force-fields by simulating: (i) spontaneous self-assembly (none form a fiber within 500 ns), (ii) stability of the fiber (observed for CHARMM Drude, GAFF, MartiniP), (iii) dimerization (observed for GROMOS, GAFF, and MartiniP), and (iv) oligomerization (observed for CHARMM Drude and MartiniP). This system shows that knowledge of the force-field behavior regarding interactions in oligomer and larger self-assembled structures is crucial for designing efficient simulation protocols for self-assembling systems.

CHARMM-GUI Drude prepper for molecular dynamics simulation using the classical Drude polarizable force field

Explicit treatment of electronic polarizability in empirical force fields (FFs) represents an extension over a traditional additive or pairwise FF and provides a more realistic model of the variations in electronic structure in condensed phase, macromolecular simulations. To facilitate utilization of the polarizable FF based on the classical Drude oscillator model, Drude Prepper has been developed in CHARMM-GUI. Drude Prepper ingests additive CHARMM protein structures file (PSF) and pre-equilibrated coordinates in CHARMM, PDB, or NAMD format, from which the molecular components of the system are identified. These include all residues and patches connecting those residues along with water, ions, and other solute molecules. This information is then used to construct the Drude FF-based PSF using molecular generation capabilities in CHARMM, followed by minimization and equilibration. In addition, inputs are generated for molecular dynamics (MD) simulations using CHARMM, GROMACS, NAMD, and OpenMM. Validation of the Drude Prepper protocol and inputs is performed through conversion and MD simulations of various heterogeneous systems that include proteins, nucleic acids, lipids, polysaccharides, and atomic ions using the aforementioned simulation packages. Stable simulations are obtained in all studied systems, including 5 μs simulation of ubiquitin, verifying the integrity of the generated Drude PSFs. In addition, the ability of the Drude FF to model variations in electronic structure is shown through dipole moment analysis in selected systems. The capabilities and availability of Drude Prepper in CHARMM-GUI is anticipated to greatly facilitate the application of the Drude FF to a range of condensed phase, macromolecular systems.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Topology Automated Force-Field Interactions (TAFFI): A Framework for Developing Transferable Force Fields

Force-field development has undergone a revolution in the past decade with the proliferation of quantum chemistry based parametrizations and the introduction of machine learning approximations of the atomistic potential energy surface. Nevertheless, transferable force fields with broad coverage of organic chemical space remain necessary for applications in materials and chemical discovery where throughput, consistency, and computational cost are paramount. Here, we introduce a force-field development framework called Topology Automated Force-Field Interactions (TAFFI) for developing transferable force fields of varying complexity against an extensible database of quantum chemistry calculations. TAFFI formalizes the concept of atom typing and makes it the basis for generating systematic training data that maintains a one-to-one correspondence with force-field terms. This feature makes TAFFI arbitrarily extensible to new chemistries while maintaining internal consistency and transferability. As a demonstration of TAFFI, we have developed a fixed-charge force-field, TAFFI-gen, from scratch that includes coverage for common organic functional groups that is comparable to established transferable force fields. The performance of TAFFI-gen was benchmarked against OPLS and GAFF for reproducing several experimental properties of 87 organic liquids. The consistent performance of these force fields, despite their distinct origins, validates the TAFFI framework while also providing evidence of the representability limitations of fixed-charge force fields.

Preparing and Analyzing Polarizable Molecular Dynamics Simulations with the Classical Drude Oscillator Model

Molecular dynamics (MD) simulations performed with force fields that include explicit electronic polarization are becoming more prevalent in the field. The increasing emergence of these simulations is a result of continual refinement against a range of theoretical and empirical target data, optimization of software algorithms for higher performance, and availability of graphical processing unit hardware to further accelerate the simulations. Polarizable MD simulations are likely to be most impactful in biomolecular systems in which heterogeneous environments or unique microenvironments exist that would lead to inaccuracies in simulations performed with fixed-charge, nonpolarizable force fields. The further adoption of polarizable MD simulations will benefit from tutorial material that specifically addresses preparing and analyzing their unique features. In this chapter, we introduce common protocols for preparing routine biomolecular systems containing proteins, including both a globular protein in aqueous solvent and a transmembrane model peptide in a phospholipid bilayer. Details and example input files are provided for preparation of the simulation system using CHARMM, performing the simulations with OpenMM, and analyzing interesting dipole moment properties in CHARMM.

Further Optimization and Validation of the Classical Drude Polarizable Protein Force Field

The CHARMM Drude-2013 polarizable force field (FF) was developed to include the explicit treatment of induced electronic polarizability, resulting in a more accurate description of the electrostatic interactions in molecular dynamics (MD) simulations. While the Drude-2013 protein FF has shown success in improving the folding properties of α-helical peptides and to reproduce experimental observables in simulations up to 1 μs, some limitations were noted regarding the stability of β-sheet structures in simulations longer than 100 ns as well as larger deviations from crystal structures in simulations of a number of proteins compared to the additive CHARMM36 protein FF. The origin of the instability has been identified and appears to be primarily due to overestimated atomic polarizabilities and induced dipole-dipole interactions on the Cβ, Cγ, and Cδ side chain atoms. To resolve this and other issues, a number of aspects of the model were revisited, resulting in Drude-2019 protein FF. Backbone parameters were optimized targeting the conformational properties of the (Ala)5 peptide in solution along with gas phase properties of the alanine dipeptide. Dipeptides that contain N-acetylated and N'-methylamidated termini, excluding Gly, Pro, and Ala, were used as models to optimize the atomic polarizabilities and Thole screening factors on selected Cβ, Cγ, and Cδ carbons by targeting quantum mechanical (QM) dipole moments and molecular polarizabilities. In addition, to obtain better conformational properties, side chain χ1 and χ2 dihedral parameters were optimized targeting QM data for the respective side chain dipeptide conformations as well as Protein Data Bank survey data based on the χ1, χ2 sampling from Hamiltonian replica-exchange MD simulations of (Ala)4-X-(Ala)4 in solution, where X is the amino acid of interest. Further improvements include optimizing nonbonded interactions between charged residues to reproduce QM interaction energies of the charged-protein model compounds and experimental osmotic pressures. Validation of the optimized Drude protein FF includes MD simulations of a collection of peptides and proteins including β-sheet structures, as well as transmembrane ion channels. Results showed that the updated Drude-2019 protein FF yields smaller overall root-mean-square differences of proteins as compared to the additive CHARMM36m and Drude-2013 FFs as well as similar or improved agreement with experimental NMR properties, allowing for long time scale simulation studies of proteins and more complex biomolecular systems in conjunction with the remainder of the Drude polarizable FF.

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.

Pairwise-additive and polarizable atomistic force fields for molecular dynamics simulations of proteins

Protein force fields have been undergoing continual development since the first complete parameter sets were introduced nearly four decades ago. The functional forms that underlie these models have many common elements for the treatment of bonded and nonbonded forces, which are reviewed here. The most widely used force fields to date use a fixed-charge convention in which electronic polarization effects are treated via a mean-field approximation during partial charge assignment. Despite success in modeling folded proteins over many years, the fixed-charge assumption has limitations that cannot necessarily be overcome within their potential energy equations. To overcome these limitations, several force fields have recently been derived that explicitly treat electronic polarization effects with straightforward extensions of the potential energy functions used by nonpolarizable force fields. Here, we review the history of the most popular nonpolarizable force fields (AMBER, CHARMM, OPLS, and GROMOS) as well as studies that have validated them and applied them to studies of protein folding and misfolding. Building upon these force fields are more recent polarizable interaction potentials, including fluctuating charge models, POSSIM, AMOEBA, and the classical Drude oscillator. These force fields differ in their implementations but all attempt to model electronic polarization in a computationally tractable manner. Despite their recent emergence in the field of protein folding, several studies have already applied these polarizable models to challenging problems in this domain, including the role of polarization in folding free energies and sequence-specific effects on the stability of α-helical structures.

FFParam: Standalone package for CHARMM additive and Drude polarizable force field parametrization of small molecules

Accurate force-field (FF) parameters are key to reliable prediction of properties obtained from molecular modeling (MM) and molecular dynamics (MD) simulations. With ever-widening applicability of MD simulations, robust parameters need to be generated for a wider range of chemical species. The CHARMM General Force Field program (CGenFF, https://cgenff.umaryland.edu/) is a tool for obtaining initial parameters for a given small molecule based on analogy with the available CGenFF parameters. However, improvement of these parameters is often required and performing their optimization remains tedious and time consuming. In addition, tools for optimization of small molecule parameters in the context of the Drude polarizable FF are not yet available. To overcome these issues, the FFParam package has been designed to facilitate the parametrization process. The package includes a graphical user interface (GUI) created using Qt libraries. FFParam supports Gaussian and Psi4 for performing quantum mechanical calculations and CHARMM and OpenMM for MM calculations. A Monte Carlo simulated annealing (MCSA) algorithm has been implemented for automated fitting of partial atomic charge, atomic polarizabilities and Thole scale parameters. The LSFITPAR program is called for automated fitting of bonded parameters. Accordingly, FFParam provides all the features required for generation and analysis of CHARMM and Drude FF parameters for small molecules. FFParam-GUI includes a text editor, graph plotter, molecular visualization, and text to table converter to meet various requirements of the parametrization process. It is anticipated that FFParam will facilitate wider use of CGenFF as well as promote future use of the Drude polarizable FF.

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.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Solvation Free Energy Calculation Using a Fixed-Charge Model: Implicit and Explicit Treatments of the Polarization Effect

In this work, IPolQ-Mod charges and the reference potential scheme are used to calculate the solvation free energies of a set of organic molecules. Both methods could capture the phase transfer of a solute with accompanying polarization cost utilizing a fixed-charge model. The IPolQ-Mod charges, which are the average of two charge sets fitted in a vacuum state and a condensed phase, take account of the polarization effect implicitly. For the reference potential method, the quantum mechanics polarization corrections are calculated explicitly by thermodynamic perturbation. The polarization effect captured by the IPolQ-Mod charges is an approximation to that of the reference potential method theoretically. In the present study, the reference potential method shows a slight improvement over the classical restrained electrostatic potential (RESP) charges, which perform pretty well in predicting the solvation free energy. However, IPolQ-Mod(MP2) shows a poor agreement with the experimental data. Compared with IPolQ-Mod(MP2), IPolQ-Mod(M06-2X) or IPolQ-Mod(ωB97X) is found to give more appropriate prediction of the molecule's dipole and the solvation free energies calculated by IPolQ-Mod(M06-2X) or IPolQ-Mod(ωB97X) are more compatible with those of the RESP charges. If the other force field parameters remain unchanged, M06-2X or ωB97X is recommended to derive the IPolQ-Mod charges.

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 systematic approach to calibrate a transferable polarizable force field parameter set for primary alcohols

In this work, parameters are optimized for a charge-on-spring based polarizable force field for linear alcohols. We show that parameter transferability can be obtained using a systematic approach in which the effects of parameter changes on physico-chemical properties calculated from simulation are predicted. Our previously described QM/MM calculations are used to attribute condensed-phase polarizabilities, and starting from the non-polarizable GROMOS 53A5/53A6 parameter set, van der Waals and Coulomb interaction parameters are optimized to reproduce pure-liquid (thermodynamic, dielectric, and transport) properties, as well as hydration free energies. For a large set of models, which were obtained by combining small perturbations of 10 distinct parameters, values for pure-liquid properties of the series methanol to butanol were close to experiment. From this large set of models, we selected 34 models without special repulsive van der Waals parameters to distinguish between hydrogen-bonding and non-hydrogen-bonding atom pairs, to make the force field simple and transparent. © 2017 Wiley Periodicals, Inc.

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.

Mapping the Drude polarizable force field onto a multipole and induced dipole model

The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.

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.

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.

Protein folding, misfolding and aggregation: The importance of two-electron stabilizing interactions

Proteins associated with neurodegenerative diseases are highly pleiomorphic and may adopt an all-α-helical fold in one environment, assemble into all-β-sheet or collapse into a coil in another, and rapidly polymerize in yet another one via divergent aggregation pathways that yield broad diversity of aggregates’ morphology. A thorough understanding of this behaviour may be necessary to develop a treatment for Alzheimer’s and related disorders. Unfortunately, our present comprehension of folding and misfolding is limited for want of a physicochemical theory of protein secondary and tertiary structure. Here we demonstrate that electronic configuration and hyperconjugation of the peptide amide bonds ought to be taken into account to advance such a theory. To capture the effect of polarization of peptide linkages on conformational and H-bonding propensity of the polypeptide backbone, we introduce a function of shielding tensors of the C^α atoms. Carrying no information about side chain-side chain interactions, this function nonetheless identifies basic features of the secondary and tertiary structure, establishes sequence correlates of the metamorphic and pH-driven equilibria, relates binding affinities and folding rate constants to secondary structure preferences, and manifests common patterns of backbone density distribution in amyloidogenic regions of Alzheimer’s amyloid β and tau, Parkinson’s α-synuclein and prions. Based on those findings, a split-intein like mechanism of molecular recognition is proposed to underlie dimerization of Aβ, tau, αS and PrP^C, and divergent pathways for subsequent association of dimers are outlined; a related mechanism is proposed to underlie formation of PrP^Sc fibrils. The model does account for: (i) structural features of paranuclei, off-pathway oligomers, non-fibrillar aggregates and fibrils; (ii) effects of incubation conditions, point mutations, isoform lengths, small-molecule assembly modulators and chirality of solid-liquid interface on the rate and morphology of aggregation; (iii) fibril-surface catalysis of secondary nucleation; and (iv) self-propagation of infectious strains of mammalian prions.

Drude Polarizable Force Field for Molecular Dynamics Simulations of Saturated and Unsaturated Zwitterionic Lipids

Additive force fields are designed to account for induced electronic polarization in a mean-field average way, using effective empirical fixed charges. The limitation of this approximation is cause for serious concerns, particularly in the case of lipid membranes, where the molecular environment undergoes dramatic variations over microscopic length scales. A polarizable force field based on the classical Drude oscillator offers a practical and computationally efficient framework for an improved representation of electrostatic interactions in molecular simulations. Building on the first-generation Drude polarizable force field for the dipalmitoylphosphatidylcholine 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecule, the present effort was undertaken to improve this initial model and expand the force field to a wider range of phospholipid molecules. New lipids parametrized include dimyristoylphosphatidylcholine (DMPC), dilauroylphosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), dipalmitoylphosphatidylethanolamine (DPPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE). The iterative optimization protocol employed in this effort led to lipid models that achieve a good balance between reproducing quantum mechanical data on model compound representative of phospholipids and reproducing a range of experimental condensed phase properties of bilayers. A parametrization strategy based on a restrained ensemble-maximum entropy methodology was used to help accurately match the experimental NMR order parameters in the polar headgroup region. All the parameters were developed to be compatible with the remainder of the Drude polarizable force field, which includes water, ions, proteins, DNA, and selected carbohydrates.

Capturing Many-Body Interactions with Classical Dipole Induction Models

The nonadditive many-body interactions are significant for structural and thermodynamic properties of condensed phase systems. In this work we examined the many-body interaction energy of a large number of common organic/biochemical molecular clusters, which consist of 18 chemical species and cover nine common organic elements, using the Møller-Plesset perturbation theory to the second order (MP2) [ Møller et al. Phys. Rev. 1934 , 46 , 618 . ]. We evaluated the capability of Thole-based dipole induction models to capture the many-body interaction energy. Three models were compared: the original model and parameters used by the AMOEBA force field, a variation of this original model where the damping parameters have been reoptimized to MP2 data, and a third model where the damping function form applied to the permanent electric field is modified. Overall, we find the simple classical atomic dipole models are able to capture the 3- and 4-body interaction energy across a wide variety of organic molecules in various intermolecular configurations. With modified Thole models, it is possible to further improve the agreement with MP2 results. These models were also tested on systems containing metal/halogen ions to examine the accuracy and transferability. This work suggests that the form of damping function applied to the permanent electrostatic field strongly affects the distance dependence of polarization energy at short intermolecular separations.

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.

Assessing Spectral Simulation Protocols for the Amide I Band of Proteins

We present a benchmark study of spectral simulation protocols for the amide I band of proteins. The amide I band is widely used in infrared spectroscopy of proteins due to the large signal intensity, high sensitivity to hydrogen bonding, and secondary structural motifs. This band has, thus, proven valuable in many studies of protein structure-function relationships. We benchmark spectral simulation protocols using two common force fields in combination with several electrostatic mappings and coupling models. The results are validated against experimental linear absorption and two-dimensional infrared spectroscopy for three well-studied proteins. We find two-dimensional infrared spectroscopy to be much more sensitive to the simulation protocol than linear absorption and report on the best simulation protocols. The findings demonstrate that there is still room for ideas to improve the existing models for the amide I band of proteins.

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 all-atom additive force field for sphingomyelin: elucidation of hydrogen bonding and of positive curvature

The C36 CHARMM lipid force field has been extended to include sphingolipids, via a combination of high-level quantum mechanical calculations on small molecule fragments, and validation by extensive molecular dynamics simulations on N-palmitoyl and N-stearoyl sphingomyelin. NMR data on these two molecules from several studies in bilayers and micelles played a strong role in the development and testing of the force field parameters. Most previous force fields for sphingomyelins were developed before the availability of the detailed NMR data and relied on x-ray diffraction of bilayers alone for the validation; these are shown to be too dense in the bilayer plane based on published chain order parameter data from simulations and experiments. The present simulations reveal O-H:::O-P intralipid hydrogen bonding occurs 99% of the time, and interlipid N-H:::O=C (26-29%, depending on the lipid) and N-H:::O-H (17-19%). The interlipid hydrogen bonds are long lived, showing decay times of 50 ns, and forming strings of lipids, and leading to reorientational correlation time of nearly 100 ns. The spontaneous radius of curvature for pure N-palmitoyl sphingomyelin bilayers is estimated to be 43-100 Å, depending on the assumptions made in assigning a bending constant; this unusual positive curvature for a two-tailed neutral lipid is likely associated with hydrogen bond networks involving the NH of the sphingosine group.

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.

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

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