Optimization of a molecular mechanics force field for type-II polyoxometalates focussing on electrostatic interactions: a case study

In this study, we have focussed on type-II polyanions such as [M(7)O(24)](6-), and we have developed and validated optimized force fields that include electrostatic and van der Waals interactions. These contributions to the total steric energy are described by the nonbonded term, which encompasses all interactions between atoms that are not transmitted through the bonds. A first validation of a stochastic technique based on genetic algorithms was previously made for the optimization of force fields dedicated to type-I polyoxometalates. To describe the new nonbonded term added in the functional, a fixed-charged model was chosen. Therefore, one of the main issues was to analyze that which partial atomic charges could be reliably used to describe these interactions in such inorganic compounds. Based on several computational strategies, molecular mechanics (MM) force field parameters were optimized using different types of atomic charges. Moreover, the influence of the electrostatic and van der Waals buffering constants and 1,4-interactions scaling factors used in the force field were also tested, either being optimized as well or fixed with respect to the values of CHARMM force field. Results show that some atomic charges are not well adapted to CHARMM parameters and lead to unrealistic MM-optimized structures or a MM divergence. As a result, a new scaling factor has been optimized for Quantum Theory of Atoms in Molecules charges and charges derived from the electrostatic potential such as ChelpG. The force fields optimized can be mixed with the CHARMM force field, without changing it, to study for the first time hepta-anions interacting with organic molecules.     

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.     

Electrostatic model for infrared intensities in a spectroscopically determined molecular mechanics force field

A new electrostatic model for the calculation of infrared intensities in molecular mechanics and molecular dynamics is presented. The model is based on atomic charges, atomic charge fluxes, and internal coordinate dipoles and their fluxes. The internal coordinate dipoles are used instead of atomic dipoles, thus simplifying the derivation of parameters. The model is designed to reproduce ab initio dipole derivatives, and the parameters can be obtained by (iterative) transformations from these, or by linear least squares fitting to them. A first application to linear alkanes has been made. For these molecules, the intensities can be predicted with an average accuracy of 30–40%. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 754–768, 1998     

The tetracycline: Mg2+ complex: a molecular mechanics force field

Tetracycline (Tc) is an important antibiotic, which binds specifically to the ribosome and several proteins, in the form of a Tc-:Mg2+ complex. To model Tc:protein and Tc:RNA interactions, we have developed a molecular mechanics force field model of Tc, which is consistent with the CHARMM force field for proteins and nucleic acids. We used structures from the Cambridge Crystallographic Data Base to identify the main Tc conformations that are likely to be present in solution and in biomolecular complexes. A conformational search was also done, using the MM3 force field to perform simulated annealing of Tc. Several resulting, low-energy structures were optimized with an ab initio model and used in developing the new Tc force field. Atomic charges and Lennard-Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with Tc at 36 different positions. We considered both a neutral and a zwitterionic Tc form, with and without bound Mg2+. The final rms deviation between the ab initio and force field energies, averaged over all forms, was just 0.35 kcal/mol. The model also reproduces the ab initio geometry and flexibility of Tc. As further tests, we did simulations of a Tc crystal, of Tc:Mg2+ and Tc:Ca2+ complexes in aqueous solution, and of a solvated complex between Tc:Mg2+ and the Tet repressor protein (TetR). With slight, ad hoc adjustments, the model can reproduce the experimental, relative, Tc binding affinities of Mg2+ and Ca2+. It performs well for the structure and fluctuations of the Tc:Mg2+:TetR complex. The model should therefore be suitable to investigate the interactions of Tc with proteins and RNA. It provides a starting point to parameterize other compounds in the large Tc family.     

Inclusion of the ligand field contribution in a polarizable molecular mechanics: SIBFA-LF

To account for the distortion of the coordination sphere that takes place in complexes containing open-shell metal cations such as Cu(II), we implemented, in sum of interactions between fragments ab initio computed (SIBFA) molecular mechanics, an additional contribution to take into account the ligand field splitting of the metal d orbitals. This term, based on the angular overlap model, has been parameterized for Cu(II) coordinated to oxygen and nitrogen ligands. The comparison of the results obtained from density functional theory computations on the one hand and SIBFA or SIBFA-LF on the other shows that SIBFA-LF gives geometric arrangements similar to those obtained from quantum mechanical computations. Moreover, the geometric improvement takes place without downgrading the energetic agreement obtained from SIBFA. The systems considered are Cu(II) interacting with six water molecules, four ammonia or four imidazoles, and four water plus two formate anions.     

A molecular mechanics force field for lignin

A CHARMM molecular mechanics force field for lignin is derived. Parameterization is based on reproducing quantum mechanical data of model compounds. Partial atomic charges are derived using the RESP electrostatic potential fitting method supplemented by the examination of methoxybenzene:water interactions. Dihedral parameters are optimized by fitting to critical rotational potentials and bonded parameters are obtained by optimizing vibrational frequencies and normal modes. Finally, the force field is validated by performing a molecular dynamics simulation of a crystal of a lignin fragment molecule and comparing simulation-derived structural features with experimental results. Together with the existing force field for polysaccharides, this lignin force field will enable full simulations of lignocellulose.     

Automatic molecular structure perception for the universal force field

The Universal Force Field (UFF) is a classical force field applicable to almost all atom types of the periodic table. Such a flexibility makes this force field a potential good candidate for simulations involving a large spectrum of systems and, indeed, UFF has been applied to various families of molecules. Unfortunately, initializing UFF, that is, performing molecular structure perception to determine which parameters should be used to compute the UFF energy and forces, appears to be a difficult problem. Although many perception methods exist, they mostly focus on organic molecules, and are thus not well‐adapted to the diversity of systems potentially considered with UFF. In this article, we propose an automatic perception method for initializing UFF that includes the identification of the system's connectivity, the assignment of bond orders as well as UFF atom types. This perception scheme is proposed as a self‐contained UFF implementation integrated in a new module for the SAMSON software platform for computational nanoscience ( http://www.samson-connect.net ). We validate both the automatic perception method and the UFF implementation on a series of benchmarks.     

Ab initio calculations and molecular mechanics (MM3) force field development for ammonium and protonated aliphatic amines

The geometries and vibrational frequencies of 11 training molecules containing the ammonium ion moiety were calculated at the MP2/6-31+G* level of theory. Various torsional energy profiles were also calculated using this basis set. From those ab initio calculations, a molecular mechanics (MM3) force field was developed using our Parameter Analysis and Refinement Toolkit System (PARTS). Using this set of parameters, the MM3 force field was found to well reproduce the molecular geometries and vibrational spectra for the all training molecules. CPU time was reduced from days to seconds. The availability of this new force field dramatically increases the feasibility of the computer-assisted drug design involving ammonium and protonated amino groups. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1371–1391, 1997     

Study of amino- and pyridyl-containing zinc(II) and cadmium(II) complexes by molecular mechanics using a force field based on the Gillespie-Kepert model

A new approach combining the molecular mechanics (MM) method and the Gillespie-Kepert model was applied to calculate the geometry and strain energy of zinc(II) and cadmium(II) complexes with amino- and pyridyl-containing ligands. High accuracy of calculations of the geometry was demonstrated for more than 20 complexes of these metals. Typical r.m.s. deviations between the calculated and experimental values (X-ray diffraction analysis) were 0.02 Å for bond lengths, 2° for bond angles, and 4° for torsion angles. The size-match selectivity of several macrocycles and polydentate open-chain ligands was studied. Correlations between the calculated strain energies of metal complexes and the experimental values of their stability constants and enthalpies of formation are discussed.     

A molecular mechanics force field for biologically important sterols

A parameterization has been performed of the biologically important sterols cholesterol, ergosterol, and lanosterol for the CHARMM27 all-atom molecular mechanics force field. An automated parameterization method was used that involves fitting the potential to vibrational frequencies and eigenvectors derived from quantum-chemical calculations. The partial charges were derived by fitting point charges to quantum-chemically calculated electrostatic potentials. To model the dynamics of the hydroxyl groups of the sterols correctly, the parameter set was refined to reproduce the energy barrier for the rotation of the hydroxyl group around the carbon connected to the hydroxyl of each sterol. The frequency-matching plots show good agreement between the CHARMM and quantum chemical normal modes. The parameters are tested in a molecular dynamics simulation of the cholesterol crystal structure. The experimental geometry and cell dimensions are well reproduced. The force field derived here is also useful for simulating other sterols such as the phytosterols sigmasterol, and campesterol, and a variety of steroids.     

Reversible peptide folding: Dependence on molecular force field used

Temperature‐dependent nuclear magnetic resonance (NMR) and CD spectra of methanol solutions of a β‐heptapeptide have been interpreted in such a way that the secondary structure, a 3₁₄‐helix, is assumed to be stable in a temperature range of between 298 and 393 K. This is in contrast to the results of a 50‐ns molecular dynamics simulation using the GROMOS 96 force field, which found a melting temperature of about 340 K. This discrepancy is addressed by further computational studies using the OPLS‐AA force field. The conformational energetics of N‐formyl‐3‐aminobutanamide in vacuo are obtained using ab initio and density functional quantum‐mechanical calculations at the HF/6‐31G*, B3LYP/6‐31G*, and B3LYP/6‐311+G* levels of theory. The results permit development of torsional parameters for the OPLS‐AA force field that reproduce the conformational energetics of the monomer. By varying the development procedure, three parameter sets are obtained that focus on reproducing either low‐energy or high‐energy conformations. These parameter sets are tested by simulating the reversible folding of the β‐heptapeptide in methanol. The melting temperature of the helix formed (>360 K) is found to be higher than the one obtained from simulations using the GROMOS 96 force field (∼340 K). Differences in the potential energy functions of the latter two force fields are evaluated and point to the origins of the difference in stability. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 774–787, 2000     

A new molecular mechanics force field for the oxidized form of blue copper proteins

A molecular mechanics force field for blue copper proteins has been developed, based on a rigid potential energy surface scan of the Cu(II)/His/His/Cys/Met chromophore, using DFT (B3LYP) calculations and the AMBER force field for the protein backbone. The strain-energy-minimized structures of the model chromophore alone are in excellent agreement with the DFT-optimized structure, and those of the entire set of cupredoxins (five structures are considered) are, within the experimental error limits, in good agreement with the single crystal structural data. However, the structural variation in the computed structures is much smaller than those in the experimental structures. It is shown that, due to the large error limits in the experimental data, a validation of the force field with experimental structural data is impossible because, within the error limits, all experimental structures considered are virtually identical. A validation on the basis of spectroscopic data and their correlation with experimental and computed structural data is proposed, and, as a first example, the correlation of intensity ratios of the charge transfer transitions with a specific distortion mode is presented. The quality of the correlation, using the computed structures, is higher than that with the X-ray structures, and this indicates that the computed structures are meaningful.     

Partial hessian fitting for determining force constant parameters in molecular mechanics

We present a new protocol for deriving force constant parameters that are used in molecular mechanics (MM) force fields to describe the bond‐stretching, angle‐bending, and dihedral terms. A 3 × 3 partial matrix is chosen from the MM Hessian matrix in Cartesian coordinates according to a simple rule and made as close as possible to the corresponding partial Hessian matrix computed using quantum mechanics (QM). This partial Hessian fitting (PHF) is done analytically and thus rapidly in a least‐squares sense, yielding force constant parameters as the output. We herein apply this approach to derive force constant parameters for the AMBER‐type energy expression. Test calculations on several different molecules show good performance of the PHF parameter sets in terms of how well they can reproduce QM‐calculated frequencies. When soft bonds are involved in the target molecule as in the case of secondary building units of metal‐organic frameworks, the MM‐optimized geometry sometimes deviates significantly from the QM‐optimized one. We show that this problem is rectified effectively by use of a simple procedure called Katachi that modifies the equilibrium bond distances and angles in bond‐stretching and angle‐bending terms. © 2016 Wiley Periodicals, Inc.     

A molecular mechanics force field for rhodium(I) carbonyl phosphine complexes and its application on the oxidative addition reactions of these complexes

The main purpose of the development of an Rh(I) Carbonyl Phosphine force field was to predict the molecular structure of Rh(I) complexes as well as to compute possible intermediates or transition states during the oxidative addition of CH₃I to these complexes. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 692–703, 2000     

Additive empirical force field for hexopyranose monosaccharides

We present an all-atom additive empirical force field for the hexopyranose monosaccharide form of glucose and its diastereomers allose, altrose, galactose, gulose, idose, mannose, and talose. The model is developed to be consistent with the CHARMM all-atom biomolecular force fields, and the same parameters are used for all diastereomers, including both the alpha- and beta-anomers of each monosaccharide. The force field is developed in a hierarchical manner and reproduces the gas-phase and condensed-phase properties of small-molecule model compounds corresponding to fragments of pyranose monosaccharides. The resultant parameters are transferred to the full pyranose monosaccharides, and additional parameter development is done to achieve a complete hexopyranose monosaccharide force field. Parametrization target data include vibrational frequencies, crystal geometries, solute-water interaction energies, molecular volumes, heats of vaporization, and conformational energies, including those for over 1800 monosaccharide conformations at the MP2/cc-pVTZ//MP2/6-31G(d) level of theory. Although not targeted during parametrization, free energies of aqueous solvation for the model compounds compare favorably with experimental values. Also well-reproduced are monosaccharide crystal unit cell dimensions and ring pucker, densities of concentrated aqueous glucose systems, and the thermodynamic and dynamic properties of the exocyclic torsion in dilute aqueous systems. The new parameter set expands the CHARMM additive force field to allow for simulation of heterogeneous systems that include hexopyranose monosaccharides in addition to proteins, nucleic acids, and lipids.     

Parameterization of a reactive force field using a Monte Carlo algorithm

Parameterization of a molecular dynamics force field is essential in realistically modeling the physicochemical processes involved in a molecular system. This step is often challenging when the equations involved in describing the force field are complicated as well as when the parameters are mostly empirical. ReaxFF is one such reactive force field which uses hundreds of parameters to describe the interactions between atoms. The optimization of the parameters in ReaxFF is done such that the properties predicted by ReaxFF matches with a set of quantum chemical or experimental data. Usually, the optimization of the parameters is done by an inefficient single‐parameter parabolic‐search algorithm. In this study, we use a robust metropolis Monte‐Carlo algorithm with simulated annealing to search for the optimum parameters for the ReaxFF force field in a high‐dimensional parameter space. The optimization is done against a set of quantum chemical data for MgSO₄ hydrates. The optimized force field reproduced the chemical structures, the equations of state, and the water binding curves of MgSO₄ hydrates. The transferability test of the ReaxFF force field shows the extend of transferability for a particular molecular system. This study points out that the ReaxFF force field is not indefinitely transferable. © 2013 Wiley Periodicals, Inc.     

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.     

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.     

Improving the Q2MM method for transition state force field modeling

The Quantum‐to‐molecular mechanics method (Q2MM) for converting quantum mechanical transition states (TSs) to molecular mechanical minima has been modified to allow a fit to the “natural” reaction mode eigenvalue. The resulting force field gives an improved representation of the energy curvature at the TS, but can potentially give false responses to steric interactions. Ways to address this problem while staying close to the “natural” TS force field are discussed. © 2014 Wiley Periodicals, Inc.     

A molecular mechanics force field for the cobalt corrinoids

A force field for the cobalt (III) corrinoids (derivatives of vitamin B₁₂) for use with a modified version of the molecular mechanics program 2(87) has been developed empirically around 19 cobalt corrinoid crystal structures. Bond lengths, bond angles and torsional angles are reproduced with r.m.s. differences of 0.01 Å, 2.4 °, and 4.2 °, respectively, within the standard deviation of the mean of these parameters found in the solid state. The axial ligand occupying the lower coordination site in the cobalamins, 5,6-dimethylbenzimidazole, is shown to have very limited rotational freedom and is constrained by the downward-pointing b and d propionamide side chains of the corrin ring. Strain-energy profiles for rotation of the side chains of the corrin ring show the existence of several local energy minima and this explains the observed variability in the orientations of these side chains in the solid state. The known change in conformation which occurs in the C ring when the e side chain is epimerized from the lower to the upper face of the corrin ring in cyano-13-epicobalamin is correctly predicted, provided the starting conformation of the C ring is unbiased. A study of cyano-8-epicobalamin indicates that an analogous conformational change does not occur in the B ring and the epimerized d side chain assumes an equatorial orientation relative to the corrin ring. Parameters for the Co---C bond in alkylcobalamins were developed and the structure of methyl- and adenosylcobalamin are accurately reproduced. An examination of the strain energy consequences of rotation of the adenosyl ligand about the Co---C bond identifies a number of low-energy conformations at least two of which, in which adenosyl lies over the “southern” and “eastern” portions of the corrin ring, respectively, have been previously deduced from NMR observations. Coordinated neopentyl in neopentylcobalamin is much more hindered to rotation about the Co---C bond and the lowest conformation finds two γ(C) atoms straddling the upwardly projecting C46 methyl group of the corrin.