Polypeptide folding using Monte Carlo sampling, concerted rotation, and continuum solvation

An efficient concerted rotation algorithm for use in Monte Carlo statistical mechanics simulations is applied to fold three polypeptides, U(1-17)T9D, alpha(1), and trpzip2, which exhibit native beta-hairpin and alpha-helix folds. The method includes flexible bond and dihedral angles, and a Gaussian bias is applied with driver bond and dihedral angles to optimize the sampling efficiency. Solvation in water is implemented with the generalized Born (GBSA) model. The computed lowest-energy manifolds for the folded structures of the two beta-hairpins agree closely with the corresponding NMR structures. In the case of the alpha(1) peptide, the folded alpha-helical state, which is observed as oligomers in concentrated solution and crystals, is not stable in isolation. The computed preference for random coil structures is in agreement with NMR experiments at low concentration. The fact that native states can be located on high dimensional energy surfaces starting from extended conformations shows that the present methodology samples all relevant parts of the conformational space. The OPLS-AA force field with the GBSA solvent model was also found to perform well in leading to clear energetic separation of the correctly folded structures from misfolded structures for the two peptides that form beta-turns.     

Structures of the gauche conformers of some substituted dimethyl ethers. Effect of adjacent atom lone pairs on methyl group asymmetry

The complete equilibrium structures of CH₃OCH₃ and of the gauche conformers of CH₃OCH₂F, HOCH₂F, CH₃OCH₂Cl and H₃OCH₂CN have been determined by ab initio gradient computation at the Hartree—Fock, double zeta-plus-polarization level. The very large asymmetries in C---H bond distances previously reported from microwave substitution structures are shown to be non-existent in the equilibrium structures and are presumably artifacts. Small differences, different in direction from those reported from the experiments and nearly an order of magnitude smaller in size, do exist. They reflect three factors: (1) a lengthening of a C---H bond which is trans to a lone pair on an adjacent atom, (2) a general shortening of C---H bonds originating at a carbon atom bearing a highly electronegative substituent, and (3) a specific interaction in which a C---X substituent shortens the nearly parallel C---H bond on the other methyl group. The last interaction, not previously reported, is mediated by withdrawal of electron density from the oxygen lone pair which is trans to both groups. Other structural features derived from the microwave studies are supported by the new results. p ]Inclusion of polarization functions in the basis set for oxygen is essential for correct determination of the COC angle and the dihedral angles. The dihedral angles of CH₃OCH₂F and HOCH₂F are not correctly determined by the computation even at this level, although the computed values are improved when d functions are used for oxygen and still more by use of two sets of oxygen d functions. Polarization functions on carbon or on fluorine have no effect on the computed torsional angles. There is no problem in computing the correct dihedral angles with the ---Cl or ---CN derivatives.     

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.     

J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.     

Beiträge zur Chemie des Hydrazins und seiner Derivate. 52. Kristall- und Molekülstrukturen der tert.-Butyloxycarbonylderivate von Cyclotetraschwefeldihydrazid und Cyclohexaschwefelhydrazid

Contributions to the Chemistry of Hydrazine and its Derivatives. 52. Crystal and Molecular Structures of the tert.-Butyloxycarbonyl Derivatives of Cyclotetrasulfurdihydrazide and Cyclohexasulfurhydrazide The structures of the tert.-butyloxycarbonyl derivatives of cyclotetrasulfurdihydrazide and cyclohexasulfurhydrazide were determined by X-ray analyses. Both sulfur(II)-nitrogen rings exist in crown conformation and contain only sp²-hybridized nitrogen atoms. Bond lengths, bond angles, and dihedral angles are discussed.     

Efficient parallelization of the energy,surface, and derivative calculations for internal coordinate mechanics

An efficient algorithm for parallelization of a molecular mechanics program operating in the space of internal coordinates such as dihedral angles, bond angles, and bond lengths is described. The iterative procedure to calculate analytical energy derivatives with respect to the internal coordinates was modified to allow parallelization. Computationally intensive modules that calculate energy and its derivatives, solvent-accessible surface, electrostatic polarization energy and that update lists of interactions were parallelized with nearly 100% efficiency. The proposed strategy for the shared-memory computer architecture is easily scalable and requires minimum changes in a program code. The overall speedup for a realistic calculation minimizing the energy of a myoglobin reaches a factor of 3 for 4 processors. © 1994 by John Wiley & Sons, Inc.     

Models of Molecular Structures of Al<Subscript>2</Subscript>Cr<Subscript>3</Subscript> and Al<Subscript>2</Subscript>Mo<Subscript>3</Subscript> Metal Clusters according to Density Functional Theory Calculations

The geometrical parameters of the molecular structures of aluminum–chromium and aluminum–molybdenum clusters Al₂Cr₃ and Al₂Mo₃ have been calculated by the OPBE/TZVP density functional theory (DFT) method with the Gaussian09 programL package. It has been found that each of these metal clusters can exist in twenty structural modifications, which significantly differ in stability and geometric parameters. Bond lengths and bond and torsion (dihedral) angles are reported for each of these modifications.     

α-氯甲硫醚自由基的构型和推拉效应

推拉效应(captodative effect)指的是,当自由基中心原子上同时连有推电子基及吸电子基时,该自由基具特殊稳定性的现象.近年来,许多化学工作者对此产生了很大的兴趣.研究该效应的方法,主要有理论计算及实验考察.Crans、Leroy等用ab initio 法首先计算了一些简单有机自由基的推拉效应.Pasto 最近探讨了动力学及热力学推拉效应.我们对氨基酸自由基作过考察,发现其有较大的推拉效应.最近,我们对α-氯甲硫醚自由基的稳定性进行了ab initio 计算.结果表明其热力学推拉效应值ΔE_(cd)~T 及动力学推拉效应值ΔE_(cd)~K 都小于零.我们先在STO-3G 水平寻找分子及自由基的     

Molecular structure of 9,10-bis[bis(4-tert-butylphenyl)methylene)-9,10-dihydroanthracene: A butterfly-shaped Thiele's hydrocarbon derivative

The molecular structure of 9,10-bis[bis(4-tert-butylphenyl)methylene)-9,10-dihydroanthracene, an anthraquinodimethane derivative having four aryl groups on exocyclic methylene positions, was experimentally and theoretically characterized. Single-crystal diffraction study revealed that the title molecule takes a butterfly shape, i.e., two exocyclic carbons rise from the molecular plane, defined by four carbons of central quinoidal ring, by 1.257(3) Å (average). The dihedral angle of the butterfly wing, i.e., the angle between the two annulated benzenes is 137.71(5)°. Characteristic bond alternation was observed for the central quinoidal moiety and the exocyclic double bond. Theoretical study indicated that this butterfly shape is the stable structure. The two optimized structures nearly reproduced the experimentally observed molecular structures, bond distances, and angles.     

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ¹ dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ¹ dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α-class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native-like energy-minimized structures, three selection criteria were used to identify a native-like structure with a 1.90-Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy-plus-free energy of hydration, or a knowledge-based mean field method) was unable to identify a native-like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native-like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition-based Importance-Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy-minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native-like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored. © 1996 John Wiley & Sons, Inc.     

Molecular structure of hexatomic heteronuclear (AlFe) metal clusters as determined by the DFT quantum-chemical calculation

Geometric parameters of molecular structures of hexatomic heteronuclear (AlFe) clusters with various number of aluminum atoms (Al₂Fe₄ and Al₃Fe₃) were calculated using the density functional hybrid method in the OPBE/TZVP approximation. It was found that the first of these clusters is able to exist in nine and the second in twenty structural modifications substantially differing from each other in their stability and geometric parameters. The values of bond lengths, planar and dihedral (torsion) angles for some of these modifications are given.     

Cyclic peroxides: dihedral angle around the peroxide bond by microwave and photoelectron spectroscopic studies

Experimental COOC dihedral angles are used to support the relation proposed by Coughlin et al. for correlating the observed photoelectron splitting n(O)⁺- with the dihedral angle around the peroxide bond in cyclic peroxides.     

Tri-peptide reference structures for the calculation of relative solvent accessible surface area in protein amino acid residues

Relative amino acid residue solvent accessibility values allow the quantitative comparison of atomic solvent-accessible surface areas in different residue types and physical environments in proteins and in protein structural alignments. Geometry-optimised tri-peptide structures in extended solvent-exposed reference conformations have been obtained for 43 amino acid residue types at a high level of quantum chemical theory. Significant increases in side-chain solvent accessibility, offset by reductions in main-chain atom solvent exposure, were observed for standard residue types in partially geometry-optimised structures when compared to non-minimised models built from identical sets of proper dihedral angles abstracted from the literature. Optimisation of proper dihedral angles led most notably to marked increases of up to 54% in proline main-chain atom solvent accessibility compared to literature values. Similar effects were observed for fully-optimised tri-peptides in implicit solvent. The relief of internal strain energy was associated with systematic variation in N, C^α and C^β atom solvent accessibility across all standard residue types. The results underline the importance of optimisation of ‘hard’ degrees of freedom (bond lengths and valence bond angles) and improper dihedral angle values from force field or other context-independent reference values, and impact on the use of standardised fixed internal co-ordinate geometry in sampling approaches to the determination of absolute values of protein amino acid residue solvent accessibility. Quantum chemical methods provide a useful and accurate alternative to molecular mechanics methods to perform energy minimisation of peptides containing non-standard (chemically modified) amino acid residues frequently present in experimental protein structure data sets, for which force field parameters may not be available. Reference tri-peptide atomic co-ordinate sets including hydrogen atoms are made freely available.     

Ab initio study of the Trinem antibiotic Sanfetrinem GV104326

We present a theoretical calculation of trinem antibiotic sanfetrinem GV104326 and its cis-isomer of proton in β-lactam ring and methoxy inversion isomer. Ab initio Hartree Fock method is employed to calculate the geometry optimization; optimized parameters, bond lengths, bond angles and dihedral angles of isomers. We also calculated the vibrational frequencies, the IR intensities, the Raman activities and the thermochemical parameters. Mulliken population analysis is used to compare bond strength of an active site. These results are compared with available experimental data and other related theoretical calculations. The calculated IR spectra are in good agreement with experiments. Calculated geometrical and conformational structures of sanfetrinem and its isomers support the previous study of the geometrical requirements for the antibacterial activities. The significance of the rotational conformation of the carboxyl group to chemical reactivities is discussed.     

Determination of sugar structures in solution from residual dipolar coupling constants: methodology and application to methyl beta-D-xylopyranoside

We have developed methodology for the determination of solution structures of small molecules from residual dipolar coupling constants measured in dilute liquid crystals. The power of the new technique is demonstrated by the determination of the structure of methyl beta-d-xylopyranoside (I) in solution. An oriented sample of I was prepared using a mixture of C(12)E(5) and hexanol in D(2)O. Thirty residual dipolar coupling constants, ranging from -6.44 to 4.99 Hz, were measured using intensity-based J-modulated NMR techniques. These include 15 D(HH), 4 (1)D(CH), and 11 (n)D(CH) coupling constants. The accuracy of the dipolar coupling constants is estimated to be < +/- 0.02 Hz. New constant-time HMBC NMR experiments were developed for the measurement of (n)D(CH) coupling constants, the use of which was crucial for the successful structure determination of I, as they allowed us to increase the number of fitted parameters. The structure of I was refined using a model in which the directly bonded interatom distances were fixed at their ab initio values, while 16 geometrical and 5 order parameters were optimized. These included 2 CCC and 6 CCH angles, and 2 CCCC and 6 CCCH dihedral angles. Vibrationally averaged dipolar coupling constants were used during the refinement. The refined solution structure of I is very similar to that obtained by ab initio calculations, with 11 bond and dihedral angles differing by 0.8 degrees or less and the remaining 5 parameters differing by up to 3.3 degrees . Comparison with the neutron diffraction structure showed larger differences attributable to crystal packing effects. Reducing the degree of order by using dilute liquid crystalline media in combination with precise measurement of small residual dipolar coupling constants, as shown here, is a way of overcoming the limitation of strongly orienting liquid crystals associated with the complexity of (1)H NMR spectra for molecules with more than 12 protons.     

A versatile method for molecular structure determinations from ground state rotational constants

A new procedure is described to determine the geometrical structure of a molecule. It starts from measured ground state rotational constants of isotopically substituted species. Internal structural parameters such as bond lengths, bond angles and dihedral angles are directly fitted with a suitable least-squares algorithm. The new method for structure determination is compared to the usual Costain—Kraitchman substitution method. It contains less stringent conditions than the latter, permits a broad range of applications and provides a reliable molecular structure.     

Crystal Structures and Spectroscopy of Anti-2,4-bis（3-R-phenyl）pentane-2,4-diols （R = Me, SMe）

Two anti-2,4-bis(3-R-phenyl)pentane-2,4-diols (1, R = Me; 2, R = SMe) have been synthesized and were characterized by X-ray diffraction, IR and UV spectra. X-ray diffractions indicate that intra- and intermolecular hydrogen bonding interactions form one-dimensional (1D) ribbons. The adjacent infinite 1D ribbons result in 3D supramolecular structures. The dihedral angles between every two benzene rings in the two diols are 31.61(12) and 31.80(7)°, respectively. UV absorption spectra of the title compounds were recorded in MeOH, C2H5OH, CH3CN, n-BuOH and cyclohexane solvents with different dielectric constants.     

THE PHOSPHAZENES–STRUCTURAL PARAMETERS AND THEIR RELATIONSHIPS TO PHYSICAL AND CHEMICAL PROPERTIES

Abstract

A systematic study of crystallographic data has revealed a number of correlations between structural parameters, (e.g., bond angles, bond lengths, dihedral angles) and physical and chemical properties in phosphazenes and related compounds. These include (a) endocyclic bond angles NPN and PNP and their relationships to group electronegativities; (b) endocyclic bond angles NPN and PNP in geminal cyclotriphosphazatrienes, N₃P₃RR′X₄ (X = F, Cl) and their relationships to basicity; (c) deviations from some relationships due to ring puckering and the use of mathematical techniques to “flatten out” these rings; (d) ³⁵Cl nuclear quadrupole resonance frequencies and P–Cl bond lengths and other relationships; (e) exocyclic bond angles viz. OPO, NPN, ClPCl, CPC etc. versus ³¹P NMR chemical shifts; (f) ring compression and deformation and unusual mass spectrometric and bulk polymerisation properties; (g) relationships in phosphazenylcyclophosphazenes between crystal structure, ⁴ J(PP) coupling constants, basicity and conformation; (h) relationships between spin-spin coupling constants, dihedral angles in, and conformations of, spiroderivatives of cyclophosphazenes–trigonal planar versus pyramidal nitrogen atoms.     

Realistic sampling of amino acid geometries for a multipolar polarizable force field

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.