Accurate geometries for “Mountain pass” regions of the Ramachandran plot using quantum chemical calculations

Unusual local arrangements of protein in Ramachandran space are not well represented by standard geometry tools used in either protein structure refinement using simple harmonic geometry restraints or in protein simulations using molecular mechanics force fields. In contrast, quantum chemical computations using small poly‐peptide molecular models can predict accurate geometries for any well‐defined backbone Ramachandran orientation. For conformations along transition regions—ϕ from −60 to 60°—a very good agreement with representative high‐resolution experimental X‐ray (≤1.5 Å) protein structures is obtained for both backbone C⁻¹‐N‐C_α angle and the nonbonded O⁻¹…C distance, while “standard geometry” leads to the “clashing” of O…C atoms and Amber FF99SB predicts distances too large by about 0.15 Å. These results confirm that quantum chemistry computations add valuable support for detailed analysis of local structural arrangements in proteins, providing improved or missing data for less understood high‐energy or unusual regions.     

Crystal structure of dehydromonopetide, (Z)-N-acetyl-α,β-dehydrophenylalanine methylamide

The crystal structure of (Z)-acetyl-α,β-dehydrophenylalanine methylamide (monoclinic Cc, a = 10.241(1), b = 15.252(1), c = 8.643(1) Å, β = 120.98(1)°, Z = 4) has been solved by x-ray diffraction to an R-factor = 0.148, and compared to that of the homologous L -phenylalanine dervative. Molecules are intermolecularly hydrogen-bonded to four neighboring molecules in a three-dimensional network with alternating layers of interacting amide bonds and orthogonally arranged phenyl rings. The existence of the C^α = C^β double bond results in a phenyl orientation that is forbidden for phenylananine (χ¹ = ?7,8°), and in shorter C^α ? C^β and C^β ? C^γ distances. The geometrical paramenters of the peptide backbone are not drastically modified by α,β-unsaturation. However, the N-C^α-C′ angle is increased by nearly 5°, and the dimensions, and therefore probably the electronic conjugation, of the N-terminal amide group to be affected by the occurrence of the vicinal C^α = C^β double bond.     

The Crystal Structure of d(CCCCGGGG): A New A-Form Variant with an Extended Backbone Conformation

Abstract

The crystal structure of d(CCCCGGGG) has been determined at a resolution of 2.25Å. The oligomers crystallize as A-DNA duplexes occupying crystallographic two-fold axes. The backbone conformation is, in general, similar to that observed in previously reported crystal structures of A-DNA fragments, except for the central linkage, where it adopts an extended structure resulting from all trans conformation at the P-05′-C5′-C4′ bonds. This type of conformation facilitates interstrand stacking between the guanines at the C-G site. The local helix twist at this step is very small (25°) compared to an overall average of 33.5°. The unique structure of the C-G base-pair step, namely the extended backbone and the distinct stacking geometry, may be an important feature in the recognition mechanism between double- stranded DNA molecules and restriction endonucleases such as Msp I, which cuts the sequence CCGG very specifically with a rate unaffected by neighboring base pairs.     

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.     

Conversion from a virtual-bond chain to a complete polypeptide backbone chain

A method for generating a complete polypeptide backbone structure from a set of C^α coordinates is presented. Initial trial values of ? and ψ for a selected residue are chosen (essentially from an identification of the conformational region of the virtual-bond backbone, e.g., and α-helical region), and values of ? and ψ for the remaining residues (both towards the N- and C-terminus) are then computed, subject to the constraint that the chain have the same virtual-bond angles and virtual-bond dihedral angles as the given set of C^α coordinates. The conversion from C^α coordinates to full backbone dihedral angles (?,ψ) involves the solution of a set of algebraic equations relating the virtual-bond angles and virtual-bond dihedral angles to standard peptide geometry and backbone dihedral angles. The procedure has been tested successfully on C^α coordinates taken from standard-geometry full-atom structures of bovine pancreatic trypsin inhibitor (BPTI). Some difficulty was encountered with error-sensitive residues, but on the whole the backbone generation was successful. Application of the method to C^α coordinates for BPTI derived from simplified model calculations (involving nonstandard geometry) showed that such coordinates may be inconsistent with the requirement that ?_Pro be near ?75°. In such a case, i.e., for residues for which the algebraic method failed, a leastsquares minimizer was then used in conjunction with the algebraic method; the mean-square deviation of the calculated C^α coordinates from the given ones was minimized by varying the backbone dihedral angles. Thus, these inconsistencies were circumvented and a full backbone structure whose C^α coordinates had an rms deviation of 0.26 Å from the given set of C^α coordinates was obtained.     

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     

Empirical Protein Energy Maps

WORK by several groups^1–5 has led to the calculation of energy maps for the peptide unit, which is the dependence of the conformational energy E_?,ψ on the torsional angles around the N-C^α bond (?) and the C^α-C bond (ψ)⁶ (Fig. 1) by using a standard set of bond lengths, valence angles and potential functions derived from small molecules. Although calculated maps are improved by refining the potential functions and increasing the number of parameters, there are differences according to the particular assumptions made. The most probable conformation of a peptide unit in proteins, using the available experimental information, is given by the following approach.     

Evaluation at atomic resolution of the role of strain in destabilizing the temperature‐sensitive T4 lysozyme mutant Arg 96 → His

Mutant R96H is a classic temperature‐sensitive mutant of bacteriophage T4 lysozyme. It was in fact the first variant of the protein to be characterized structurally. Subsequently, it has been studied extensively by a variety of experimental and computational techniques, but the reasons for the loss of stability of the mutant protein remain controversial. In the crystallographic refinement of the mutant structure at 1.9 Å resolution one of the bond angles at the site of substitution appeared to be distorted by about 11^°, and it was suggested that this steric strain was one of the major factors in destabilizing the mutant. Different computationally‐derived models of the mutant structure, however, did not show such distortion. To determine the geometry at the site of mutation more reliably, we have extended the resolution of the data and refined the wildtype (WT) and mutant structures to be better than 1.1 Å resolution. The high‐resolution refinement of the structure of R96H does not support the bond angle distortion seen in the 1.9 Å structure determination. At the same time, it does confirm other manifestations of strain seen previously including an unusual rotameric state for His96 with distorted hydrogen bonding. The rotamer strain has been estimated as about 0.8 kcal/mol, which is about 25% of the overall reduction in stability of the mutant. Because of concern that contacts from a neighboring molecule in the crystal might influence the geometry at the site of mutation we also constructed and analyzed supplemental mutant structures in which this crystal contact was eliminated. High‐resolution refinement shows that the crystal contacts have essentially no effect on the conformation of Arg96 in WT or on His96 in the R96H mutant.     

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.     

Conformational behavior of α,α-dialkylated peptides

The preferred conformations of N-acetyl-N′-methyl amides of some dialkylglycines have been determined by empirical conformational-energy calculations; minimum-energy conformations were located by minimizing the energy with respect to all the dihedral angles of the molecules. The conformational space of these compounds is sterically restricted, and low-energy conformations are found only in the regions of fully extended and helical structures. Increasing the bulkiness of the substituents on the C^α, the fully extended conformation becomes gradually more stable than the helical structure preferred in the cases of dimethylglycine. This trend is, however, strongly dependent on the bond angles between the substituents on the C^α atom: In particular, helical structures are favored by standard values (111°) of the N-C^α-C′ angle, while fully extended conformations are favored by smaller values of the same angle, as experimentally observed, for instance, in the case of α,α-di-n-propylglycine.     

The determinants of bond angle variability in protein/peptide backbones: A comprehensive statistical/quantum mechanics analysis

The elucidation of the mutual influence between peptide bond geometry and local conformation has important implications for protein structure refinement, validation, and prediction. To gain insights into the structural determinants and the energetic contributions associated with protein/peptide backbone plasticity, we here report an extensive analysis of the variability of the peptide bond angles by combining statistical analyses of protein structures and quantum mechanics calculations on small model peptide systems. Our analyses demonstrate that all the backbone bond angles strongly depend on the peptide conformation and unveil the existence of regular trends as function of ψ and/or φ. The excellent agreement of the quantum mechanics calculations with the statistical surveys of protein structures validates the computational scheme here employed and demonstrates that the valence geometry of protein/peptide backbone is primarily dictated by local interactions. Notably, for the first time we show that the position of the H^α hydrogen atom, which is an important parameter in NMR structural studies, is also dependent on the local conformation. Most of the trends observed may be satisfactorily explained by invoking steric repulsive interactions; in some specific cases the valence bond variability is also influenced by hydrogen‐bond like interactions. Moreover, we can provide a reliable estimate of the energies involved in the interplay between geometry and conformations. Proteins 2015; 83:1973–1986. © 2015 Wiley Periodicals, Inc.     

Crystal and molecular structure of benzyloxycarbonyl-α-aminoisobutyryl-L-prolyl methylamide: The observation of an X2-Pro3 Type III β-Turn

The crystal and molecular structure of N-benzyloxycarbonyl-α-aminoisobutyryl-L -prolyl methylamide, the amino terminal dipeptide fragment of alamethicin, has been determined using direct methods. The compound crystallizes in the orthorhombic system with the space group P2₁2₁2₁. Cell dimensions are a = 7.705 Å, b = 11.365 Å, and c = 21.904 Å. The structure has been refined using conventional procedures to a final R factor of 0.054. The molecular structure possesses a 4 → 1 intramolecular N-H—O hydrogen bond formed between the CO group of the urethane moiety and the NH group of the methylamide function. The peptide backbone adopts the type III β-turn conformation, with ?₂ = ?51.0°, ψ₂ = ?39.7°, ?₃ = ?65.0°, ψ₃ = ?25.4°. An unusual feature is the occurrence of the proline residue at position 3 of the β-turn. The observed structure supports the view that Aib residues initiate the formation of type III β-turn conformations. The pyrrolidine ring is puckered in C^γ-exo fashion.     

Structure of the complex formed by bovine trypsin and bovine pancreatic trypsin inhibitor. II. Crystallographic refinement at 1.9 A resolution

The crystal structure of the complex formed by bovine trypsin and bovine pancreatic trypsin inhibitor has been refined with data to 1.9 Å resolution, using a procedure described by Deisenhofer &; Steigemann (1974) in their refinement of the crystal structure of the free inhibitor. This procedure involves cycles consisting of phase calculation using the current atomic model, Fourier synthesis using these phases and the observed structure factor amplitudes and Diamond's real-space refinement (Diamond, 1971,1974). At various stages, difference Fourier syntheses are calculated to detect and correct gross errors in the model and to localize solvent molecules.The refinement progressed smoothly, starting with the model obtained from the isomorphous Fourier map at 2.6 Å resolution. The R-factor is 0.23 for 20,500 significantly measured reflections to 1.9 Å resolution, using an over-all temperature factor of 20 Ų. The estimated standard deviation of atomic positions is 0.09 Å.An objective assessment of the upper limit of the error in the atomic coordinates of the final model is possible by comparing the inhibitor component in the model of the complex with the refined structure of the free inhibitor (Deisenhofer &; Steigemann, 1974). The mean deviation of main-chain atoms of the two molecular models in internal segments is 0.25 Å, of main-chain dihedral angles 5.1 ° and side-chain dihedral angles 6.5 °.A comparison of the trypsin component with α-chymotrypsin (Birktoft &; Blow, 1972) showed a mean deviation of main-chain atoms of 0.75 Å. The structures are closely similar and the various deletions and insertions cause local structural differences only.     

Spatial structure of dimeric a genetically engineered variant of green fluorescent protein EGFP-K162Q in the P61 crystal space group

The spatial structure of dimeric green fluorescent protein EGFP-K162Q with MDELYK (EGFPv) C-terminal deletion has been assigned in the P6₁ space group with resolution 1.34 Å by X-ray diffraction analysis. The results have been compared with X-ray diffraction data of monomeric EGFP (green biomarker with enhanced photophysical properties) assigned in another crystal space group, P2₁2₁2₁, with resolution 1.50 and 1.35 Å. Subunits in the EGFPv dimeric structure are located at 75° angle with the contact area ～800 Ų. The dimeric framework is stabilized by the six hydrogen bonds and central hydrophobic core of six residues. The root-mean-square deviation value for C^α atoms in 3–230 residues of the P6₁ and P2₁2₁2₁ crystal structures is 0.55 Å. The differential characteristics of EGFPv-P6₁ structure, compared to that of P2₁2₁2₁, is a noticeably different orientation of the Glu222 side chain, and a new conformation of the 155–159 loop fragment, characterized by deviations among the C^α atoms of superimposed structures reaching 4.6 Å for Lys156 and 5.5 Å for Lys158.     

Accommodation of a D-Phe residue into a right-handed 310-helix: Structure of Boc-D-Phe-(Aib)4-Gly-L-Leu-(Aib)2-Ome,an analogue of the amino terminal segment of antiamoebins and emerimicins

The crystal structure of the nonapeptide Boc-D -Phe-Aib-Aib-Aib-Aib-Gly-Leu-Aib-AibOMe (I), which is an analogue of the N-terminal sequence of antiamoebins and emerimicins, establishes a completely 3₁₀-helical conformation with seven successive intramolecular 4 → 1 hydrogen bonds. The average, ?, ψ values for residues 1–8 are ?59° and ?32°, respectively. Crystal parameters are C₄₇H₇₇N₉O₁₂, space group P1, a = 10.636(4) Å, b = 11.239(4) Å, c = 12.227(6) Å, α = 101.17(4)°, β = 97.22(4)°, γ = 89.80(3)°, Z = 1, R = 5.95% for 3018 data with |F₀| > 3α(F), resolution 0.93 Å. The use of the torsion angle κ = C(i ? 1)N(i)C^α(i)C^β(i), where κ = 68° for D -Phe and κ = 164° for L -Leu, confirms the opposite configurations of these residues. The ?, ψ values of ?62° and ?32° at D -Phe are unusual, since this region is characteristic of residues with L configurations. Peptide I possesses only two chiral residues of opposing configuration. The observed right-handed 3₁₀-helical structure suggests that helix sense has probably been determined by the stereo-chemical preferences of the Leu residue. © 1993 John Wiley & Sons, Inc.     

Crystallographic characterization of the α,γ C12 helix in hybrid peptide sequences

The solid‐state conformations of two αγ hybrid peptides Boc‐[Aib‐γ⁴(R)Ile]₄‐OMe 1 and Boc‐[Aib‐γ⁴(R)Ile]₅‐OMe 2 are described. Peptides 1 and 2 adopt C₁₂‐helical conformations in crystals. The structure of octapeptide 1 is stabilized by six intramolecular 4 → 1 hydrogen bonds, forming 12 atom C₁₂ motifs. The structure of peptide 2 reveals the formation of eight successive C₁₂ hydrogen‐bonded turns. Average backbone dihedral angles for αγ C₁₂ helices are peptide 1 , Aib; φ (°) = ?57.2 ± 0.8, ψ (°) = ?44.5 ± 4.7; γ⁴(R)Ile; φ (°) = ?127.3 ± 7.3, θ₁ (°) = 58.5 ± 12.1, θ₂ (°) = 67.6 ± 10.1, ψ (°) = ?126.2 ± 16.1; peptide 2 , Aib; φ (°) = ?58.8 ± 5.1, ψ (°) = ?40.3 ± 5.5; ψ⁴(R)Ile; φ (°) = ?123.9 ± 2.7, θ₁ (°) = 53.3 θ 4.9, θ ₂ (°) = 61.2 ± 1.6, ψ (°) = ?121.8 ± 5.1. The tendency of γ⁴‐substituted residues to adopt gauche–gauche conformations about the C^α–C^β and C^β–C^γ bonds facilitates helical folding. The αγ C₁₂ helix is a backbone expanded analog of α peptide 3₁₀ helix. The hydrogen bond parameters for α peptide 3₁₀ and α‐helices are compared with those for αγ hybrid C₁₂ helix. Copyright © 2016 European Peptide Society and John Wiley & Sons.     

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.     

Observation of a sterically unfavorable side-chain conformation in a leucyl residue: Crystal and molecular structure of L-leucyl–L-leucine · DMSO solvate

The crystal structure of a dipeptide L -leucyl–L -leucine (C₁₂H₂₄N₂O₃) has been determined. The crystals are monoclinic, space group P2₁, with a = 5.434(4) Å, b = 15.712(7) Å, c = 11.275(2) Å, β = 100.41(1)°, and Z = 2. The crystals contain one molecule of dimethyl sulfoxide (DMSO) as solvent of crystallization for each dipeptide molecule. The structure has been solved by direct methods and refined to a final R index of 0.059 for 920 reflections (sinθ/λ ? 0.60 Å^?1) with I ? 2σ (I). The trans peptide unit shows substantial degree of non-planarity (Δω = 14°). The peptide backbone adopts an extended conformation with torsion angles of ψ₁ = 138(1)°, ω₁ = 166(1)°, ?₂ = ? 149.3(7)°, ψ₂₁ = 164.2(7)°, and ψ₂₂ = ? 15(1)°. For the first leucyl residue, the side-chain conformation is specified by the torsion angles ¹χ₁ = 176.7(7)°, ¹χ₂₁ = 62(1)°, ¹χ₂₂ = ? 177.4(8)°; the second leucyl residue adopts a Sterically unfavorable conformation with ²χ₁ = 61(1)°, ²χ₂₁ = 97(1)°, and ²χ₂₂ = ?151(1)°. The packing involves head-to-tail interaction of peptide molecules and segregation of polar and nonpolar regions. The DMSO molecule is strongly hydrogen bonded to the terminal NH group. © 1994 John Wiley & Sons, Inc.     

Peptide design 310-helical conformation of a linear pentapeptide containing two dehydrophenylalanines,Boc-Gly-ΔZPhe-Leu-ΔZPhe-Ala-NHCH3

α, β-Dehydroamino acids are expected to provide conformational constraint to the peptide backbone. A pentapeptide containing two dehydrophenylalanines (Δ^ZPhe) separated by one L -amino acid has been synthesized and its solid state conformation determined. The pentapeptide, Boc-Gly-Δ^ZPhe-Leu-Δ^ZPhe-Ala-NHCH₃, crystallizes from aqueous methanol in the orthorhombic space group P2₁2₁2₁. There are four formula units, C₃₅H₄₆N₆O₇, in a unit cell of dimensions a = 10.155(3), b = 15.175(1), and c = 23.447(2) Å, at room temperature. The structure was solved by direct methods program, SIR88, and refined to a final R = 0.038 based on 3049 reflections with I > 2σ(I). All the peptide links are trans and the backbone conformation of the pentapeptide can be described as a 3₁₀-helix, with mean ?, ψ values of ?65.1° and ?22.8° (the value is averaged over the first four residues). There are four intramolecular 4 → 1 type hydrogen bonds characteristic of 3₁₀-type helices. In the crystal, the helices are held together by intermolecular N? H…?O?C head-to-tail and lateral hydrogen bonding between symmetry related molecules. This mode of packing is similar to the packing motifs observed so often in other oligopeptides that adopt a 3₁₀-helical structure. © 1993 John Wiley & Sons, Inc.     

PCS-based structure determination of protein–protein complexes

A simple and fast nuclear magnetic resonance method for docking proteins using pseudo-contact shift (PCS) and ¹H^N/¹⁵N chemical shift perturbation is presented. PCS is induced by a paramagnetic lanthanide ion that is attached to a target protein using a lanthanide binding peptide tag anchored at two points. PCS provides long-range (~40 Å) distance and angular restraints between the lanthanide ion and the observed nuclei, while the ¹H^N/¹⁵N chemical shift perturbation data provide loose contact-surface information. The usefulness of this method was demonstrated through the structure determination of the p62 PB1-PB1 complex, which forms a front-to-back 20 kDa homo-oligomer. As p62 PB1 does not intrinsically bind metal ions, the lanthanide binding peptide tag was attached to one subunit of the dimer at two anchoring points. Each monomer was treated as a rigid body and was docked based on the backbone PCS and backbone chemical shift perturbation data. Unlike NOE-based structural determination, this method only requires resonance assignments of the backbone ¹H^N/¹⁵N signals and the PCS data obtained from several sets of two-dimensional ¹⁵N-heteronuclear single quantum coherence spectra, thus facilitating rapid structure determination of the protein–protein complex.