Assignment of secondary structure from Cα coordinates

A multiple regression analysis has established a nonlinear relationship between the backbone dihedral angles and the C^α coordinates obtained from the x-ray crystal structures of 14 proteins. The regression equations have been applied to predict specific dihedral angles of each residue in the backbone of 24 proteins. Overall this method (Nonlinear Regression Distance Torsion) predicts values of ϕ and ψ within a ±45° window of those found in the x-ray structure with an accuracy of 94 and 91% and within a ±30° window of 88 and 81%. Two methods for the assignment of motif from C^α coordinates are reported. For the first method, motif is assigned from the dihedral angles predicted using the regression equations. By the second method, motif of the ith residue is assigned from the distance C^α_i-1 to C^α_i+2 (v₆) and torsional angle C^α_i-1, C^α_i, C^α_i+1, C^α_i+2 (v₁₃). For the 24 proteins, 23.7% of the residues by the former method and 19.6% by the latter method are assigned differently than in the Protein Data Bank. © 1997 John Wiley & Sons, Inc.     

Studies on the conformation of amino acids. IX. Conformations of butyl, seryl, threonyl, cystennyl, and valyl residues in a dipeptide unit

Potential energies of conformation of a dipeptide unit with butyl, seryl, threonyl, eysteinyl, and valyl side groups have been computed by using classical energy expressions. The presence of a γ-atom introduces characteristic restrictions on the backbone rotational angles ? and ψ the γ-atom itself is restricted to three staggered positions about the C^α—C^β bond. The important results are that a γ-carbon in position I (χ¹ ? 60°) cannot be accommodated in the standard right-and left-handed α-helices, whereas a γ-oxygen or sulfur could easily be accommodated in the right-handed α-helix. Further, a γ-carbon or a heteroatom in position II (χ¹ ? 180°) does not favor a conformation ψ ? 180°, compared to two other positions. The valyl side group significantly reduces the allowed ? and ψ values and energetically prefers a β-conformation compared to right-or left-handed α-helical conformations. The less favorable α-helical conformation is possible only for γ (III, II) combination of the valyl residue. The observed ?, ψ, and χ¹ values of all the amino acid residues in the three protein molecules, lysozyme, myoglobin, and chymotrypsin are compared with the theoretical predictions and the agreement is excellent. The results bring out the important fact that even in large molecules, the conformation of local segments are predominantly governed by the short-range intramolecular interactions.     

NMR Structures of a Nonapeptide from DNA Binding Domain of Human Polymerase-α Determined by Iterative Complete-Relaxation-Matrix Approach

Abstract

Nuclear magnetic resonance structures of a nonapeptide, ERFKCPCPT, selected from the DNA binding domain of human polymerase-a, were determined by complete relaxation matrix analysis of transverse NOE data. The structures exhibit a type III turn with residues KCPC, and the remaining residues exhibit non-ordered structures. The turn was confirmed by α, N (i,i+3) connectivity, a low temperature coefficient of NH chemical shift (?3.1 × 1O^?3) of the fourth residue, ³J_NHα coupling constants, and characteristic CD peaks at 228 and 200 nm. Furthermore, ø and ψ dihedral angles for the i + 1, and i + 2 residues of the tum are found to be?80 and?41 and?60 and?40 degrees. The first proline residue is trans- while the second exists in both eis- and trans- configurations, with trans- being more than 80% populated. The trans-configuration was established from C5α-P6α correlation and ø and ψ angles of the proline. The five-membered proline ring is in DOWN puckered (C-β-exo/C-γ-endo) conformation. The structure of the peptide reveals that the two cysteine thiols are?5 A° apart and appropriately positioned to covalently bind cis-diamminedichloroplatinum(II), a widely used anti-cancer drug.     

Studies on the conformation of amino acids. X. Conformations of norvalyl, leucyl and aromatic side groups in a dipeptide unit

Backbone-side group conformations of amino acid residues including one or two δ-carbons in the side group have been investigated. Conformational energies of norvalyl, leucyl, phenylalanyl, tyrosyl, tryptophenyl, and histidinyl side groups in a dipeptide unit have been calculated by using classical energy expressions. The side group conformations about the C^α—C^β and C^β—C^γ bonds are restricted to specific values of the respective rotational angles. Thus, most favourable positions of γ- and δ-atoms of a linear side-chain (norvalyl) are restricted to (γ_I, δ_II) (γ_II, δ_I), (γ_II, δ_II), (γ_III, δ_II), and (γ_III, δ_III), whereas those of the side-chain branching at a sp³ γ-atom (leueyl) are further restricted. It is also shown that there is a definite correlation between the orientations of the two peptide planes and that of the planar group of the aromatic side chain of phenylalanyl type residues. The studies bring out an important fact that while the γ-atoms have definite and characteristic effects on the backbone rotational angles ? and ψ, the δ atoms and beyond have no effects on the preferred ? and ψ values. Thus, the preferred backbone conformations are independent of the preferred side group conformations beyond the γ-atom and vice versa. The observed ?, ψ, χ¹, and χ² values of amino acids, simple peptides, and of the three protein molecules lysozyme, myoglobin, and chymotrypsin have been compared with the theoretical predictions, and the agreement is found to be excellent.     

What stabilizes the 314‐helix in β3‐peptides? A conformational analysis using molecular simulation

β‐Peptides are analogs of natural α‐peptides and form a variety of remarkably stable structures. Having an additional carbon atom in the backbone of each residue, their folded conformation is not only influenced by the side‐chain sequence but also and foremost by their substitution pattern. The precise mechanism by which the side chains interact with the backbone is, however, hitherto not completely known. To unravel the various effects by which the side chains influence the backbone conformation, we quantify to which extent the dihedral angles of a β³‐substited peptide with an additional methyl group on the central C_α‐atom can be regarded as independent degrees of freedom and analyze the distributions of these dihedral angles. We also selectively capture the steric effect of substituents on the C_α‐ and C_β‐atoms of the central residue by alchemically changing them into dummy atoms, which have no nonbonded interactions. We find that the folded state of the β³‐peptide is primarily stabilized by a steric exclusion of large parts of the unfolded state (entropic effect) and only subsequently by mutual dependence of the ψ‐dihedral angles (enthalpic effect). The folded state of β‐peptides is stabilized by a different mechanism than that of α‐peptides. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Relationship between conformation and geometry as evidenced by molecular dynamics simulation of Cα,α-dialkylated glycines

The relationship between the local backbone conformation and bond angles at C^α of symmetrically substituted C^α,α-dialkylated glycines (C^α,α-dimethylglycine or α-aminoisobutyric acid, Aib; C^α,α-diethylglycine, Deg; C^α,α-di-n-propylglycine, Dpg) has been investigated by molecular dynamics (MD) simulation adopting flat bottom harmonic potentials, instead of the usual harmonic restraints, for the C^α bond angles. The MD simulations show that the C^α bond angles are related to the local backbone conformation, irrespectively of the side-chain length of Aib, Deg, and Dpg residues. Moreover, the N-C^α-C′ (τ) angle is the most sensitive conformational parameter and, in the folded form, is always larger and more flexible than in the extended one. © 1998 John Wiley & Sons, Inc. Biopoly 46: 239–244, 1998     

The reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

Accurate measurements of the effects of deuteration at backbone amide positions on the chemical shifts of 15N, 13Cα, 13Cβ, 13CO and 1Hα nuclei in proteins

An approach towards accurate NMR measurements of deuterium isotope effects on the chemical shifts of all backbone nuclei in proteins (¹⁵N, ¹³C_α, ¹³CO, ¹H_α) and ¹³C_β nuclei arising from ¹H-to-D substitutions at amide nitrogen positions is described. Isolation of molecular species with a defined protonation/deuteration pattern at successive backbone nitrogen positions in the polypeptide chain allows quantifying all deuterium isotope shifts of these nuclei from the first to the fourth order. Some of the deuterium isotope shifts measured in the proteins ubiquitin and GB1 can be interpreted in terms of backbone geometry via empirical relationships describing their dependence on (φ; ψ) backbone dihedral angles. Because of their relatively large variability and notable dependence on the protein secondary structure, the two- and three-bond ¹³C_α isotope shifts, ²ΔC_α(N_iD) and ³ΔC_α(N_i+1D), and three-bond ¹³C_β isotope shifts, ³ΔC_β(N_iD), are useful reporters of the local geometry of the protein backbone.     

Use of proton Nuclear Overhauser Effects for the determination of the conformations of amino acid residues in oligopeptides

The use of the Nuclear Overhauser Effect to determine backbone and side-chain conformations of oligopeptides is discussed. The distance between the H^α proton of a given residue and the amide proton of the following residue depends only on the dihedral angle ψ. A calibration curve is given for the determination of ψ from the Nuclear Overhauser Effect involving these protons. In amino acids with branched side chains, e.g., threonine, isoleucine, and valine, the Nuclear Overhauser Effect involving the H^β proton and the amide proton in either the same or the following residue gives limited information about both χ¹ and either or ψ. The Nuclear Overhauser Effect involving the H^α and H^γ protons in leucine gives information about χ¹ and χ².     

Intramolecular steric effects and hydrogen bonding in regular conformations of polyamino acids

A survey has been made, by using computer methods, of the types of helices which polypeptide chains can form, taking into account steric requirements and intramolecular hydrogen-bonding interactions. The influence on these two requirements, of small variations in the bond angles of the peptide residues, or of small changes in the overall dimensions of the helix (pitch and residues per turn), have been assessed for the special case of the α-helix. Criteria for the formation of acceptable hydrogen bonds have also been applied to helices of other types, viz., the 3, γ^?, ω^?, and π-helices. It was shown that the N? H … O and H … O? C angles in hydrogen bonds are sensitive to changes in either the NC^αC′ bond angle or in the rotational angles about the N? C^α and C^α? C′ bonds. However, the variants of the α-helix observed experimentally in myoglobin can all be constructed without distortion of the hydrogen bonds. For α-helices, the steric and hydrogen bonding requirements are more easily fulfilled with an NC^αC′ bond angle of 111°, rather than 109.5°. The decreased stability observed for the left-handed α-helix relative to the right-handed one for L -amino acids is due essentially only to interactions of the C^β atom of the side chains with atoms in adjacent peptide units in the backbone, and interactions with atoms in adjacent turns of the helical backbone are not significantly different in the two helices. Restrictions in the freedom of rotation of bulky side chains may have significant kinetic effects during the formation of the α-helix from the “random coil” state.     

β-Turn conformations in crystal structures of model peptides containing α,α-Di-n-propylglycine and α,α-Di-n-butylglycine

The crystal state conformations of three peptides containing the α,α-dialkylated residues. α,α-di-n-propylglycine (Dpg) and α,α-di-n-butylglycine (Dbg), have been established by x-ray diffraction. Boc-Ala-Dpg-Alu-OMe (I) and Boc-Ala-Dbg-Ala-OMe (III) adopt distorted type II β-turn conformations with Ala (1) and Dpg/Dbg (2) as the corner residues. In both peptides the conformational angles at the Dxg residue (I: ? = 66.2°, ψ = 19.3°; III: ? = 66.5°. ψ = 21.1°) deviate appreciably from ideal values for the i + 2 residue in a type II β-turn. In both peptides the observed (N…O) distances between the Boc CO and Ala (3) NH groups are far too long (1: 3.44 Å: III: 3.63 Å) for an intramolecular 4 → 1 hydrogen bond. Boc-Ala-Dpg-Ata-NHMe (II) crystallizes with two independent molecules in the asymmetric unit. Both molecules HA and HB adopt consecutive β-turn (type III-III in HA and type III-I in IIB) or incipient 3₁₀-helical structures, stabilized by two intramolecular 4 → 1 hydrogen bonds. In all four molecules the bond angle N-C^α-C′ (τ) at the Dxg residues are ≥ 110°. The observation of conformational angles in the helical region of ?,ψ space at these residues is consistent with theoretical predictions. © 1995 John Wiley & Sons, Inc.     

Evaluation of Protein Dihedral Angle Prediction Methods

Tertiary structure prediction of a protein from its amino acid sequence is one of the major challenges in the field of bioinformatics. Hierarchical approach is one of the persuasive techniques used for predicting protein tertiary structure, especially in the absence of homologous protein structures. In hierarchical approach, intermediate states are predicted like secondary structure, dihedral angles, C^α-C^α distance bounds, etc. These intermediate states are used to restraint the protein backbone and assist its correct folding. In the recent years, several methods have been developed for predicting dihedral angles of a protein, but it is difficult to conclude which method is better than others. In this study, we benchmarked the performance of dihedral prediction methods ANGLOR and SPINE X on various datasets, including independent datasets. TANGLE dihedral prediction method was not benchmarked (due to unavailability of its standalone) and was compared with SPINE X and ANGLOR on only ANGLOR dataset on which TANGLE has reported its results. It was observed that SPINE X performed better than ANGLOR and TANGLE, especially in case of prediction of dihedral angles of glycine and proline residues. The analysis suggested that angle shifting was the foremost reason of better performance of SPINE X. We further evaluated the performance of the methods on independent ccPDB30 dataset and observed that SPINE X performed better than ANGLOR.     

Sequential resonance assignments in protein 1H nuclear magnetic resonance spectra: Computation of sterically allowed proton-proton distances and statistical analysis of proton-proton distances in single crystal protein conformations

Two different, theoretical studies of intramolecular proton-proton distances in polypeptide chains are described. Firstly, the distances between amide, C^α and C^β protons of neighbouring residues in the amino acid sequence, which correspond to the sterically allowed values for the dihedral angles φ_i, ψ_i and χ_i¹, were computed. Secondly, the frequency with which short distances occur between amide, C^α and C^β protons of neighbouring and distant residues in the amino acid sequence were statistically evaluated in a representative sample of globular protein crystal structures. Both approaches imply that semi-quantitative measurements of short, non-bonding proton-proton distances, e.g. by nuclear Overhauser experiments, should present a reliable and generally applicable method for sequential, individual resonance assignments in protein ¹H nuclear magnetic resonance spectra. Similar calculations imply that corresponding distance measurements can be used for resonance assignments in the side-chains of the aromatic amino acid residues, asparagine and glutamine, where the complete spin systems cannot usually be identified from through-bond spin-spin coupling connectivities.     

Effects of side-chain orientation on the <Superscript>13</Superscript>C chemical shifts of antiparallel β-sheet model peptides

The dependence of the ¹³C chemical shift on side-chain orientation was investigated at the density functional level for a two-strand antiparallel β-sheet model peptide represented by the amino acid sequence Ac-(Ala)₃-X-(Ala)₁₂-NH₂ where X represents any of the 17 naturally occurring amino acids, i.e., not including alanine, glycine and proline. The dihedral angles adopted for the backbone were taken from, and fixed at, observed experimental values of an antiparallel β-sheet. We carried out a cluster analysis of the ensembles of conformations generated by considering the side-chain dihedral angles for each residue X as variables, and use them to compute the ¹³C chemical shifts at the density functional theory level. It is shown that the adoption of the locally-dense basis set approach for the quantum chemical calculations enabled us to reduce the length of the chemical-shift calculations while maintaining good accuracy of the results. For the 17 naturally occurring amino acids in an antiparallel β-sheet, there is (i) good agreement between computed and observed ¹³C^α and ¹³C^β chemical shifts, with correlation coefficients of 0.95 and 0.99, respectively; (ii) significant variability of the computed ¹³C^α and ¹³C^β chemical shifts as a function of χ¹ for all amino acid residues except Ser; and (iii) a smaller, although significant, dependence of the computed ¹³C^α chemical shifts on χ^ξ (with ξ ≥ 2) compared to χ¹ for eleven out of seventeen residues. Our results suggest that predicted ¹³C^α and ¹³C^β chemical shifts, based only on backbone (φ,ψ) dihedral angles from high-resolution X-ray structure data or from NMR-derived models, may differ significantly from those observed in solution if the dihedral-angle preferences for the side chains are not taken into account. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Proton Nuclear Magnetic Resonance Studies on Huwentoxin-I from the Venom of the Spider Selenocosmia huwena: 2. Three-Dimensional Structure in Solution

The three-dimensional structure in aqueous solution of native huwentoxin-I, a neurotoxin from the venom of the spider Selenocosmia huwena, has been determined from two-dimensional ¹H NMR data recorded at 500 and 600 MHz. Structural constraints consisting of interproton distances inferred from NOEs and dihedral angles from spin–spin coupling constants were used as input for distance geometry calculation with the program XPLOR 3.1. The best 10 structures have NOE violations <0.3 Å, dihedral violations <2°, and pairwise root-mean-square differences of 1.08 (±0.20) Å over backbone atoms (N, C^α;, C). The molecule adopts a compact structure consisting of a small triple-stranded antiparallel β-sheet and five β-turns. A small hydrophobic patch consisting of Phe 6, Trp 28, and Trp 31 is located on one side of the molecule. All six lysine residues are distributed on the molecular surface. The three disulfidc bridges are buried within the molecule. The structure contains an “inhibitor cystine knot motif” which is adopted by several other small proteins, such as ω-conotoxin, agatoxin IVA, and gurmarin.     

Spatial configuration of single-stranded polynucleotides. Calculations of average dimensions and Nmr coupling constants

The probability distributions of the torsional angles (Φ′, ω′, ω, Φ, and ψ), which fix the structure of nucleotide backbone, have been calculated using the results of energy calculations based on extended Huckel theory (EHT), complete neglect of differential overlap (CNDO), perturbative configuration interaction using localized orbitals (PCILO), and classical potential functions (CPF) methods. Statistical average values of the vicinal ¹H? ¹H, ¹H? ³¹P, and ¹³C? ³¹P nmr coupling constants 〈J〉 have been calculated from the generalized Karplus relations using the probability distribution in the Φ′, Φ, and ψ space. Experimental 〈J〉 values for polyribouridylic acid (polyU) support the theoretical predictions for these torsional angles. Using Monte Carlo technique, random coils of single-stranded polynucleotides have been simulated and the mean-square end-to-end distance 〈r²〉 has been calculated. Molecular orbital methods (EHT, CNDO, and PCILO) suggest considerable flexibility around O? P bonds, leading to fairly small values for the characteristic ratio (C_∞ ～ 4). Observed values of the unperturbed characteristic ratio for polynucleotides are quite large (C_∞ ～ 18) suggesting a relatively rigid nucleotide backbone. The results based on molecular orbital calculations can be reconciled with the experimental values by introducing an additional stabilization of ～2 kcal mol^?1 for the predicted minimum energy ragion (Φ′ ～ 240°, ω′ ～ 290°, ω 290°, Φ 180°, and ψ 60°). Such a stabilization may arise from the association of water molecules and metal ions with the phosphate group and (or) Coulomb interaction between neighboring phosphate groups. The calculations provide a semiquantitative estimate of torsional rigidity in the nucleotide backbone.     

Crystal structure of the bovine α-chymotrypsin:kunitz inhibitor complex. An example of multiple protein:protein recognition sites

The crystal structure of bovine α-chymotrypsin (α-CHT) in complex with the bovine basic pancreatic trypsin inhibitor (BPTI) has been solved and refined at 2.8 Å resolution (R-factor=0.18). The proteinase:inhibitor complex forms a compact dimer (two α-CHT and two BPTI molecules), which may be stabilized by surface-bound sulphate ions, in the crystalline state. Each BPTI molecule, at opposite ends, is contacting both proteinase molecules in the dimer, through the reactive site loop and through residues next to the inhibitor's C-terminal region. Specific recognition between α-CHT and BPTI occurs at the (re)active site interface according to structural rules inferred from the analysis of homologous serine proteinase:inhibitor complexes. Lys15, the P₁ residue of BPTI, however, does not occupy the α-CHT S₁ specificity pocket, being hydrogen bonded to backbone atoms of the enzyme surface residues Gly216 and Ser217. © 1997 John Wiley & Sons, Ltd.     

An attempt to evaluate the influence of neighboring amino acids (n-1) and (n+1) on the backbone conformation of amino acid (n) in proteins. Use in predicting the three-dimensional structure of the polypeptide backbone of other proteins

From φ, ψ data on eleven proteins, a 20 × 20 × 20 Table of tripeptides has been computed to evaluate the influence of nearest neighbors (n ? 1) and (n + 1) on the φ, ψ angles of amino acid (n). From this Table, having removed values for horse cytochrome c and using the sequences of 18 cytochromes c and the procedure of Kabat &; Wu (1972), an attempt was made to select a set of φ, ψ angles for positions 2 to 103 of cytochrome c and compare them with the values obtained from the atomic co-ordinates. Agreement was good for 56, intermediate for 29 and poor for 17 residues. Eleven of the 17 with poor agreement were residues contacting the heme or adjacent to a contacting residue. Moreover, 6 of the 17 poor values were in regions of the φ, ψ plot for which no occurrences in the ten known proteins were reported, and for four others known values were minimal so that no basis for selection existed. Frequency distributions on the Ramachandran plot (Ramachandran &; Sasisekharan, 1968) of all φ, ψ values in the eleven known proteins are given as well as a contour plot for such frequencies. The uses and limitations of the procedure are discussed and the need for obtaining accurate estimates of errors in experimentally determined φ, ψ angles is emphasised.