CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.     

Bond detectors for molecular dynamics simulations,Part I: Hydrogen bonds

Charge sensitivity analysis in AMBER force‐field resolution has been used in quest for detectors of hydrogen bonds (HBs). The process of HB formation was investigated on ab initio classical trajectories (B3LYP/6‐31G*) of different nucleobase pairs. Several charge sensitivities, namely: electronegativity, hardness, Fukui function (FF), and polarization matrix, were analyzed. The global and constrained equilibria were considered. It was demonstrated that FF indices and polarization matrix elements are good detectors of HB formation. © 2013 Wiley Periodicals, Inc.     

A polarizable,charge transfer model of water using the drude oscillator

The transfer of small amounts of charge between neighboring particles can be a significant part of interactions among particles. A model is developed for treating charge transfer (CT) combined with the Drude model for polarizability to create an efficient model for liquid water which includes both CT and polarizability. The model is shown to be accurate for a variety of liquid properties, including the density as a function of temperature and the dielectric constant. A new model for water with CT and polarization is developed and applied to the liquid. The inclusion of CT increases the accuracy of many properties, like the density as a function of temperature, indicating the importance of charge redistribution as induced by other particles. © 2016 Wiley Periodicals, Inc.     

An efficient parallelization scheme for molecular dynamics simulations with many-body, flexible, polarizable empirical potentials: application to water

An efficient parallelization scheme for classical molecular dynamics simulations with flexible, polarizable empirical potentials is presented. It is based on the standard Ewald summation technique to handle the long-range electrostatic and induction interactions. The algorithm for this parallelization scheme is designed for systems containing several thousands of polarizable sites in the simulation box. Its performance is evaluated during molecular dynamics simulations under periodic boundary conditions with unit cell sizes ranging from 128 to 512 molecules employing two flexible polarizable water models [DC(F) and TTM2.1-F] containing 1 and 3 polarizable sites, respectively. The time-to-solution for these two polarizable models is compared with the one for a flexible, pairwise-additive water model (TIP4F). The benchmarks were performed on both shared and distributed memory platforms. As a result of the efficient calculation of the induced dipole moments, a superlinear scaling as a function of the number of the processors is observed. To the best of our knowledge, this is the first reported results of parallel scaling and performance for simulations of liquid water with a polarizable potential under periodic boundary conditions.     

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.     

Paramfit: Automated optimization of force field parameters for molecular dynamics simulations

The generation of bond, angle, and torsion parameters for classical molecular dynamics force fields typically requires fitting parameters such that classical properties such as energies and gradients match precalculated quantum data for structures that scan the value of interest. We present a program, Paramfit, distributed as part of the AmberTools software package that automates and extends this fitting process, allowing for simplified parameter generation for applications ranging from single molecules to entire force fields. Paramfit implements a novel combination of a genetic and simplex algorithm to find the optimal set of parameters that replicate either quantum energy or force data. The program allows for the derivation of multiple parameters simultaneously using significantly fewer quantum calculations than previous methods, and can also fit parameters across multiple molecules with applications to force field development. Paramfit has been applied successfully to systems with a sparse number of structures, and has already proven crucial in the development of the Assisted Model Building with Energy Refinement Lipid14 force field. © 2014 Wiley Periodicals, Inc.     

Molecular dynamics simulation of hydrated DPPC monolayers using charge equilibration force fields

We present results of molecular dynamics simulations of a model DPPC-water monolayer using charge equilibration (CHEQ) force fields, which explicitly account for electronic polarization in a classical treatment of intermolecular interactions. The surface pressure, determined as the difference between the monolayer and pure water surface tensions at 323 K, is predicted to be 22.92 ±1.29 dyne/cm, just slightly below the broad range of experimental values reported for this system. The surface tension for the DPPC-water monolayer is predicted to be 42.35 ±1.16 dyne/cm, in close agreement with the experimentally determined value of 40.9 dyne/cm. This surface tension is also consistent with the value obtained from DPPC monolayer simulations using state-of-the-art nonpolarizable force fields. The current results of simulations predict a monolayer-water potential difference relative to the pure water-air interface of 0.64 ±0.02 Volts, an improved prediction compared to the fixed-charge CHARMM27 force field, yet still overestimating the experimental range of 0.3 to 0.45 Volts. As the charge equilibration model is a purely charge-based model for polarization, the current results suggest that explicitly modeled polarization effects can offer improvements in describing interfacial electrostatics in such systems.     

Molecular dynamics simulations of liquid methanol and methanol-water mixtures with polarizable models

A polarizable model for simulation of liquid methanol, compatible with the COS/G2 water model, has been developed using the Charge-on-Spring (COS) technique. The model consists of three point charges, with one polarizable center on the oxygen atom. The Lennard-Jones parameters on the oxygen atom together with the molecular polarizability were varied to reproduce the experimental heat of vaporization and density of liquid methanol at ambient conditions. We examined the energies of various methanol dimers in the gas phase and compared them with values obtained from ab initio calculations. The model was then used to study the thermodynamic, dynamic, structural, and dielectric properties of liquid methanol as well as of a methanol-water mixture. A microscopic picture of the structure of pure liquid methanol and of the methanol-water mixture is provided. Good agreement was found between the results from our model simulations and available experimental and ab initio calculation data. In particular, the experimental dielectric permittivity of 32 could be reproduced, which had been shown to be difficult when using nonpolarizable models.     

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations

A first-generation fluctuating charge (FQ) force field to be ultimately applied for protein simulations is presented. The electrostatic model parameters, the atomic hardnesses, and electronegativities, are parameterized by fitting to DFT-based charge responses of small molecules perturbed by a dipolar probe mimicking a water dipole. The nonbonded parameters for atoms based on the CHARMM atom-typing scheme are determined via simultaneously optimizing vacuum water-solute geometries and energies (for a set of small organic molecules) and condensed phase properties (densities and vaporization enthalpies) for pure bulk liquids. Vacuum solute-water geometries, specifically hydrogen bond distances, are fit to 0.19 A r.m.s. error, while dimerization energies are fit to 0.98 kcal/mol r.m.s. error. Properties of the liquids studied include bulk liquid structure and polarization. The FQ model does indeed show a condensed phase effect in the shifting of molecular dipole moments to higher values relative to the gas phase. The FQ liquids also appear to be more strongly associated, in the case of hydrogen bonding liquids, due to the enhanced dipolar interactions as evidenced by shifts toward lower energies in pair energy distributions. We present results from a short simulation of NMA in bulk TIP4P-FQ water as a step towards simulating solvated peptide/protein systems. As expected, there is a nontrivial dipole moment enhancement of the NMA (although the quantitative accuracy is difficult to assess). Furthermore, the distribution of dipole moments of water molecules in the vicinity of the solutes is shifted towards larger values by 0.1-0.2 Debye in keeping with previously reported work.     

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.     

Assessment of biomolecular force fields for molecular dynamics simulations in a protein crystal

Different biomolecular force fields (OPLS‐AA, AMBER03, and GROMOS96) in conjunction with SPC, SPC/E and TIP3P water models are assessed for molecular dynamics simulations in a tetragonal lysozyme crystal. The root mean square deviations for the C_a atoms of lysozymes are about 0.1 to 0.2 nm from OPLS‐AA and AMBER03, smaller than 0.4 nm from GROMOS96. All force fields exhibit similar pattern in B‐factors, whereas OPLS‐AA and AMBER03 accurately reproduce experimental measurements. Despite slight variations, the primary secondary structures are well conserved using different force fields. Water diffusion in the crystal is approximately ten‐fold slower than in bulk phase. The directional and average water diffusivities from OPLS‐AA and AMBER03 along with SPC/E model match fairly well with experimental data. Compared to GROMOS96, OPLS‐AA and AMBER03 predict larger hydrophilic solvent‐accessible surface area of lysozyme, more hydrogen bonds between lysozyme and water, and higher percentage of water in hydration shell. SPC, SPC/E and TIP3P water models have similar performance in most energetic and structural properties, but SPC/E outperforms in water diffusion. While all force fields overestimate the mobility and electrical conductivity of NaCl, a combination of OPLS‐AA for lysozyme and the Kirkwood‐Buff model for ions is superior to others. As attributed to the steric restraints and surface interactions, the mobility and conductivity in the crystal are reduced by one to two orders of magnitude from aqueous solution. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

CHARMM force field and molecular dynamics simulations of protonated polyethylenimine

As a gene delivery vector, polyethylenimine (PEI) shows one of the highest transfection efficiencies, while effectively protecting DNA from enzyme degradation. The distinctive charge pattern of protonated PEI is widely considered responsible for fundamental process such as DNA condensation into PEI/DNA polyplexes (which are able to enter cells via endocytosis), proton sponge effect (which triggers the release of polyplexes from endosome), and release of DNA from polyplexes (to be further processed inside the nucleus). Our investigations are largely motivated by the crucial need for a realistic molecular mechanics force field (FF) for PEI, and, accordingly, we focus on two major issues: (1) development of a new atomistic (CHARMM) FF for PEI in different protonation states, rigorously derived from high‐quality ab initio calculations performed on model polymers, and (2) molecular dynamics investigations of solvated PEI, providing a detailed picture of the dynamic structuring thereof in dependence on their size and protonation state. The modeled PEI chains are essentially described in terms of gyration radius, end‐to‐end distance, persistence length, radial distribution functions, coordination numbers, and diffusion coefficients. They turn out to be more rigid than in other computational studies and we find diffusion coefficients in fair agreement with experimental data. The developed atomistic FF proves adequate for the realistic modeling of the size and protonation behavior of linear PEI, either as individual chains or composing polyplexes. © 2017 Wiley Periodicals, Inc.     

Charge distributions for molecular dynamics simulations from self-consistent polarization method

Partial atomic charges are important force field parameters. They are usually computed by applying quantum-chemical calculations and the assumed population scheme. In this study polarization consistent scheme of deriving a charge distribution inside solute molecule is proposed. The environment effect is explicitly taken into account by distributing solvent molecules around the solute target. The performed analysis includes a few computational schemes (HF, MP2, B3LYP, and M026X), basis sets (cc-pvnz, n = 2, 3, …, 6), and electrostatically derived charge distributions (KS, CHELP, CHELPG, and HLY). It is demonstrated that the environment effect is very important and cannot be disregarded. The second solvation shell should be included to achieve the charge convergence. Huge corrections to charge distribution are due to induction and dispersion. The B3LYP/cc-pvqz level of theory is recommended for deriving the charges within self-consistent polarization scheme.     

FAMUSAMM: An algorithm for rapid evaluation of electrostatic interactions in molecular dynamics simulations

Within molecular dynamics simulations of protein–solvent systems the exact evaluation of long-range Coulomb interactions is computationally demanding and becomes prohibitive for large systems. Conventional truncation methods circumvent that computational problem, but are hampered by serious artifacts concerning structure and dynamics of the simulated systems. To avoid these artifacts we have developed an efficient and yet sufficiently accurate approximation scheme which combines the structure-adapted multipole method (SAMM) [C. Niedermeier and P. Tavan, J. Chem. Phys., 101 , 734 (1994)] with a multiple-time-step method. The computational effort for MD simulations required within our fast multiple-time-step structure-adapted multipole method (FAMUSAMM) scales linearly with the number of particles. For a system with 36,000 atoms we achieve a computational speed-up by a factor of 60 as compared with the exact evaluation of the Coulomb forces. Extended test simulations show that the applied approximations do not seriously affect structural or dynamical properties of the simulated systems. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1729–1749, 1997     

Force-field modeling through quantum mechanical calculations: molecular dynamics simulations of a nematogenic molecule in its condensed phases

Interaction energy of the 4-n-pentyloxy-4'-cyanobiphenyl (5OCB) dimer is computed at MP2 level, for many geometrical arrangements using the Fragmentation Reconstruction Method (FRM). DFT calculations are performed for a number of geometries of the monomer. The resulting database is used to parameterize an atomistic intra- and inter-molecular force-field suitable for classical bulk simulations. Several structural and dynamical properties in 5OCB isotropic and liquid crystalline phases are computed from molecular dynamics simulation mainly in the NPT ensemble. Lengthy runs (more than 70 ns) and large sample sizes (up to 806 molecules) were used to determine the nematic to isotropic transition temperature up to a precision of few K. Good agreement was found in most of the investigated properties, thus validating the accuracy of the proposed model potential, only derived by quantum mechanical calculations.     

Importance of explicit smeared lone‐pairs in anisotropic polarizable molecular mechanics. Torture track angular tests for exchange‐repulsion and charge transfer contributions

A correct representation of the short‐range contributions such as exchange‐repulsion (E _rep) and charge‐transfer (E _ct) is essential for the soundness of separable, anisotropic polarizable molecular mechanics potentials. Within the context of the SIBFA procedure, this is aimed at by explicit representations of lone pairs in their expressions. It is necessary to account for their anisotropic behaviors upon performing not only in‐plane, but also out‐of‐plane, variations of a probe molecule or cation interacting with a target molecule or molecular fragment. Thus, E _rep and E _ct have to reproduce satisfactorily the corresponding anisotropies of their quantum chemical (QC) counterparts. A significant improvement of the out‐of‐plane dependencies was enabled when the sp² and sp localized lone‐pairs are, even though to a limited extent, delocalized on both sides of the plane, above and below the atom bearer but at the closely similar angles as the in‐plane lone pair. We report calibration and validation tests on a series of monoligated complexes of a probe Zn(II) cation with several biochemically relevant ligands. Validations are then performed on several polyligated Zn(II) complexes found in the recognition sites of Zn‐metalloproteins. Such calibrations and validations are extended to representative monoligated and polyligated complexes of Mg(II) and Ca(II). It is emphasized that the calibration of all three cations was for each ΔE contribution done on a small training set bearing on a limited number of representative N , O , and S monoligated complexes. Owing to the separable nature of ΔE , a secure transferability is enabled to a diversity of polyligated complexes. For these the relative errors with respect to the target ΔE (QC) values are generally < 3%. Overall, the article proposes a full set of benchmarks that could be useful for force field developers. © 2017 Wiley Periodicals, Inc.     

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.