Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.     

Estimating and modeling charge transfer from the SAPT induction energy

Recent studies using quantum mechanics energy decomposition methods, for example, SAPT and ALMO, have revealed that the charge transfer energy may play an important role in short ranged inter‐molecular interactions, and have a different distance dependence comparing with the polarization energy. However, the charge transfer energy component has been ignored in most current polarizable or non‐polarizable force fields. In this work, first, we proposed an empirical decomposition of SAPT induction energy into charge transfer and polarization energy that mimics the regularized SAPT method (ED‐SAPT). This empirical decomposition is free of the divergence issue, hence providing a good reference for force field development. Then, we further extended this concept in the context of AMOEBA polarizable force field, proposed a consistent approach to treat the charge transfer phenomenon. Current results show a promising application of this charge transfer model in future force field development. © 2017 Wiley Periodicals, Inc.     

Empirical force fields for biological macromolecules: overview and issues

Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.     

Polarizable empirical force field for sulfur‐containing compounds based on the classical Drude oscillator model

Condensed‐phase computational studies of molecules using molecular mechanics approaches require the use of force fields to describe the energetics of the systems as a function of structure. The advantage of polarizable force fields over nonpolarizable (or additive) models lies in their ability to vary their electronic distribution as a function of the environment. Toward development of a polarizable force field for biological molecules, parameters for a series of sulfur‐containing molecules are presented. Parameter optimization was performed to reproduce quantum mechanical and experimental data for gas phase properties including geometries, conformational energies, vibrational spectra, and dipole moments as well as for condensed phase properties such as heats of vaporization, molecular volumes, and free energies of hydration. Compounds in the training set include methanethiol, ethanethiol, propanethiol, ethyl methyl sulfide, and dimethyl disulfide. The molecular volumes and heats of vaporization are in good accordance with experimental values, with the polarizable model performing better than the CHARMM22 nonpolarizable force field. Improvements with the polarizable model were also obtained for molecular dipole moments and in the treatment of intermolecular interactions as a function of orientation, in part due to the presence of lone pairs and anisotropic atomic polarizability on the sulfur atoms. Significant advantage of the polarizable model was reflected in calculation of the dielectric constants, a property that CHARMM22 systematically underestimates. The ability of this polarizable model to accurately describe a range of gas and condensed phase properties paves the way for more accurate simulation studies of sulfur‐containing molecules including cysteine and methionine residues in proteins. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Binding structures of tri‐N‐acetyl‐β‐glucosamine in hen egg white lysozyme using molecular dynamics with a polarizable force field

Lysozyme is a well‐studied enzyme that hydrolyzes the β‐(1,4)‐glycosidic linkage of N‐acetyl‐β‐glucosamine (NAG)_n oligomers. The active site of hen egg‐white lysozyme (HEWL) is believed to consist of six subsites, A‐F that can accommodate six sugar residues. We present studies exploring the use of polarizable force fields in conjunction with all‐atom molecular dynamics (MD) simulations to analyze binding structures of complexes of lysozyme and NAG trisaccharide, (NAG)₃. MD trajectories are applied to analyze structures and conformation of the complex as well as protein–ligand interactions, including the hydrogen‐bonding network in the binding pocket. Two binding modes (ABC and BCD) of (NAG)₃ are investigated independently based on a fixed‐charge model and a polarizable model. We also apply molecular mechanics with generalized born and surface area (MM‐GBSA) methods based on MD using both nonpolarizable and polarizable force fields to compute binding free energies. We also study the correlation between root‐mean‐squared deviation and binding free energies of the wildtype and W62Y mutant; we find that for this prototypical system, approaches using the MD trajectories coupled with implicit solvent models are equivalent for polarizable and fixed‐charge models. © 2012 Wiley Periodicals, Inc.     

Implementation of extended Lagrangian dynamics in GROMACS for polarizable simulations using the classical Drude oscillator model

Explicit treatment of electronic polarization in empirical force fields used for molecular dynamics simulations represents an important advancement in simulation methodology. A straightforward means of treating electronic polarization in these simulations is the inclusion of Drude oscillators, which are auxiliary, charge‐carrying particles bonded to the cores of atoms in the system. The additional degrees of freedom make these simulations more computationally expensive relative to simulations using traditional fixed‐charge (additive) force fields. Thus, efficient tools are needed for conducting these simulations. Here, we present the implementation of highly scalable algorithms in the GROMACS simulation package that allow for the simulation of polarizable systems using extended Lagrangian dynamics with a dual Nosé–Hoover thermostat as well as simulations using a full self‐consistent field treatment of polarization. The performance of systems of varying size is evaluated, showing that the present code parallelizes efficiently and is the fastest implementation of the extended Lagrangian methods currently available for simulations using the Drude polarizable force field.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.     

Calculations on the force constants of triatomic group II metal halides

A comparison between various polarizable ion models for calculating bending force constants of linear MX₂ molecules is presented. A convergence test is applied to the models. Further, the contribution of an induced dipole-induced quadrupole interaction term to the force constant, is examined. The criteria for a useful comparison between calculated and experimental values of force constants are discussed.     

Molecular dynamics simulations using the drude polarizable force field on GPUs with OpenMM: Implementation,validation, and benchmarks

Presented is the implementation of the Drude force field in the open‐source OpenMM simulation package allowing for access to graphical processing unit (GPU) hardware. In the Drude model, electronic degrees of freedom are represented by negatively charged particles attached to their parent atoms via harmonic springs, such that extra computational overhead comes from these additional particles and virtual sites representing lone pairs on electronegative atoms, as well as the associated thermostat and integration algorithms. This leads to an approximately fourfold increase in computational demand over additive force fields. However, by making the Drude model accessible to consumer‐grade desktop GPU hardware it will be possible to perform simulations of one microsecond or more in less than a month, indicating that the barrier to employ polarizable models has largely been removed such that polarizable simulations with the classical Drude model are readily accessible and practical.     

Recent advances in sensing and biosensing with arrays of nanoelectrodes

This review deals with recent advances in the field of electrochemical sensing and biosensing with nanoelectrode ensembles (NEEs) and nanoelectrode arrays (NEAs), focusing mainly on articles published since 2015. At first, a brief introduction on the properties and possible advantages which characterize electroanalytical signals at the NEE/NEA is presented, followed by an overview on the most recent theoretical advances concerning the modeling of relevant electrochemical signals. Novel nanofabrication methods and nanoelectrode materials are discussed together with original (bio)funtionalization procedures, suitable to obtain more sensitive and reliable sensors. Advanced applications of NEE/NEA-based sensors in the biological and biomedical field are presented, including their integration with living cells and application for neurochemical studies. Advances, present limits, and prospects for research in the area are finally discussed. As far as future research trends are concerned, on the one hand, there is a need for development of theoretical models which take into account specific effects that can rule electrochemistry with arrays of nanosized electrodes, such as double layer and quantum mechanical effects. On the other hand, frontier studies concerning the application of the NEE/NEA to the biomedical and neurochemical fields can open new tracks both to fundamental knowledge and application.     

A polarizable empirical force field for molecular dynamics simulation of liquid hydrocarbons

Electronic polarizability is usually treated implicitly in molecular simulations, which may lead to imprecise or even erroneous molecular behavior in spatially electronically inhomogeneous regions of systems such as proteins, membranes, interfaces between compounds, or mixtures of solvents. The majority of available molecular force fields and molecular dynamics simulation software packages does not account explicitly for electronic polarization. Even the simplest charge‐on‐spring (COS) models have only been developed for few types of molecules. In this work, we report a polarizable COS model for cyclohexane, as this molecule is a widely used solvent, and for linear alkanes, which are also used as solvents, and are the precursors of lipids, amino acid side chains, carbohydrates, or nucleic acid backbones. The model is an extension of a nonpolarizable united‐atom model for alkanes that had been calibrated against experimental values of the density, the heat of vaporization and the Gibbs free energy of hydration for each alkane. The latter quantity was used to calibrate the parameters governing the interaction of the polarizable alkanes with water. Subsequently, the model was tested for other structural, thermodynamic, dielectric, and dynamic properties such as trans/gauche ratios, excess free energy, static dielectric permittivity, and self‐diffusion. A good agreement with the experimental data for a large set of properties for each considered system was obtained, resulting in a transferable set of polarizable force‐field parameters for CH₂, CH₃, and CH₄ moieties. © 2014 Wiley Periodicals, Inc.     

Comparing polarizable force fields to ab initio calculations reveals nonclassical effects in condensed phases

In a recent work [Giese and York J. Chem. Phys. 120, 9903 (2004)] showed that many-body force field models based solely on pairwise Coulomb screening cannot simultaneously reproduce both gas-phase and condensed-phase polarizability limits. In particular, polarizable force fields applied to bifurcated water chains have been demonstrated to be overpolarized with respect to ab initio methods. This behavior was ascribed to the neglect of coupling between many-body exchange and polarization. In the present article we reproduce those results using different ab initio levels of theory and a polarizable model based on the chemical-potential equalization principle. Moreover we show that, when hydrogen-bond (H-bond) forming systems are considered, an additional nonclassical effect, i.e., intermolecular charge transfer, must be taken into account. Such effect, contrarily to that of coupling between many-body exchange and polarization, makes classical polarizable force fields underpolarized. In the case of water at standard conditions, being H-bonded geometries much more probable than the bifurcated ones, intermolecular charge transfer is the dominant effect.     

How Good Are Coarse‐Grained Polymer Models? A Comparison for Atactic Polystyrene

This review provides an overview of the various coarse‐grained models that have been developed in the past few years for amorphous polystyrene. Different techniques to develop the force fields and different mapping schemes lead to models that perform differently depending on the properties investigated. This review collects and compares the models to guide the reader in the choice of the best model for the application of interest. It is expected that the central features of the various coarse‐graining procedures will also apply to systems other than polystyrene and that some of the conclusions about different coarse‐graining strategies are general.     

Structure and dynamics of the solvation of bovine pancreatic trypsin inhibitor in explicit water: a comparative study of the effects of solvent and protein polarizability

To isolate the effects of the inclusion of polarizability in the force field model on the structure and dynamics of the solvating water in differing electrostatic environments of proteins, we present the results of molecular dynamics simulations of the bovine pancreatic trypsin inhibitor (BPTI) in water with force fields that explicitly include polarization for both the protein and the water. We use three model potentials for water and two model potentials for the protein. Two of the water models and one of the protein models are polarizable. A total of six systems were simulated representing all combinations of these polarizable and nonpolarizable protein and water force fields. We find that all six systems behave in a similar manner in regions of the protein that are weakly electrostatic (either hydrophobic or weakly hydrophilic). However, in the vicinity of regions of the protein with relatively strong electrostatic fields (near positively or negatively charged residues), we observe that the water structure and dynamics are dependent on both the model of the protein and the model of the water. We find that a large part of the dynamical dependence can be described by small changes in the local environments of each region that limit the local density of non-hydrogen-bonded waters, precisely the water molecules that facilitate the dynamical relaxation of the water-water hydrogen bonds. We introduce a simple method for rescaling for this effect. When this is done, we are able to effectively isolate the influence of polarizability on the dynamics. We find that the solvating water's relaxation is most affected when both the protein and the water models are polarizable. However, when only one model (or neither) is polarizable, the relaxation is similar regardless of the models used.     

Molecular dynamics simulations of methane hydrate using polarizable force fields

Molecular dynamics simulations of methane hydrate have been carried out using the polarizable AMOEBA and COS/G2 force fields. Properties calculated include the temperature dependence of the lattice constant, the OC and OO radial distribution functions, and the vibrational spectra. Both the AMOEBA and COS/G2 force fields are found to successfully account for the available experimental data, with overall somewhat better agreement with experiment being found for the AMOEBA model. Comparison is made with previous results obtained using TIP4P and SPC/E effective two-body force fields and the polarizable TIP4P-FQ force field, which allows for in-plane polarization only. Significant differences are found between the properties calculated using the TIP4P-FQ model and those obtained using the other models, indicating an inadequacy of restricting explicit polarization to in-plane only.     

Polarizable empirical force field for alkanes based on the classical Drude oscillator model

Recent extensions of potential energy functions used in empirical force field calculations have involved the inclusion of electronic polarizability. To properly include this extension into a potential energy function it is necessary to systematically and rigorously optimize the associated parameters based on model compounds for which extensive experimental data are available. In the present work, optimization of parameters for alkanes in a polarizable empirical force field based on a classical Drude oscillator is presented. Emphasis is placed on the development of parameters for CH3, CH2, and CH moieties that are directly transferable to long chain alkanes, as required for lipids and other biomolecules. It is shown that a variety of quantum mechanical and experimental target data are reproduced by the polarizable model. Notable is the proper treatment of the dielectric constant of pure alkanes by the polarizable force field, a property essential for the accurate treatment of, for example, hydrophobic solvation in lipid bilayers. The present alkane force field will act as the basis for the aliphatic moieties in an extensive empirical force field for biomolecules that includes the explicit treatment of electronic polarizability.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

Ab initio based polarizable force field parametrization

Experimental and simulation studies of anion-water systems have pointed out the importance of molecular polarization for many phenomena ranging from hydrogen-bond dynamics to water interfaces structure. The study of such systems at molecular level is usually made with classical molecular dynamics simulations. Structural and dynamical features are deeply influenced by molecular and ionic polarizability, which parametrization in classical force field has been an object of long-standing efforts. Although when classical models are compared to ab initio calculations at condensed phase, it is found that the water dipole moments are underestimated by approximately 30%, while the anion shows an overpolarization at short distances. A model for chloride-water polarizable interaction is parametrized here, making use of Car-Parrinello simulations at condensed phase. The results hint to an innovative approach in polarizable force fields development, based on ab initio simulations, which do not suffer for the mentioned drawbacks. The method is general and can be applied to the modeling of different systems ranging from biomolecular to solid state simulations.