Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

Solid-state NMR analysis of a peptide (Gly-Pro-Gly-Gly-Ala)6-Gly derived from a flagelliform silk sequence of Nephila clavipes

Solid-state NMR is especially useful when the structures of peptides and proteins should be analyzed by taking into account the structural distribution, that is, the distribution of the torsion angle of the individual residue. In this study, two-dimensional spin-diffusion solid-state NMR spectra of 13C-double-labeled model peptides (GPGGA)6G of flagelliform silk were observed for studying the local structure in the solid state. The spin-diffusion NMR spectra calculated by assuming the torsion angles of the beta-spiral structure exclusively could not reproduce the observed spectra. In contrast, the spectra calculated by taking into account the statistical distribution of the torsion angles of the individual central residues in the sequences Ala-Gly-Pro, Gly-Pro-Gly, Pro-Gly-Gly, Gly-Gly-Ala, and Gly-Ala-Gly from PDB data could reproduce the observed spectra well. This indicates that the statistical distribution of the torsion angles should be considered for the structural model of (GPGGA)6G similar to the case of the model peptide of elastin.     

The role played by environmental residues on sidechain torsional angles within homologous families of proteins: A new method of sidechain modeling

We investigated the conservation of sidechain conformation for each residue within a homologous family of proteins in the Protein Data Bank (PDB) and performed sidechain modeling using this information. The information was represented by the probability of conserved sidechain torsional angles obtained from many families of proteins, and these were calculated for a pair of residues at topologically equivalent positions as a result of structural alignment. Probabilities were obtained for a pair of same amino acids and for a pair of different amino acids. The correlation between environmental residues and the fluctuation of probability was examined for the pair of same amino acid residues, and the simple probability was calculated for the pair of different amino acids. From the results on the same amino acid pairs, 17 amino acids, except for Ala, Gly, and Pro, were divided into two types: those that were influenced and those that were not influenced by the environmental residues. From results on different amino acid pairs, a replacement between large residues, such as Trp, Phe, and Tyr, was performed assuming conservation of their torsional angles within a homologous family of proteins. We performed sidechain modeling for 11 known proteins from their native and modeled backbones, respectively. With the native backbones, the percentage of the χ₁ angle correct within 30° was found to be 67% and 80% for all and core residues, respectively. With the modeled backbones, the percentage of the correct χ₁ angle was found to be 60% and 72% for all and core residues, respectively. To estimate an upper limit on the accuracy for predicting sidechain conformations, we investigated the probability of conserved sidechain torsional angles for highly similar proteins having > 90% sequence identity and <2.5-Å X-ray resolution. In those proteins, 83% of the sidechain conformations were conserved for the χ₁ angle. Proteins 31:355–369, 1998. © 1998 Wiley-Liss, Inc.     

Nucleic acid model building: the multiple backbone solutions associated with a given base morphology

A constrained model building procedure is used to generate nucleic acid structures of the familiar A-, B-, and Z-DNA duplexes. Attention is focused upon the multiple structural solutions associated with the arrangements of nucleic acid base pairs rather than the optimum sugar-phosphate structure. The glycosyl (chi) and sugar torsions (both the ring puckering and the exocyclic C5'-C4' (psi) torsion) are treated as independent variables and the resulting O3'...O5' distances are used as closure determinants. When such distances conform to the known geometry of phosphate chemical bonding, an intervening phosphorus atom with correct C-O-P valence angles can be located. Four sequential torsion angles--phi', omega', omega and phi--about the C3'-O3'-P-O5'-C5' bonds are then obtained as dependent variables. The resulting structures are categorized in terms of conformation, ranked in potential energy, and analyzed for torsional correlations. The numerical results are quite interesting with implications regarding nucleic acid models constructed to fit less than ideal experimental data. The multiple solutions to the problem are useful for comprehending the conformational complexities of the local sugar-phosphate backbone and for understanding the transitions between different helical forms. According to these studies, unique characterization of a nucleic acid duplex involves more than the determination of its base pair morphology, its sugar puckering preferences, or its groove binding features.     

Index to Subjects,Vol. 27

Abstract

A constrained model building procedure is used to generate nucleic acid structures of the familiar A-, B-, and Z-DNA duplexes. Attention is focused upon the multiple structural solutions associated with the arrangements of nucleic acid base pairs rather than the optimum sugar-phosphate structure. The glycosyl (χ) and sugar torsions (both the ring puckering and the exocyclic C5′-C4′ (ψ) torsion) are treated as independent variables and the resulting O3′…O5′ distances are used as closure determinants. When such distances conform to the known geometry of phosphate chemical bonding, an intervening phosphorus atom with correct C-O-P valence angles can be located. Four sequential torsion angles- φ,ω,ω,ω and φ about the C3′-O3′-P-O5′-C5′ bonds are then obtained as dependent variables. The resulting structures are categorized in terms of conformation, ranked in potential energy, and analyzed for torsional correlations. The numerical results are quite interesting with implications regarding nucleic acid models constructed to fit less than ideal experimental data. The multiple solutions to the problem are useful for comprehending the conformational complexities of thelocal sugar-phosphate backbone and for understanding the transitions between different helical forms. According to these studies, unique characterization of a nucleic acid duplex involves more than the determination of its base pair morphology, its sugar puckering preferences, or its groove binding features.     

Differentiable, multi-dimensional, knowledge-based energy terms for torsion angle probabilities and propensities

Rotatable torsion angles are the major degrees of freedom in proteins. Adjacent angles are highly correlated and energy terms that rely on these correlations are intensively used in molecular modeling. However, the utility of torsion based terms is not yet fully exploited. Many of these terms do not capture the full scale of the correlations. Other terms, which rely on lookup tables, cannot be used in the context of force-driven algorithms because they are not fully differentiable. This study aims to extend the usability of torsion terms by presenting a set of high-dimensional and fully-differentiable energy terms that are derived from high-resolution structures. The set includes terms that describe backbone conformational probabilities and propensities, side-chain rotamer probabilities, and an elaborate term that couples all the torsion angles within the same residue. The terms are constructed by cubic spline interpolation with periodic boundary conditions that enable full differentiability and high computational efficiency. We show that the spline implementation does not compromise the accuracy of the original database statistics. We further show that the side-chain relevant terms are compatible with established rotamer probabilities. Despite their very local characteristics, the new terms are often able to identify native and native-like structures within decoy sets. Finally, force-based minimization of NMR structures with the new terms improves their torsion angle statistics with minor structural distortion (0.5 A RMSD on average). The new terms are freely available in the MESHI molecular modeling package. The spline coefficients are also available as a documented MATLAB file.     

基于K-mer扭转角偏好的蛋白质结构类型预测

蛋白质的序列、结构和功能多种多样.大量研究表明蛋白质的结构与其氨基酸序列的排序有关,并且局部的氨基酸序列环境对蛋白质的结构具有一定的影响.本文提出一种新的基于5-mer氨基酸扭转角统计偏好的蛋白质结构类型预测方法,在该方法通过PDB数据库中5-mer中间氨基酸的扭转角统计偏好来进行结构类型的预测.新方法可以通过计算机仿...     

Statistical analysis of RNA backbone

Local conformation is an important determinant of RNA catalysis and binding. The analysis of RNA conformation is particularly difficult due to the large number of degrees of freedom (torsion angles) per residue. Proteins, by comparison, have many fewer degrees of freedom per residue. In this work, we use and extend classical tools from statistics and signal processing to search for clusters in RNA conformational space. Results are reported both for scalar analysis, where each torsion angle is separately studied, and for vectorial analysis, where several angles are simultaneously clustered. Adapting techniques from vector quantization and clustering to the RNA structure, we find torsion angle clusters and RNA conformational motifs. We validate the technique using well-known conformational motifs, showing that the simultaneous study of the total torsion angle space leads to results consistent with known motifs reported in the literature and also to the finding of new ones.     

Conformational studies of nucleic acids: III. Empirical multiple correlation functions for nucleic acid torsion angles

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, alpha (O3'-P-O5'-C5'), delta (C5'-C4'-C3'-O3') and epsilon (C4'-C3'-O3'-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, alpha, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.     

A novel exhaustive search algorithm for predicting the conformation of polypeptide segments in proteins

We present a fast ab initio method for the prediction of local conformations in proteins. The program, PETRA, selects polypeptide fragments from a computer-generated database (APD) encoding all possible peptide fragments up to twelve amino acids long. Each fragment is defined by a representative set of eight straight phi/psi pairs, obtained iteratively from a trial set by calculating how fragments generated from them represent the protein databank (PDB). Ninety-six percent (96%) of length five fragments in crystal structures, with a resolution better than 1.5 A and less than 25% identity, have a conformer in the database with less than 1 A root-mean-square deviation (rmsd). In order to select segments from APD, PETRA uses a set of simple rule-based filters, thus reducing the number of potential conformations to a manageable total. This reduced set is scored and sorted using rmsd fit to the anchor regions and a knowledge-based energy function dependent on the sequence to be modelled. The best scoring fragments can then be optimized by minimization of contact potentials and rmsd fit to the core model. The quality of the prediction made by PETRA is evaluated by calculating both the differences in rmsd and backbone torsion angles between the final model and the native fragment. The average rmsd ranges from 1.4 A for three residue loops to 3.9 A for eight residue loops.     

TANGLE: two-level support vector regression approach for protein backbone torsion angle prediction from primary sequences

Protein backbone torsion angles (Phi) and (Psi) involve two rotation angles rotating around the C(α)-N bond (Phi) and the C(α)-C bond (Psi). Due to the planarity of the linked rigid peptide bonds, these two angles can essentially determine the backbone geometry of proteins. Accordingly, the accurate prediction of protein backbone torsion angle from sequence information can assist the prediction of protein structures. In this study, we develop a new approach called TANGLE (Torsion ANGLE predictor) to predict the protein backbone torsion angles from amino acid sequences. TANGLE uses a two-level support vector regression approach to perform real-value torsion angle prediction using a variety of features derived from amino acid sequences, including the evolutionary profiles in the form of position-specific scoring matrices, predicted secondary structure, solvent accessibility and natively disordered region as well as other global sequence features. When evaluated based on a large benchmark dataset of 1,526 non-homologous proteins, the mean absolute errors (MAEs) of the Phi and Psi angle prediction are 27.8° and 44.6°, respectively, which are 1% and 3% respectively lower than that using one of the state-of-the-art prediction tools ANGLOR. Moreover, the prediction of TANGLE is significantly better than a random predictor that was built on the amino acid-specific basis, with the p-value<1.46e-147 and 7.97e-150, respectively by the Wilcoxon signed rank test. As a complementary approach to the current torsion angle prediction algorithms, TANGLE should prove useful in predicting protein structural properties and assisting protein fold recognition by applying the predicted torsion angles as useful restraints. TANGLE is freely accessible at http://sunflower.kuicr.kyoto-u.ac.jp/~sjn/TANGLE/.     

Conformational Studies of Nucleic Acids: III. Empirical Multiple Correlation Functions for Nucleic Acid Torsion Angles

Abstract

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, α (03′-P-05′-C5′), δ (C5′-C4′-C3′-03′) and ε (C4′-C3′-03′-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, α, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.     

Influence of phase angle between axial and torsional loadings on fatigue fractures of bone

Fatigue fractures of cortical bone involve combined axial-torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0 degrees and 90 degrees phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures.     

Distance dependent centroid to centroid force fields using high resolution decoys

Simplified force fields play an important role in protein structure prediction and de novo protein design by requiring less computational effort than detailed atomistic potentials. A side chain centroid based, distance dependent pairwise interaction potential has been developed. A linear programming based formulation was used in which non-native "decoy" conformers are forced to take a higher energy compared with the corresponding native structure. This model was trained on an enhanced and diverse protein set. High quality decoy structures were generated for approximately 1400 nonhomologous proteins using torsion angle dynamics along with restricted variations of the hydrophobic cores of the native structure. The resulting decoy set was used to train the model yielding two different side chain centroid based force fields that differ in the way distance dependence has been used to calculate energy parameters. These force fields were tested on an independent set of 148 test proteins with 500 decoy structures for each protein. The side chain centroid force fields were successful in correctly identifying approximately 86% native structures. The Z-scores produced by the proposed centroid-centroid distance dependent force fields improved compared with other distance dependent C(alpha)-C(alpha) or side chain based force fields.     

Theoretical conformational analysis of methylamide of N-acetyl-L-lysine]

The spatial structure of the methylamide of N-acetyl-L-lysine has been analysed taking into account non-bonded and electrostatic interactions, torsional energy, bond angles distortion and hydrogen bonding. Conformational capacities of the backbone and mutual dependence of spatial structures of the backbone and the side chain was described by conformational maps obtained by energy minimisation, the dihedral angles and the bond angles of the side chain being varied for every phi, psi point. Every possible combination for phi, psi, x1-x5-angles was used corresponding to the stable form of the backbone and to torsion potential minima of the initial approximations in the calculation of preferred conformations of the molecule. Comparisons are made between stable forms of the methylamide of N-acetyl-L-lysine and Lys residues in proteins with known structure.     

Conformational studies of nucleic acids: IV. The conformational energetics of oligonucleotides: d(ApApApA) and ApApApA

Utilizing a new method for modeling furanose pseudorotation (D. A. Pearlman and S.-H. Kim, J. Biomol. Struct. Dyn. 3, 85 (1985)) and the empirical multiple correlations between nucleic acid torsion angles we derived in the previous report (D. A. Pearlman and S.-H. Kim, previous paper in this issue), we have made an energetic examination of the entire conformational spaces available to two nucleic acid oligonucleotides: d(ApApApA) and ApApApA. The energies are calculated using a semi-empirical potential function. From the resulting body of data, energy contour map pairs (one for the DNA molecule, one for the RNA structure) have been created for each of the 21 possible torsion angle pairs in a nucleotide repeating unit. Of the 21 pairs, 15 have not been reported previously. The contour plots are different from those made earlier in that for each point in a particular angle-angle plot, the remaining five variable torsion angles are rotated to the values which give a minimum energy at this point. The contour maps are overall quite consistent with the experimental distribution of oligonucleotide data. A number of these maps are of particular interest: delta (C5'-C4'-C3'-O3')-chi (O4'-C1'-N9-C4), where the energetic basis for an approximately linear delta-chi correlation can be seen: zeta (C3'-O3'-P-O5')-delta, in which the experimentally observed linear correlation between zeta and delta in DNA(220 degrees less than zeta less than 280 degrees) is clearly predicted; zeta-epsilon (C4'-C3'-O3'-P), which shows that epsilon increases with decreasing zeta less than 260 degrees; alpha (O3'-P-O5'-C5')-gamma (O5'-C5'-C4'-C3') where a clear linear correlation between these angles is also apparent, consistent with experiment; and several others. For the DNA molecule studied here, the sugar torsion delta is predicted to be the most flexible, while for the RNA molecule, the greatest amount of flexibility is expected to reside in alpha and gamma. Both the DNA and RNA molecules are predicted to be highly polymorphic. Complete energy minimization has been performed on each of the minima found in the energy searches and the results further support this prediction. Possible pathways for B-form to A-form DNA interconversion suggested by the results of this study are discussed. The results of these calculations support use of the new sugar modeling technique and torsion angle correlations in future conformational studies of nucleic acids.     

Determination of the local structure of the protein insectotoxin I5A from the scorpion Buthus eupeus from 1H-NMR spectroscopy data

The local structure (torsion angles phi, psi and chi 1 of amino acid residues) of insectotoxin I5A (35 residues) of scorpion Buthus eupeus has been determined from cross-peak integral intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra and spin coupling constants of vicinal H--NC alpha--H and H--C alpha C beta--H protons. The local structure determination was carried out by fitting complete relaxation matrix of peptide unit protons (protons of a given residue and NH proton of the next residue in the amino acid sequence) with experimental NOESY cross-peak intensities. The obtained intervals of backbone torsional angles phi and psi consistent with NMR data were determined for all but Gly residues. The predominant C alpha--C beta rotamer of the side chain has been unambiguously determined for 42% of the insectotoxin amino acid residues whereas for another 46% residues experimental data are fitted equally well with two rotamers. Stereospecific assignments were obtained for 38% of beta-methylene groups. The determined torsional angles phi, psi and chi 1 correspond to the sterically allowed conformations of the amino acid residues and agree with the insectotoxin secondary structure established earlier by 1H NMR spectroscopy.     

The J-coupling Restrained Molecular Mechanics (JrMM) Protocol - An Efficient Alternative for Deriving DNA Endocyclic Torsion Angle Constraints Part II: Experimental Application of the JrMM Protocol

Abstract

The J-coupling restrained molecular mechanics (JrMM) protocol, which correlates deoxyribose endocyclic torsion angles and vicinal proton-proton torsion angle φ_{1′ 2′} in Part I of this study, is demonstrated to be a viable alternative to efficiently derive the endocyclic torsion angle constraints for the determination of the solution structures of DNA molecules. Extensive testing demonstrating the validity of the JrMM-derived torsion angle constraints in the restrained molecular dynamics and energy minimization structural refinement processes is performed theoretically using an energy-minimized B-DNA model and experimentally using a DNA hexamer d(CGTACG)₂. The results show that only a 0.2 Å difference exists between the RMSD values of the refined structures using the ideal and the JrMM-derived endocyclic torsion angle constraints. The JrMM-derived torsion angles are also determined to be in good agreement with the torsion angles derived through the use of the vicinal J-derived torsion angles. These results show that through the use of reliably measured J_{1′ 2′} values and computer simulation method, the endocyclic torsion angle constraints can be derived reliably and efficiently. Thus the JrMM method serves as an alternative strategy to generate endocyclic torsion angle constraints for the determination of the solution structures of DNA molecules.