A QSPR for the Tg of polymers: The Koehler-Hopfinger approach using the tripos 5.2 force field

The Koehler Hopfinger model^1,2 has been modified. The modification has worked fairly well with the Tripos 5.2 Force Field together with charges calculated using the Gasteiger Marsili method. This modification has been checked using the same monomers as those used in the original reference. The table, with monomers from a few chemical functionalities such as acrylates, ethers etc. was subjected to a Hierarchical Cluster Analysis which provided justification for creating “designer” equations for each class of chemical functionality. The “designer” equations for acrylates and olefins are described. The scheme utilized the Partial Least Squares (PLS) method as available within Sybyl 5.41 in order to draw the correlations.     

Assessment of performance of the general purpose polarizable force field QMPFF3 in condensed phase

The recently introduced force field (FF) QMPFF3 is thoroughly validated in gas, liquid, and solid phases. For the first time, it is demonstrated that a physically well-grounded general purpose FF fitted exclusively to a comprehensive set of high level vacuum quantum mechanical data applied as it is to simulation of condensed phase provides high transferability for a wide range of chemical compounds. QMPFF3 demonstrates accuracy comparable with that of the FFs explicitly fitted to condensed phase data, but due to high transferability it is expected to be successful in simulating large molecular complexes.     

The general harmonic force field of formaldehyde

The use of recently available frequency, ¹³C frequency shift, Coriolis coupling, and centrifugal distortion data enables the GHFF of formaldehyde to be determined with some degree of precision. Excellent agreement is obtained between the experimentally determined interaction force constants and those predicted by the most recent ab initio calculations of Meyer and Pulay.     

The general quartic force field of HCN

Although it has been generally thought that Fermi resonance occurs only between vibrational states which lie within about 100 cm⁻¹, it is now apparent that there is an important resonance in the vibrational spectrum of HCN between the states 02⁰0 at about 1411 cm⁻¹ and 00⁰1 at 3311 cm⁻¹ and another resonance between 02⁰0 and 10⁰0 at about 2096 cm⁻¹. Moreover, the J dependence of these resonances leads to important effects in the rotation—vibration spectrum. There are similar resonances in DCN. These resonances have been taken into account in the determination of new estimates of the force constants in the general quartic valence force field of HCN.     

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.     

A general quadratic force field for the diazirine molecule

A general quadratic force field has been calculated for the vibrations of the diazirine molecule by the refinement of a series of force constants obtained recently ab initio by Wiberg et al. for cyclopropene. The calculated force constants have been refined to fit the frequencies for the H₂CN₂ and D₂CN₂ species and the isotopic shifts of the H¹³CN₂ and H₂C¹⁵N₂ species.     

The general valence force field of perchloryl fluoride

The i.r. specta of FClO₃ in Ne, N₂ and Ar matrices were recorded and the ³⁵Cl³⁷Cl isotopic shifts were measured. The Coriolis constants of the E-species vibrations were redetermined and together with the isotopic data used for the computation of a general valence force field. The A₁ block, for which only isotopic frequencies are available, was fixed with the help of ab initio force constant calculations. It is shown that ν₂ and ν₃ are best described as an antisymmetric and a symmetric combination, respectively, of the CIF stretching and the ClO₃ bending motions. Comparison with 13 previously published force fields demonstrates the inadequacy of underdetermined force fields for strongly coupled systems, such as FClO₃. The ClO and ClF stretching force constants were found to be 9.76 and 3.49 mdyn Å⁻¹, respectively, in good agreement with those expected for a mainly covalent ClF single and ClO double bonds.     

An improved general harmonic force field for ethylene

The recent availability of certain critical experimental data, both from this and other laboratories, for isotopic species of the ethylene molecule, has enabled the previously published GHFF to be redetermined with much greater precision. Several significant changes in the force constants occur, bringing the empirical values into better overall agreement with ab initio values. Calculated data using the new force field are considered to be sufficiently reliable to be used with confidence in spectroscopic and structural applications and are listed.     

Development and testing of a general amber force field

We describe here a general Amber force field (GAFF) for organic molecules. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most organic and pharmaceutical molecules that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited number of atom types, but incorporates both empirical and heuristic models to estimate force constants and partial atomic charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallographic structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 A, which is comparable to that of the Tripos 5.2 force field (0.25 A) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 A, respectively). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermolecular energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 A and 1.2 kcal/mol, respectively. These data are comparable to results from Parm99/RESP (0.16 A and 1.18 kcal/mol, respectively), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to experiment) is about 0.5 kcal/mol. GAFF can be applied to wide range of molecules in an automatic fashion, making it suitable for rational drug design and database searching.     

Performance of the general amber force field in modeling aqueous POPC membrane bilayers

The aim of this work was to answer the question of whether the general amber force field (GAFF) is good enough to simulate fully hydrated POPC membrane bilayers. The test system contained 128 POPC and 2985 TIP3P water molecules. The equilibration was carried out in a nonarbitrary manner to reach the stable liquid-crystalline phase. The simulations were performed by using particle mesh Ewald electrostatics implemented in molecular dynamics packages Amber8 (NPT ensembles) and NAMD2 (NPgammaT ensembles). The computational results were assessed against the following experimental membrane properties: (i) area per lipid, (ii) area compressibility modulus, (iii) order parameter, (iv) gauche conformations per acyl chain, (v) lateral diffusion coefficients, (vi) electron density profile, and (vii) bound water at the lipid/water interface. The analyses revealed that the tested force field combination approximates the experimental values at an unexpectedly good level when the NPgammaT ensemble is applied with a surface tension of 60 mN m(-1) per bilayer. It is concluded that the GAFF/TIP3P combination can be utilized for aqueous membrane bilayer simulations, as it provides acceptable accuracy for biomolecular modeling.     

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     

A general quadratic force field for the pyridazine molecule: out-of-plane B1 normal modes

On the basis of Raman and infrared data for pyridazine-d_o′, −3, 6-d₂, and −d₄ we are carrying out a normal coordinate treatment using a general quadratic force field (GQFF) on a non-redundant basis. The BB^* matrix has been set up and diagonalized to obtain the linear redundancy relations. Afterwards, using the Schmidt's process, we constructed the independent coordinates used in our calculations. To date we have completed the refinement of the calculations of the force constants for the B₁ specie.     

Vectorizing a general purpose molecular dynamics simulation program

A molecular dynamics program for arbitrary molecular mixtures is presented. All intramolecular degrees of freedom are treated explicitly, which means that the program is based on central forces only. A double time step technique has been devised in order to separate rapidly varying, covalent forces from slowly varying ones. Typically, the ratio between the different time steps is about 10, with only a minor computational effort spent in the evaluation of the covalent forces. The program source code is arranged so as to obtain maximal efficiency on a vector processor, while still being portable. On a Cray 1A, a typical simulation of an ion-chelate in aqueous solution with 984 atoms requires a total of 29 μs/interaction with a spherical cutoff distance of 10Å.     

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001     

A supervised fitting approach to force field parametrization with application to the SIBFA polarizable force field

A supervised, semiautomated approach to force field parameter fitting is described and applied to the SIBFA polarizable force field. The I‐NoLLS interactive, nonlinear least squares fitting program is used as an engine for parameter refinement while keeping parameter values within a physical range. Interactive fitting is shown to avoid many of the stability problems that frequently afflict highly correlated, nonlinear fitting problems occurring in force field parametrizations. The method is used to obtain parameters for the H₂O, formamide, and imidazole molecular fragments and their complexes with the Mg²⁺ cation. Reference data obtained from ab initio calculations using an auc‐cc‐pVTZ basis set exploit advances in modern computer hardware to provide a more accurate parametrization of SIBFA than has previously been available. © 2014 Wiley Periodicals, Inc.     

Combination of the CHARMM27 force field with united-atom lipid force fields

Computer simulations offer a valuable way to study membrane systems, from simple lipid bilayers to large transmembrane protein complexes and lipid-nucleic acid complexes for drug delivery. Their accuracy depends on the quality of the force field parameters used to describe the components of a particular system. We have implemented the widely used CHARMM22 and CHARMM27 force fields in the GROMACS simulation package to (i) combine the CHARMM22 protein force field with two sets of united-atom lipids parameters; (ii) allow comparisons of the lipid CHARMM27 force field with other lipid force fields or lipid-protein force field combinations. Our tests do not show any particular issue with the combination of the all-atom CHARMM22 force field with united-atoms lipid parameters, although pertinent experimental data are lacking to assess the quality of the lipid-protein interactions. The conversion utilities allow automatic generation of GROMACS simulation files with CHARMM nucleic acids and protein parameters and topologies, starting from pdb files using the standard GROMACS pdb2gmx method. CMAP is currently not implemented.     

Extension of the CHARMM general force field to sulfonyl‐containing compounds and its utility in biomolecular simulations

Presented is an extension of the CHARMM General Force Field (CGenFF) to enable the modeling of sulfonyl‐containing compounds. Model compounds containing chemical moieties such as sulfone, sulfonamide, sulfonate, and sulfamate were used as the basis for the parameter optimization. Targeting high‐level quantum mechanical and experimental crystal data, the new parameters were optimized in a hierarchical fashion designed to maintain compatibility with the remainder of the CHARMM additive force field. The optimized parameters satisfactorily reproduced equilibrium geometries, vibrational frequencies, interactions with water, gas phase dipole moments, and dihedral potential energy scans. Validation involved both crystalline and liquid phase calculations showing the newly developed parameters to satisfactorily reproduce experimental unit cell geometries, crystal intramolecular geometries, and pure solvent densities. The force field was subsequently applied to study conformational preference of a sulfonamide based peptide system. Good agreement with experimental IR/NMR data further validated the newly developed CGenFF parameters as a tool to investigate the dynamic behavior of sulfonyl groups in a biological environment. CGenFF now covers sulfonyl group containing moieties allowing for modeling and simulation of sulfonyl‐containing compounds in the context of biomolecular systems including compounds of medicinal interest. © 2012 Wiley Periodicals, Inc.     

CHARMM36 all‐atom additive protein force field: Validation based on comparison to NMR data

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side‐chain amino‐ and methyl‐containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ₁ and χ₂ dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs. © 2013 Wiley Periodicals, Inc.     

New-generation amber united-atom force field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.