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.     

Do the neighboring residues in a polypeptide affect the electron distribution of an amino acid significantly? A quantitative study using the quantum theory of atoms in molecules (QTAIM)

Geometries, as well as bond and atomic properties obtained with the atoms-in-molecules theory applied on B3LYP/6-31++G//B3LYP/6-31G charge densities, of the N-formyl amides of the nine tripeptides obtained by combining glycine, alanine, and serine around a central glycine residue were analyzed to check how the properties of the central residue are modified by other amino acids bonded to it. All of the molecules were optimized from an alpha-helix conformation that was also displayed by the optimized structure. Significant variations of the geometry (especially remarkable for dihedral angles) and atomic properties of the central glycine residue are observed when it is attached to a serine residue whose side chain is involved in a hydrogen bond.     

An ab initio study of the p,π interaction: IV. Interaction of an ether oxygen atom with a carbonyl group

RHF/6-311G(d) calculations were performed for the H₃COCOH molecule with full geometry optimization and at varied angles of rotation of the methoxy group about the C-O bond, with all the other geometric parameters optimized. The molecule can exist in two stable conformations with the dihedral angle O¹C¹O²C² of 0.00° and 179.99°. The influence of the rotation angle on the population of the p _y orbital of the carbonyl oxygen atom in compounds with different types of the adjacent bond is essentially similar. The results obtained are inconsistent with the concept of the p,π conjugation involving the p _y orbitals of the planar molecular fragment (orbitals whose symmetry axes are perpendicular to this fragment).     

A simple graphical approach to predict local residue conformation using NMR chemical shifts and density functional theory

The dependency of amino acid chemical shifts on φ and ψ torsion angle is, independently, studied using a five‐residue fragment of ubiquitin and ONIOM(DFT:HF) approach. The variation of absolute deviation of ¹³C^α chemical shifts relative to φ dihedral angle is specifically dependent on secondary structure of protein not on amino acid type and fragment sequence. This dependency is observed neither on any of ¹³C^β, and ¹H^α chemical shifts nor on the variation of absolute deviation of ¹³C^α chemical shifts relative to ψ dihedral angle. The ¹³C^α absolute deviation chemical shifts (ADCC) plots are found as a suitable and simple tool to predict secondary structure of protein with no requirement of highly accurate calculations, priori knowledge of protein structure and structural refinement. Comparison of Full‐DFT and ONIOM(DFT:HF) approaches illustrates that the trend of ¹³C^α ADCC plots are independent of computational method but not of basis set valence shell type. © 2016 Wiley Periodicals, Inc.     

A sequence and structural study of transmembrane helices

A comparison is made between the distribution of residue preferences, three dimensional nearest neighbour contacts, preferred rotamers, helix-helix crossover angles and peptide bond angles in three sets of proteins: a non-redundant set of accurately determined globular protein structures, a set of four-helix bundle structures and a set of membrane protein structures. Residue preferences for the latter two sets may reflect overall helix stabilising propensities but may also highlight differences arising out of the contrasting nature of the solvent environments in these two cases. The results bear out the expectation that there may be differences between residue type preferences in membrane proteins and in water soluble globular proteins. For example, the -branched residue types valine and isoleucine are considerably more frequently encountered in membrane helices. Likewise, glycine and proline, residue types normally associated with `helix-breaking' propensity are found to be relatively more common in membrane helices. Three dimensional nearest neighbour contacts along the helix, preferred rotamers, and peptide bond angles are very similar in the three sets of proteins as far as can be ascertained within the limits of the relatively low resolution of the membrane proteins dataset. Crossing angles for helices in the membrane protein set resemble the four helix bundle set more than the general non-redundant set, but in contrast to both sets they have smaller crossing angles consistent with the dual requirements for the helices to form a compact structure while having to span the membrane. In addition to the pairwise packing of helices we investigate their global packing and consider the question of helix supercoiling in helix bundle proteins.     

Verification of the correlation between geometric parameters of molecules and the parameters of their 1H NMR spectra

The dihedral and bond direction angles between all pairs of vicinal protons of the arabinofuranose residue were calculated from the coordinatees of the hydrogen atoms found by an X-ray study of 3-O-acetyl-β-L -arabinofuranose 1,2,5-orthobenzoate. The values found were compared with those calculated with the help of correlation equations previously proposed by Karplus and recently by the authors, linking the values of those angles with the spin-spin coupling constants of vicinal protons [³J(H,H′)]. It has been found that the best agreement between the angles found crystallographically and calculated from the ¹H NMR data can be achieved using the equation which includes bond direction angles and the sum of the chemical shifts of the protons involved.     

The conformational dependence of vicinal 13C13C spin–spin coupling constants in alicyclic compounds

A series of alicyclic compounds with dihedral angles of 0°, 60°, 90°, 120° and 180° between a ¹³C-labelled carbon atom and a carbon atom separated by three bonds from the label has been synthesized. The vicinal ¹³C¹³C spin coupling constants were measured, and from the results a Karplus-type relationship between ¹³C¹³C spin coupling and dihedral angle is proposed.     

Correlation of dihedral angles with 13C chemical shifts of quaternary carbon atoms of some phenothiazine derivatives

A direct relationship between the ¹³C nmr chemical shifts of the quaternary carbon atoms of the central ring of phenothiazine and the dihedral angle of the respective derivatives has been observed. This correlation allows for the useful and quick estimation of the dihedral angles of novel phenothiazines from readily obtainable ¹³C nmr solution measurements. In addition, the change in the dihedral angle appears to be directly related to the S-C_4a-C_10a bond angle; however, the C_4a-S-C_5a bond angle is not affected by changes in the dihedral angle. This indicates that the “flattening” of the phenothiazine tricyclic ring system is compensated for by the vertical displacement of the sulfur atom, by changes in hybridization of N₁₀, and by other angular distortions of the middle ring.     

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     

Intramolecular Hydrogen Bonding In N-(2-Amino-2-Deoxy-β-D-Glucopyranoside)-N'-Carbamoyl-L-Dipeptidylesters: An Infrared And 1H Nmr Study

ABSTRACT

Ten N-(2-amino-2-deoxy-β-D-glucopyranoside)-N'-carbamoyl-L-dipeptidylesters with different amino acid sequences in the dipeptide unit were studied by means of IR and ¹H NMR spectroscopy. In the IR spectra three bands at 3453, 3420 and 3390 cm^-1 were observed which could be assigned to the free NH, the intramolecularly hydrogen bonded NH species forming five-membered, C₅, and seven-membered, C₇, rings, respectively. Comparing the NH band positions which correspond to the C₇ rings of the Gly-Xaa and the Xaa-Gly dipeptidylesters, the signals of the Xaa-Gly sequence were shifted by 10 cm^-1 to lower wave numbers indicating stronger hydrogen bonds. The temperature effect dv/dT was an order of magnitude larger for the C₇ associates than for C₅ showing the highest enthalpy of the C₇ hydrogen bond. The ¹H NMR spectra give three separate signals for the NH groups. The temperature coefficient ?δ/?T was the largest for N-1-H indicating the formation of less stable hydrogen bonds (C₇). The solvent induced changes of the chemical shift of the NH signals was lowest for the N-3-H signal. Obviously the deshielding properties on this function do not vary in dependence of the solvent polarity. The hydrogen/deuterium exchange rate was lowest for the N-6-H proton indicating the lower accessibility of this proton. Combining the results of both spectroscopic methods it can be concluded that the N-1-H forms only C₇ rings whereas N-6-H can participate in C₅ and C₇ intramolecular hydrogen bonds. The strength of the formed C₇ associates depends on the amino acid sequence in the dipeptide residue.     

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.     

Small-amplitude protein conformational dynamics: Second-order analytic relation between cartesian coordinates and dihedral angles

An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time-dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second-order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first-order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second-order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second-order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.     

简化的系统搜索法及其在构象分析中的应用

多肽的构象研究除了可以用X-射线晶体学及二维核磁共振等实验方法外,理论计算的方法有系统搜索法、蒙特卡洛方法、距离几何方法、分子动力学方法及能量极小化等.系统搜索法具有构象空间搜索彻底的特点,相对来说找到系统整体极小值的可能性较大,但由于其计算量较大,对于多肽及蛋白质很难实现.我们对系统搜索法进行了简化,不是同时旋转所有的二面角,而是成对地进行,以迭代的方法达到收敛,最后得到可能的构象.     

A Novel Long‐Range n to π* Interaction Secures the Smallest known α‐Helix in Water

The introduction of an amide bond linking side chains of the first and fifth amino acids forms a cyclic pentapeptide that optimally stabilizes the smallest known α‐helix in water. The origin of the stabilization is unclear. The observed dependence of α‐helicity on the solvent and cyclization linker led us to discover a novel long‐range n to π* interaction between a main‐chain amide oxygen and a uniquely positioned carbonyl group in the linker of cyclic pentapeptides. CD and NMR spectra, NMR and X‐ray structures, modelling, and MD simulations reveal that this first example of a synthetically incorporated long‐range n to π* CO???C^γ=Ο interaction uniquely enforces an almost perfect and remarkably stable peptide α‐helix in water but not in DMSO. This unusual interaction with a covalent amide bond outside the helical backbone suggests new approaches to synthetically stabilize peptide structures in water.     

Relative importance of secondary structure and solvent accessibility to the stability of protein mutants. A case study with amino acid properties and energetics on T4 and human lysozymes

Understanding the factors influencing the stability of protein mutants is an important task in molecular and computational biology. In this work, we have approached this problem by examining the relative importance of secondary structure and solvent accessibility of the mutant residue for understanding/predicting the stability of protein mutants. We have used hydrophobic, electrostatic and hydrogen bond free energy terms and nine unique physicochemical, energetic and conformational properties of amino acids in the present study and these parameters have been related with changes in thermal stability (DeltaTm) of all the single mutants of lysozymes based on single and multiple correlation coefficients. As expected the properties reflecting hydrophobicity and hydrophobic free energy play a major role to distinguish stabilizing and destabilizing mutants. The hydrophobic free energy due to carbon and nitrogen atoms distinguish the stability of coil and strand mutations to the accuracy of 100 and 90%, respectively. In agreement with previous results, the subgroup classification based on secondary structure and the information about its location in the structure yielded good relationship with the experimental DeltaTm. We revealed that the secondary structure information is equally or more important than solvent accessibility for understanding the stability of protein mutants. The comparison of amino acid properties with free-energy terms indicate that the energetic contribution explains the mutant stability better in coil region whereas the amino acid properties do better in strand region. Further, the combination of free energies with amino acid properties increased the correlation significantly. The present study demonstrates the importance of classifying the mutants based on secondary structure to the stability of proteins upon mutations.     

2‐Ethylsulfanyl‐7‐(furan‐2‐yl)‐4‐(thiophen‐2‐yl)pyrazolo[1,5‐a][1,3,5]triazine: π‐stacked chains of hydrogen‐bonded R22(10) dimers

In the title compound, C₁₅H₁₂N₄OS₂, the bond distances in the fused heterocyclic system show evidence for aromatic‐type delocalization in the pyrazole ring with some bond fixation in the triazine ring. The thiophenyl substituent is slightly disordered over two sets of atomic sites having occupancies of 0.934 (4) and 0.066 (4). The non‐H atoms in the entire molecule are nearly coplanar, with the planes of the furanyl substituent and the major orientation of the thiophenyl substituent making dihedral angles of 5.72 (17) and 1.8 (3)°, respectively, with that of the fused ring system. Molecules are linked into centrosymmetric R₂²(10) dimers by C—H...O hydrogen bonds and these dimers are further linked into chains by a single π–π stacking interaction. Comparisons are made with some related 4,7‐diaryl‐2‐(ethylsulfanyl)pyrazolo[1,5‐a][1,3,5]triazines which contain variously substituted aryl groups in place of the furanyl and thiophenyl substituents in the title compound.     

Different intermolecular interactions in azido[2‐(diphenylphosphino)benzaldehyde semicarbazonato‐κ2P,N1,O]nickel(II)

The title compound, [Ni(C₂₀H₁₇N₃OP)(N₃)], is the first complex with a semicarbazide‐based ligand having a P atom as one of the donors. The influence of the P atom on the deformation of the coordination geometry of the Ni^II ion is evident but less expressed than in the cases of complexes with analogous seleno‐ and thiosemicarbazide ligands. The torsion angles involving the two bonds formed by the P atom within the six‐membered chelate ring have the largest values [C—P—Ni—N = 24.3 (2)° and C—C—P—Ni = −24.2 (4)°], suggesting that the P atom considerably influences the conformation of the ring. Two types of N—H...N hydrogen bond connect the complex units into chains.     

Novel C<Subscript>β</Subscript>–C<Subscript>γ</Subscript> Bond Cleavages of Tryptophan-Containing Peptide Radical Cations

In this study, we observed unprecedented cleavages of the C_β–C_γ bonds of tryptophan residue side chains in a series of hydrogen-deficient tryptophan-containing peptide radical cations (M^•+) during low-energy collision-induced dissociation (CID). We used CID experiments and theoretical density functional theory (DFT) calculations to study the mechanism of this bond cleavage, which forms [M – 116]⁺ ions. The formation of an α-carbon radical intermediate at the tryptophan residue for the subsequent C_β–C_γ bond cleavage is analogous to that occurring at leucine residues, producing the same product ions; this hypothesis was supported by the identical product ion spectra of [LGGGH – 43]⁺ and [WGGGH – 116]⁺, obtained from the CID of [LGGGH]^•+ and [WGGGH]^•+, respectively. Elimination of the neutral 116-Da radical requires inevitable dehydrogenation of the indole nitrogen atom, leaving the radical centered formally on the indole nitrogen atom ([Ind]^•-2), in agreement with the CID data for [WGGGH]^•+ and [W_1-CH3GGGH]^•+; replacing the tryptophan residue with a 1-methyltryptophan residue results in a change of the base peak from that arising from a neutral radical loss (116 Da) to that arising from a molecule loss (131 Da), both originating from C_β–C_γ bond cleavage. Hydrogen atom transfer or proton transfer to the γ-carbon atom of the tryptophan residue weakens the C_β–C_γ bond and, therefore, decreases the dissociation energy barrier dramatically.     

Analysis and prediction of RNA-binding residues using sequence, evolutionary conservation, and predicted secondary structure and solvent accessibility

Identification and prediction of RNA-binding residues (RBRs) provides valuable insights into the mechanisms of protein-RNA interactions. We analyzed the contributions of a wide range of factors including amino acid sequence, evolutionary conservation, secondary structure and solvent accessibility, to the prediction/characterization of RBRs. Five feature sets were designed and feature selection was performed to find and investigate relevant features. We demonstrate that (1) interactions with positively charged amino acids Arg and Lys are preferred by the egatively charged nucleotides; (2) Gly provides flexibility for the RNA binding sites; (3) Glu with negatively charged side chain and several hydrophobic residues such as Leu, Val, Ala and Phe are disfavored in the RNA-binding sites; (4) coil residues, especially in long segments, are more flexible (than other secondary structures) and more likely to interact with RNA; (5) helical residues are more rigid and consequently they are less likely to bind RNA; and (6) residues partially exposed to the solvent are more likely to form RNA-binding sites. We introduce a novel sequence-based predictor of RBRs, RBRpred, which utilizes the selected features. RBRpred is comprehensively tested on three datasets with varied atom distance cutoffs by performing both five-fold cross validation and jackknife tests and achieves Matthew's correlation coefficient (MCC) of 0.51, 0.48 and 0.42, respectively. The quality is comparable to or better than that for state-of-the-art predictors that apply the distancebased cutoff definition. We show that the most important factor for RBRs prediction is evolutionary conservation, followed by the amino acid sequence, predicted secondary structure and predicted solvent accessibility. We also investigate the impact of using native vs. predicted secondary structure and solvent accessibility. The predictions are sufficient for the RBR prediction and the knowledge of the actual solvent accessibility helps in predictions for lower distance cutoffs.     

Normal mode analysis based on an elastic network model for biomolecules in the Protein Data Bank,which uses dihedral angles as independent variables

We have developed a computer program, named PDBETA, that performs normal mode analysis (NMA) based on an elastic network model that uses dihedral angles as independent variables. Taking advantage of the relatively small number of degrees of freedom required to describe a molecular structure in dihedral angle space and a simple potential-energy function independent of atom types, we aimed to develop a program applicable to a full-atom system of any molecule in the Protein Data Bank (PDB). The algorithm for NMA used in PDBETA is the same as the computer program FEDER/2, developed previously. Therefore, the main challenge in developing PDBETA was to find a method that can automatically convert PDB data into molecular structure information in dihedral angle space. Here, we illustrate the performance of PDBETA with a protein–DNA complex, a protein–tRNA complex, and some non-protein small molecules, and show that the atomic fluctuations calculated by PDBETA reproduce the temperature factor data of these molecules in the PDB. A comparison was also made with elastic-network-model based NMA in a Cartesian-coordinate system.