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     

Assessment of standard force field models against high‐quality ab initio potential curves for prototypes of π–π, CH/π, and SH/π interactions

Several popular force fields, namely, CHARMM, AMBER, OPLS‐AA, and MM3, have been tested for their ability to reproduce highly accurate quantum mechanical potential energy curves for noncovalent interactions in the benzene dimer, the benzene‐CH₄ complex, and the benzene‐H₂S complex. All of the force fields are semi‐quantitatively correct, but none of them is consistently reliable quantitatively. Re‐optimization of Lennard‐Jones parameters and symmetry‐adapted perturbation theory analysis for the benzene dimer suggests that better agreement cannot be expected unless more flexible functional forms (particularly for the electrostatic contributions) are employed for the empirical force fields. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

1H‐Azepine‐4‐amino‐4‐carboxylic Acid: A New α,α‐Disubstituted Ornithine Analogue Capable of Inducing Helix Conformations in Short Ala‐Aib Pentapeptides

A very efficient synthesis of orthogonally protected 1H‐azepine‐4‐amino‐4‐carboxylic acid, abbreviated as Azn, a conformationally restricted analogue of ornithine, was realized. It was obtained on a gram scale in good overall yield in five steps, three of which did not require isolation of the intermediates, starting from the readily available 1‐amino‐4‐oxo‐cyclohexane‐4‐carboxylic acid. Both enantiomers were used for the preparation of pentapeptide models containing Ala, Aib, and Azn. Conformational studies using both spectroscopic techniques (NMR, CD) and molecular dynamics on model 5‐mer peptides showed that the (R)‐Azn isomer possesses a marked helicogenic effect.     

CHARMM general force field: A force field for drug‐like molecules compatible with the CHARMM all‐atom additive biological force fields

The widely used CHARMM additive all‐atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug‐like molecules is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chemical groups present in biomolecules and drug‐like molecules, including a large number of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concentrating on an extensible force field. Statistics related to the quality of the parametrization with a focus on experimental validation are presented. Additionally, the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3‐phenoxymethylpyrrolidine will allow users to readily extend the force field to chemical groups that are not explicitly covered in the force field as well as add functional groups to and link together molecules already available in the force field. CGenFF thus makes it possible to perform “all‐CHARMM” simulations on drug‐target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Numerical Simulation of the Effect of Solvent Viscosity on the Motions of a β‐Peptide Heptamer

This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a β‐peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐(S,S)‐β³‐HAla(αMe)‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a β‐peptide on solvent viscosity has two regimes; a result that was observed in another computational study for α‐peptides.     

Reparameterizations of the χ Torsion and Lennard‐Jones σ Parameters Improve the Conformational Characteristics of Modified Uridines

The currently available force field parameters for modified RNA residues in AMBER show significant deviations in conformational properties from experimental observations. The examination of the transferability of the recently revised torsion parameters revealed that there was an overall improvement in the conformational properties for some of the modifications but the improvements were still insufficient in describing the sugar pucker preferences (J. Chem. Inf. Model. 2014, 54, 1129–1142). Here, we report an approach for the development and fine tuning of the AMBER force field parameters for 2‐thiouridine, 4‐thiouridine, and pseudouridine with diverse conformational preferences. The χ torsion parameters were reparameterized at the individual nucleoside level. The effect of combining the revised γ torsion parameter and modifying the Lennard‐Jones σ parameters were also tested by directly comparing the conformational preferences obtained from our extensive molecular dynamics simulations with those from experimental observations. © 2016 Wiley Periodicals, Inc.     

2,2′‐[(Disulfanediyl)bis{5‐[(1E)‐(2‐hydroxybenzylidene)amino]‐1,3‐thiazole‐4,2‐diyl}]diphenol: synthesis,crystal structure and calculation of molecular hyperpolarizability

The title Schiff base compound {systematic name: 2‐[5‐[(E )‐(2‐hydroxybenzylidene)amino]‐4‐(2‐{5‐[(E )‐(2‐hydroxybenzylidene)amino]‐2‐(2‐hydroxyphenyl)‐1,3‐thiazol‐4‐yl}disulfanyl)‐1,3‐thiazol‐2‐yl]phenol}, C₃₂H₂₂N₄O₄S₄, incorporating a disulfanediyl (dithio) linkage, was obtained from the condensation reaction between two equivalents of salicylaldehyde and one equivalent of dithiooxamide in dimethylformamide, and was characterized by elemental analysis, IR spectroscopic analysis and single‐crystal X‐ray diffraction. A one‐dimensional chain is formed along the b axis via double intermolecular C—H…S hydrogen bonds. The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energies and some related molecular parameters were calculated at the B3LYP/6‐311G(d,p) level of theory. The molecular hyperpolarizability was also calculated.     

Determination of side‐chain‐rotamer and side‐chain and backbone virtual‐bond‐stretching potentials of mean force from AM1 energy surfaces of terminally‐blocked amino‐acid residues,for coarse‐grained simulations of protein structure and folding. I. The method

In this and the accompanying article, we report the development of new physics‐based side‐chain‐rotamer and virtual‐bond‐deformation potentials which now replace the respective statistical potentials used so far in our physics‐based united‐reside UNRES force field for large‐scale simulations of protein structure and dynamics. In this article, we describe the methodology for determining the corresponding potentials of mean force (PMF's) from the energy surfaces of terminally‐blocked amino‐acid residues calculated with the AM1 quantum‐mechanical semiempirical method. The approach is based on minimization of the AM1 energy for fixed values of the angles λ for rotation of the peptide groups about the C^α ··· C^α virtual bonds, and for fixed values of the side‐chain dihedral angles χ, which formed a multidimensional grid. A harmonic‐approximation approach was developed to extrapolate from the energy at a given grid point to other points of the conformational space to compute the respective contributions to the PMF. To test the applicability of the harmonic approximation, the rotamer PMF's of alanine and valine obtained with this approach have been compared with those obtained by using a Metropolis Monte Carlo method. The PMF surfaces computed with the harmonic approximation are more rugged and have more pronounced minima than the MC‐calculated surfaces but the harmonic‐approximation‐and MC‐calculated PMF values are linearly correlated. The potentials derived with the harmonic approximation are, therefore, appropriate for UNRES for which the weights (scaling factors) of the energy terms are determined by force‐field optimization for foldability. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

All‐atom polarizable force field for DNA based on the classical drude oscillator model

Presented is a first generation atomistic force field (FF) for DNA in which electronic polarization is modeled based on the classical Drude oscillator formalism. The DNA model is based on parameters for small molecules representative of nucleic acids, including alkanes, ethers, dimethylphosphate, and the nucleic acid bases and empirical adjustment of key dihedral parameters associated with the phosphodiester backbone, glycosidic linkages, and sugar moiety of DNA. Our optimization strategy is based on achieving a compromise between satisfying the properties of the underlying model compounds in the gas phase targeting quantum mechanical (QM) data and reproducing a number of experimental properties of DNA duplexes in the condensed phase. The resulting Drude FF yields stable DNA duplexes on the 100‐ns time scale and satisfactorily reproduce (1) the equilibrium between A and B forms of DNA and (2) transitions between the BI and BII substates of B form DNA. Consistency with the gas phase QM data for the model compounds is significantly better for the Drude model as compared to the CHARMM36 additive FF, which is suggested to be due to the improved response of the model to changes in the environment associated with the explicit inclusion of polarizability. Analysis of dipole moments associated with the nucleic acid bases shows the Drude model to have significantly larger values than those present in CHARMM36, with the dipoles of individual bases undergoing significant variations during the MD simulations. Additionally, the dipole moment of water was observed to be perturbed in the grooves of DNA. © 2014 Wiley Periodicals, Inc.     

Strike a balance: optimization of backbone torsion parameters of AMBER polarizable force field for simulations of proteins and peptides

Based on the AMBER polarizable model (ff02), we have re-optimized the parameters related to the main-chain (Phi, Psi) torsion angles by fitting to the Boltzmann-weighted average quantum mechanical (QM) energies of the important regions (i.e., beta, P(II), alpha(R), and alpha(L) regions). Following the naming convention of the AMBER force field series, this release will be called ff02pol.rl The force field has been assessed both by energetic comparison against the QM data and by the replica exchange molecular dynamics simulations of short alanine peptides in water. For Ace-Ala-Nme, the simulated populations in the beta, P(II) and alpha(R) regions were approximately 30, 43, and 26%, respectively. For Ace-(Ala)(7)-Nme, the populations in these three regions were approximately 24, 49, and 26%. Both were in qualitative agreement with the NMR and CD experimental conclusions. In comparison with the previous force field, ff02pol.rl demonstrated good balance among these three important regions. The optimized torsion parameters, together with those in ff02, allow us to carry out simulations on proteins and peptides with the consideration of polarization.     

Polarizable simulations with second order interaction model (POSSIM) force field: Developing parameters for protein side‐chain analogues

A previously introduced polarizable simulations with second‐order interaction model (POSSIM) force field has been extended to include parameters for small molecules serving as models for peptide and protein side‐chains. Parameters have been fitted to permit reproducing many‐body energies, gas‐phase dimerization energies, and geometries and liquid‐phase heats of vaporization and densities. Quantum mechanical and experimental data have been used as the target for the fitting. The POSSIM framework combines accuracy of a polarizable force field and computational efficiency of the second‐order approximation of the full‐scale induced point dipole polarization formalism. The resulting parameters can be used for simulations of the parameterized molecules themselves or their analogues. In addition to this, these force field parameters are currently being used in further development of the POSSIM fast polarizable force field for proteins. © 2012 Wiley Periodicals, Inc.     

Update on phosphate and charged post‐translationally modified amino acid parameters in the GROMOS force field

In this study, we propose newly derived parameters for phosphate ions in the context of the GROMOS force field parameter sets. The non‐bonded parameters used up to now lead to a hydration free energy, which renders the dihydrogen phosphate ion too hydrophobic when compared to experimentally derived values, making a reparametrization of the phosphate moiety necessary. Phosphate species are of great importance in biomolecular simulations not only because of their crucial role in the backbone of nucleic acids but also as they represent one of the most important types of post‐translational modifications to protein side‐chains and are an integral part in many lipids. Our re‐parametrization of the free dihydrogen phosphate (H PO ) and three derivatives (methyl phosphate, dimethyl phosphate, and phenyl phosphate) leads, in conjunction with the previously updated charged side‐chains in the GROMOS parameter set 54A8, to new nucleic acid backbone parameters and a 54A8 version of the widely used GROMOS protein post‐translational modification parameter set. © 2017 Wiley Periodicals, Inc.     

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

The polarizable empirical CHARMM force field based on the classical Drude oscillator has been extended to the nitrogen‐containing heteroaromatic compounds pyridine, pyrimidine, pyrrole, imidazole, indole, and purine. Initial parameters for the six‐membered rings were based on benzene with nonbond parameter optimization focused on the nitrogen atoms and adjacent carbons and attached hydrogens. In the case of five‐member rings, parameters were first developed for imidazole and transferred to pyrrole. Optimization of all parameters was performed against an extensive set of quantum mechanical and experimental data. Ab initio data were used for the determination of initial electrostatic parameters, the vibrational analysis, and in the optimization of the relative magnitudes of the Lennard‐Jones (LJ) parameters, through computations of the interactions of dimers of model compounds, model compound‐water interactions, and interactions of rare gases with model compounds. The absolute values of the LJ parameters were determined targeting experimental heats of vaporization, molecular volumes, heats of sublimation, crystal lattice parameters, and free energies of hydration. Final scaling of the polarizabilities from the gas‐phase values by 0.85 was determined by reproduction of the dielectric constants of pyridine and pyrrole. The developed parameter set was extensively validated against additional experimental data such as diffusion constants, heat capacities, and isothermal compressibilities, including data as a function of temperature. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

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.     

Gold(I) Vinylidene Complexes as Reactive Intermediates and Their Tendency to π‐Backbond

We herein report a computational study of the bonding in gold(I) vinylidene complexes and compare them to their carbene and CO analogues. The relevance of these intermediates is analysed for the intramolecular cyclisation leading to vinyl sulfonates.     

Planarity of benzoylthiocarbazate tuberculostatics. III. Diesters of 3‐(2‐hydroxybenzoyl)dithiocarbazic acid

Searches for new tuberculostatic agents are important considering the occurrence of drug‐resistant strains of Mycobacterium tuberculosis . The structures of three new potentially tuberculostatic compounds, namely isopropyl methyl (2‐hydroxybenzoyl)carbonohydrazonodithioate, C₁₂H₁₆N₂O₂S₂, (Z )‐benzyl methyl (2‐hydroxybenzoyl)carbonohydrazonodithioate, C₁₆H₁₆N₂O₂S₂, and dibenzyl (2‐hydroxybenzoyl)carbonohydrazonodithioate propan‐2‐ol monosolvate, C₂₂H₂₀N₂O₂S₂·C₃H₈O, were determined by X‐ray diffraction. The mutual orientation of the three main fragments of the compounds, namely an aromatic ring, a dithioester group and a hydrazide group, can influence the biological activity of the compounds. In all three of the structures studied, the C(=O)NH group is in the anti conformation. In addition, the presence of the hydroxy group in the ortho position of the aromatic ring in all three structures leads to the formation of an intramolecular hydrogen bond stabilizing the planarity of the molecules.     

2‐(4′‐Pyridyl‐N‐oxide)‐Substituted Hemithioindigos as Photoresponsive Guests for a Super Aryl‐Extended Calix[4]pyrrole Receptor

We report the synthesis of two 2‐(4′‐pyridyl‐N‐oxide)‐substituted hemithioindigos (HTIs). We probed their photoisomerization by using UV/Vis and ¹H NMR spectroscopy techniques. Light irradiation at λ=450 nm provoked the isomerization of the HTI Z isomer to the E counterpart to a large extent (≈80 % at the photostationary state). ¹H NMR titration experiments revealed the formation of thermodynamically and kinetically stable 1:1 inclusion complexes of the (Z)‐HTI isomers with a super aryl‐extended host (association constant>10⁴ m ^?1). Photoirradiation at λ=450 nm of the inclusion complexes induced the isomerization of the bound HTI N‐oxide to afford the (E)‐HTI?calix[4]pyrrole complex. We determined accurate association constant values for the 1:1 inclusion complexes of the (Z)‐ and (E)‐HTI isomers by using isothermal titration calorimetry experiments. The results showed that the stability constants of the (E)‐HTI complexes were 2.2–2.8‐fold lower than those of the (Z)‐HTI counterparts, which explains the lack of light‐induced release of the former to the bulk solution.     

Competition Between Concerted and Stepwise Dynamics in the Triplet Di‐π‐Methane Rearrangement

The molecular dynamics of the triplet‐state Zimmerman di‐π‐methane rearrangement of dibenzobarrelene were computed with B3LYP and M06‐2X density functionals. All productive quasiclassical trajectories involve sequential formation and cleavage of C? C bonds and an intermediate with lifetimes ranging from 13 to 1160 fs. Both dynamically concerted and stepwise trajectories are found. The average lifetime of this intermediate is significantly shorter than predicted by either transition‐state theory or the Rice–Ramsperger–Kassel–Marcus model, thus indicating the non‐statistical nature of the reaction mechanism.     

Estimation of Stability Constants of Copper(II) Complexes with α‐Amino Acids Using Connectivity Index 3χv. Common Model for the Binary and Ternary Complexes

Models for estimation of the first (K₁), second (K₂), and overall stability constant (β₂) of copper(II) chelates with naturally occurring amino acids, based on the valence connectivity index of the 3rd order (³ χ ^v), were improved by introduction of a square term and a new graph representation for mono‐complexes (ML^cor). The models gave SE=0.07, 0.05–0.07 and 0.05–0.08 for lg K₁, lg K₂ and lg β₂ constants, respectively; models that encompass both binary and ternary bis‐complexes included indicator variable. We also validated our models on the test set which included two mono‐, two binary and two ternary Cu(II) chelates with α‐aminobutanoic acid and α‐aminopentanoic acid, not included into the calibration. The absolute differences between experimental and predicted stability constants were in the range of 0.01–0.16.