(φ,ψ)₂ motifs: a purely conformation-based fine-grained enumeration of protein parts at the two-residue level

A deep understanding of protein structure benefits from the use of a variety of classification strategies that enhance our ability to effectively describe local patterns of conformation. Here, we use a clustering algorithm to analyze 76,533 all-trans segments from protein structures solved at 1.2 Å resolution or better to create a purely φ,ψ-based comprehensive empirical categorization of common conformations adopted by two adjacent φ,ψ pairs (i.e., (φ,ψ)₂ motifs). The clustering algorithm works in an origin-shifted four-dimensional space based on the two φ,ψ pairs to yield a parameter-dependent list of (φ,ψ)₂ motifs, in order of their prominence. The results are remarkably distinct from and complementary to the standard hydrogen-bond-centered view of secondary structure. New insights include an unprecedented level of precision in describing the φ,ψ angles of both previously known and novel motifs, ordering of these motifs by their population density, a data-driven recommendation that the standard C^α_i…C^α_i + 3 < 7 Å criteria for defining turns be changed to 6.5 Å, identification of β-strand and turn capping motifs, and identification of conformational capping by residues in polypeptide II conformation. We further document that the conformational preferences of a residue are substantially influenced by the conformation of its neighbors, and we suggest that accounting for these dependencies will improve protein modeling accuracy. Although the CUEVAS-4D(r₁₀?₁₄) ‘parts list’ presented here is only an initial exploration of the complex (φ,ψ)₂ landscape of proteins, it shows that there is value to be had from this approach, and it opens the door to more in-depth characterizations at the (φ,ψ)₂ level and at higher dimensions.     

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.     

Ramachandran analysis of conserved glycyl residues in homologous proteins of known structure

High conservation of glycyl residues in homologous proteins is fairly frequent. It is commonly understood that glycine tends to be highly conserved either because of its unique Ramachandran angles or to avoid steric clash that would arise with a larger side chain. Using a database of aligned 3D structures of homologous proteins we identified conserved Gly in 288 alignment positions from 85 families. Ninety‐six of these alignment positions correspond to conserved Gly residue with (φ, ψ) values allowed for non‐glycyl residues. Reasons for this observation were investigated by in‐silico mutation of these glycyl residues to Ala. We found in 94% of the cases a short contact exists between the C^β atom of the introduced Ala with the atoms which are often distant in the primary structure. This suggests the lack of space even for a short side chain thereby explaining high conservation of glycyl residues even when they adopt (φ, ψ) values allowed for Ala. In 189 alignment positions, the conserved glycyl residues adopt (φ, ψ) values which are disallowed for Ala. In‐silico mutation of these Gly residues to Ala almost always results in steric hindrance involving C^β atom of Ala as one would expect by comparing Ramachandran maps for Ala and Gly. Rare occurrence of the disallowed glycyl conformations even in ultrahigh resolution protein structures are accompanied by short contacts in the crystal structures and such disallowed conformations are not conserved in the homologues. These observations raise the doubt on the accuracy of such glycyl conformations in proteins.     

Characterizing aqueous solution conformations of a peptide backbone using Raman optical activity computations

Mounting spectroscopic evidence indicates that alanine predominantly adopts extended polyproline II (PPII) conformations in short polypeptides. Here we analyze Raman optical activity (ROA) spectra of N-acetylalanine-N′-methylamide (Ala dipeptide) in H₂O and D₂O using density functional theory on Monte Carlo (MC) sampled geometries to examine the propensity of Ala dipeptide to adopt compact right-handed (α_R) and left-handed (α_L) helical conformations. The computed ROA spectra based on MC-sampled α_R and PPII peptide conformations contain all the key spectral features found in the measured spectra. However, there is no significant similarity between the measured and computed ROA spectra based on the α_L- and β-conformations sampled by the MC methods. This analysis suggests that Ala dipeptide populates the α_R and PPII conformations but no substantial population of α_L- or β-structures, despite sampling α_L- and β-structures in our MC simulations. Thus, ROA spectra combined with the theoretical analysis allow us to determine the dominant populated structures. Including explicit solute-solvent interactions in the theoretical analysis is essential for the success of this approach.     

Coiling of beta-pleated sheets

To form strongly twisted β-sheets, strands have to be coiled as well as twisted (Nishikawa &; Scherga, 1976). I show that strands coil in the appropriate right-handed direction if their main-chain torsion angles fulfil the following conditions: ψ_i ? ?φ_{i + 1}, ψ_{i + 1} > ?φ_{i + 2}, ψ_{i + 2} ? ?φ_{i + 3}, ψ_{i + 3} > ?φ_{i + 4}…Lactate dehydrogenase, pancreatic trypsin inhibitor, thermolysin and concanavalin A contain strongly twisted β-sheets and in each case the strands are coiled by their φ, ψ values fulfilling these conditions.     

De novo design of α,β-didehydrophenylalanine containing peptides: from models to applications

The de novo design of peptides and proteins has emerged as an approach for investigating protein structure and function. The success relies heavily on the ability to design relatively short peptides that can adopt stable secondary structures. To this end, substitution with α,β-dehydroamino acids, especially α,β-didehydrophenylalanine (ΔPhe or ΔF) has blossomed in manifold directions, providing a rich diversity of well-defined structural motifs. Introduction of α,β-didehydrophenylalanine induces β-bends in small and 3(10)-helices in longer peptide sequences. Most favorable conformation of ΔF residues are (φ,ψ) ～(60°, 30°), (-60°, -30°), (-60°, 150°), and (60°, -150°). These features have been exploited in designing helix-turn-helix, helical bundle arrangements, and glycine zipper type super secondary structural motifs. The unusual capability of α,β-didehydrophenylalanine ring to form a variety of multicentered interactions (N-H…O, C-H…O, C-H…π, and N-H…π) suggests its possible exploitation for future de novo design of supramolecular structures. This work has now been extended to the de novo design of peptides with antibiotic, antifibrillization activity, etc. More recently, self-assembling properties of small dehydropeptides have been explored. This review focuses primarily on the structural and functional behavior of α,β-didehydrophenylalanine containing peptides.     

Quantum-chemical and empirical calculations on phospholipids. VII. The conformational behaviour of the phosphatidylcholine headgroup in layer systems

Starting from single molecule calculations the intermolecular interactions of the glycerophosphatidylcholine (GPC) headgroup with its nearest neighbours in a layer crystal were taken into account using 1-6-12 interatomic potential functions. By use of a steepest descent energy minimisation procedure over all variable torsion angles (θ₁, α₁ … α₆) of the GPC headgroup the minima of the seven-dimensional energy hypersurface were calculated. The torsion angles and the energies of the most stable conformations are given in polar coordinates. The components of the headgroup dipolar moment of these conformations were calculated to be μ₆ = 3.0 … 9.5 D, μ_⊥ = 17.5 … 24 D, μ = 18.5 … 25 D using the net atomic charge distribution in space. The results demonstrate a high flexibility of the GPC headgroup. Around the C-1O-11 bond (α₁), only antiperiplanar conformations are allowed. The $\text{α}{}_4\text{α}{}_5\text{(α}{}_6\text{)}$ correlation diagram shows that the choline group exists in mirror-image enantiomeric conformations. Our results yield a foundation of models of the dynamical behaviour of the phosphatidylcholine headgroup at the level of conformational behaviour and are in agreement with experimental data.     

Beyond basins: φ,ψ preferences of a residue depend heavily on the φ,ψ values of its neighbors

The Ramachandran plot distributions of nonglycine residues from experimentally determined structures are routinely described as grouping into one of six major basins: β, P_II, α, α_L, ξ and γ'. Recent work describing the most common conformations adopted by pairs of residues in folded proteins [i.e., (φ,ψ)₂‐motifs] showed that commonly described major basins are not true single thermodynamic basins, but are composed of distinct subregions that are associated with various conformations of either the preceding or following neighbor residue. Here, as documentation of the extent to which the conformational preferences of a central residue are influenced by the conformations of its two neighbors, we present a set of φ,ψ‐plots that are delimited simultaneously by the φ,ψ‐angles of its neighboring residues on both sides. The level of influence seen here is typically greater than the influence associated with considering the identities of neighboring residues, implying that the use of this heretofore untapped information can improve the accuracy of structure prediction algorithms and low resolution protein structure refinement.     

Biophysical study of molecular mechanism of abortificient action of prostaglandins II. The study of the long and short range interaction between different fragments of PGF2α, PGF1β and PGA1

This paper reports the study of the long and short range interactions between the ring-chain and chain-chain portions for three different forms of prostaglandins (PGF_2α, PGF_1β and PGA₁) for the possible rotations around C₁₂-C₁₃ (θ), C₇-C₈ (ψ) and C₁₄-C₁₅ (φ). The calculations were based on the long range interaction formalism of Claverie and Rein, using longitudinal and transverse polarizability data. Although the chain-chain interactions play predominant role in the stabilization of molecular geometry in the normal crystallographic forms, it is found that the ring-chain interactions and especially the interactions between the carboxylic chain and the ring vary in a specific way. They lead to the formation of several low lying conformations with the total interaction energy differing by few kcal/mole. The significant differences between the interaction energies of the active and inactive forms (in relation to their abortificient action) are noted and their relevance to the specificity of the molecular mechanism of the action discussed.     

Quantitative f torsion angle analysis in Desulfovibrio vulgaris flavodoxin based on six f related 3 J couplings

Quantitative φ-dihedral angle determinations of non-glycine and non-proline residues in Desulfovibrio vulgaris flavodoxin are carried out on the exclusive basis of ³ J coupling constants. In total 124 ³ JHNH _α , 123 ³ JHNC _′i , 118 ³ JHNC _β , 117 ³ JC′ _i–1Hα , 109 ³ JC′ _i–1C′i , and 103 ³ JC′ _i–1Hβ values form the experimental basis for translating J coupling data into geometry information using various combinations of Karplus parameters given in the literature. In addition, each backbone torsional angle φ is adjusted assuming different models of local geometry, either a rigid torsion, a Gaussian distribution centered at a distinct angle, or a two-site jump model. Numerical optimization is followed by a statistical significance evaluation to assess the results. It is found that experimental coupling constants of most of the residues involved in secondary structure elements agree best with those predicted from rigid local conformations. For dihedral angles in loop regions, mobility effects are not negligible, and a single torsion (Glu 42) is likely to adopt two distinct adjustments. However, α-helix conformations with –60° < φ < –45° give rise to an alternate solution with φ≈+170° with similar statistical significance when using the four traditionally determined proton-involved ³ J couplings. This ambiguity is efficiently avoided only when taking advantage of the complete data set comprising six available experimental ³ J coupling constants and of the degeneracy intrinsic to the Karplus relation. The optimized φ conformations are compared with reference values from the crystal structure of flavodoxin.     

Conformational characteristics of polypeptides containing isolated L-proline residues with cis peptide bonds

The conformational characteristics of the peptide sequence X-l-Pro, where X  Gly or l-Ala and the peptide bond joining X and l-Pro is cis, are evaluated. Semi-empirical potential functions are used to estimate the contributions to the conformational energy made by the non-bonded van der Waals' and electrostatic interactions and the intrinsic torsional potentials about the NC^a and C^aC′ bonds. Rotations φ₁ and ψ₁ about the NC^a and C^aC′ bonds in residue X and rotation ψ₂ about the C^aC′ bond in l-Pro are permitted, while the angle of rotation φ₂ about the NC^a bond in l-Pro is fixed at 120 ° by the pyrrolidine ring. The presence of the cis peptide bond connecting X and l-Pro renders the backbone rotations φ₁, ψ₁ in X dependent upon the rotation ψ₂ about the C^aC′ bond in l-Pro. (Interdependence of rotations in neighboring residues joined by a cis peptide bond was previously observed in l-alanine oligomers.) The number of energetically allowed conformations for the Gly and l-Ala residues preceding a cis peptide bond l-Pro residue are found to be substantially reduced from those permitted when the peptide bond is trans or when l-Pro is replaced by an amino acid residue. On the other hand, ψ₂ = 100 to 160 ° (cis′) and 300 to 0 ° (trans′) are found to be the lowest energy conformations of the l-Pro residue irrespective of the cis or trans conformation of the X-l-Pro peptide bond.     

Coarse-Grained Simulation of Full-Length Integrin Activation

Integrin conformational dynamics are critical to their receptor and signaling functions in many cellular processes, including spreading, adhesion, and migration. However, assessing integrin conformations is both experimentally and computationally challenging because of limitations in resolution and dynamic sampling. Thus, structural changes that underlie transitions between conformations are largely unknown. Here, focusing on integrin αvβ₃, we developed a modified form of the coarse-grained heterogeneous elastic network model (hENM), which allows sampling conformations at the onset of activation by formally separating local fluctuations from global motions. Both local fluctuations and global motions are extracted from all-atom molecular dynamics simulations of the full-length αvβ₃ bent integrin conformer, but whereas the former are incorporated in the hENM as effective harmonic interactions between groups of residues, the latter emerge by systematically identifying and treating weak interactions between long-distance domains with flexible and anharmonic connections. The new hENM model allows integrins and single-point mutant integrins to explore various conformational states, including the initiation of separation between α- and β-subunit cytoplasmic regions, headpiece extension, and legs opening.     

Stereochemistry of nucleic acids and their constituents. IV. Allowed and preferred conformations of nucleosides,nucleoside mono-, di-, tri-, tetraphosphates,nucleic acids and polynucleotides

A uniform notation and convention is suggested to describe the torsional angles in nucleic acids and their derivatives. The torsional angle χ, relating the stereochemistry of the base with respect to the sugar, shows more variation for the β-purine glycosides than for the β-pyrimidine glycosides. This variation is attributed to the fact that the β-purine derivatives may form intramolecular O(5′)-H…N(3) hydrogen bonding. The χ values for the α-purine and α-pyrimidine glycosides show preference for the –syn-clinal (or anti) conformation. The mode of puckering of the sugar also influences the χ value. The various possible conformations for the furanose ring are described by the torsional angles τ₀ τ₁, τ₂, τ₃, τ₄, about the five ring bonds. From an analysis of the torsional angles (ω, ?, ψ, ψ′, ?′, ω′) about the sugar phosphate bonds in the x-ray structures of the known nucleosides, nucleotides, phosphodiesters, nucleic acids, and related compounds, and from a consideration of molecular models, it is found that the possible conformations for the backbone of helical nucleic acids is strikingly limited. Most importantly, the preferred conformation of the nucleotide unit in poly nucleotides and nucleic acids turns out to be the same as that found for the nucleotide in the crystal structure. It is observed that base “stacking” is a consequence of the restricted backbone conformation. The torsional angles are illustrated in the form of conformational “wheels”. Interrelation between the torsion angles about successive pairs of sugar-phosphate bonds are presented in the form of conformational maps: ω,?; ?,ψ; ψ.ψ′; ψ′,?′; ?′,ω′; ω′,ω. The ω′,ω map shows the perferred conformations about the inter-nucleotide bonds of right- and left-handed helices and the possible conformations of phosphodiesters. The preferred conformation of the pyrophosphate and triphosphate is that in which the phosphate oxygens display a staggered arrangement when viewed along the P–P axis. A plausible structure and conformation for the ATPM^2? backbound complex is presented. This structure differs from that proposed by SzentGyorgi in that the metal (only transition metals are considered here) is not bound to the NH₂ nitrogen of adenine, but rather is simultaneously bound to N(7) of the ring and three phosphates (α, β, γ), or N(7) of the ring and two phosphates (β, γ). The remaining metal coordination may be satisfied by solvent–metal or enzyme–metal bonds.     

Anticodons,Frameshifts, and Hidden Periodicities in tRNA Sequences

Abstract

Fourier analysis of the short-range periodicities for the complete set of sequences coding for tRNA genes in genome of Bacillus subtilis proves that periodicities with periods p = 2, 3, 4, and 6 sites are the inherent properties of tRNAs. The related periodicities should be understood in a broad statistical sense and their identifying needs the elaborate statistical methods. To improve the statistics, the analysis of significant periodicities was performed for the binary R-Y, S-W, and K-M sequences. Generally, such short-range periodicities are produced via biased positioning of particular nucleotides rather than via the tandem multiplication and subsequent modifications of repeats, though the latter mechanism may also be realized. Quasi-coherently piercing long segments of tRNA, the short-range periodicities create the effective long-range structural coupling between the acceptor stem and the anticodon loop and may participate in the mechanisms of molecular recognition. The periodicities with p = 2 and 4 provide the natural ground for the translation with spontaneous or programmed frameshifting and are present in tRNAs decoding the most frameshift-prone codons. The observation of short-range periodicities suggests that the mechanisms of amino-acylation of tRNAs and codon-anticodon pairing are not independent. Their study may also provide the important information related to the origin and evolution of the genetic code.     

Logical analysis of the mechanism of protein folding III. Prediction of the strong long-range interactions.

It has been found that strong long-range interactions occur in regions having large β-structural potentials. As has been described previously (Nagano, 1974), interactions among regions having both helical and β-structural potentials (αβ-gaβ interactions) are also very important. Accordingly, an idea is presented in this paper that the relative stability of a protein conformation could be estimated by a relatively simple mathematical function of sequence and conformation. The function P(p,q) is called the non-energy part of pseudo-free energy, because minimization of the sum of P(p,q) and energy functions (cf. Levitt, 1974; Warme &; Scheraga, 1974) can be expected to lead to a plausible model of a protein. A merit of the function is that it can help us decide which way to go in manipulating a temporarily built model, e.g. towards a helix-rich protein or towards a β-structure-rich protein. The estimation of P(p,q) as an artificial potential does not use much computer time because only the co-ordinates of the β-carbon atoms (α-carbon atoms if the residue is Gly) are used. It is composed of terms of the long-range interactions P_L and short-range interactions P_S. The term P_L represents the relative strength of helix-helix interactions, helix-β-candidate interactions and β-candidate-β-candidate interactions. It is assumed that both helical and β-structural potentials can be measured as the differences between the predicted function for helix and β-structure, respectively, as defined previously (Nagano, 1973), and the corresponding largest values ever found. A hypothesis that two residues distantly separated in the primary sequence contribute less to the stability of the whole molecule is finally discarded because the true conformation of concanavalin A becomes very unstable compared with its false conformation folded like the main part of subtilisin. The parameters thus determined indicate that the helix-β-candidate interactions are almost as important as the β-candidate-β-candidate interactions. Both helix and loop prediction functions are combined to give the short-range interactions term, P_S, according to whether the region is really helical or not, and to whether it is really looped or not. The function P(p,q) can be used as a criterion for judging whether the predicted conformation is realistic or false, because the parameters can be adjusted to give, within limits, reasonable values of −10 kcal/residue for true conformations and higher than −5 kcal/residue for false conformations.As an application of the present theory of protein folding, the tertiary structure of bacteriophage T4 lysozyme is predicted and presented in Figure 1, prior to the X-ray structure becoming available.     

Local mobility of the lac repressor molecule

The rotational mobility of lac repressor from Escherichia coli was investigated by nanosecond fluorescence depolarization spectroscopy. A single rotational correlation time (φ) of the repressor was observed by monitoring the emission anisotropic decay of the intrinsic tryptophan fluorescence. The small value of φ (9·5 ns) suggests that one or both of the two tryptophan residues in the repressor are located in a flexible segment of the protein molecule. This segmental flexibility is enhanced by binding of inducer (isopropyl-β-d-thiogalactoside) to the repressor while it is restrained by binding of anti-inducer (glucose) or small DNA fragments, as indicated by the changes in φ. Further time-dependent emission anisotropy studies with an extrinsic fluorescent probe, N-(iodoacetylaminoethyl)-5-naphthylamine-1-sulfonate, covalently attached to the repressor yielded two rotational correlation times. The shorter φ_S (6·7 ns) also corresponds to a segmental flexibility whereas the longer φ_L (118 ns) represents the rotational motion of the entire repressor molecule. Both the values of φ_S and φ_L vary by addition of inducer or anti-inducer in a manner similar to that observed for the intrinsic tryptophan fluorescence but they are insensitive to addition of DNA fragments. The changes in local mobility of the lac repressor molecule observed in these studies may provide some insight into how inducer (or anti-inducer) destabilizes (or stabilizes) the repressor-operator complex.     

Toward engineering efficient peptidomimetics. Screening conformational landscape of two modified dehydroaminoacids

Effective peptidomimetics should posses structural rigidity and appropriate interaction pattern leading to potential spatial and electronic matching to the target receptor site. Rational design of such small bioactive molecules could push chemical synthesis and molecular modeling toward faster progress in medicinal chemistry. Conformational properties of N‐t‐butoxycarbonyl‐glycine‐(E/Z)‐dehydrophenylalanine N′,N′‐dimethylamides (Boc‐Gly‐(E/Z)‐ΔPhe‐NMe₂) in chloroform were studied by NMR and IR spectroscopy. The experimental findings were supported by extensive calculations at DFT(B3LYP, M06‐2X) and MP2 levels of theory and the β‐turn tendency for both isomers of the studied dipeptide were determined in vacuum and in solution. The theoretical data and experimental IR results were used as an additional information for the NMR‐based determination of the detailed solution conformations of the peptides. The obtained results reveal that N‐methylation of C‐terminal amide group changes dramatically the conformational properties of studied dehydropeptides. Theoretical conformational analysis reveals that the tendency to adopt β‐turn conformations is much weaker for the N‐methylated Z isomer (Boc‐Gly‐(Z)‐ΔPhe‐NMe₂), both in vacuum and in polar environment. On the contrary, N‐methylated E isomer (Boc‐Gly‐(E)‐ΔPhe‐NMe₂) can easily adopt β‐turn conformation, but the backbone torsion angles (φ₁, ψ₁, φ₂, ψ₂) are off the limits for common β‐turn types. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 28–40, 2014.     

Chirality in amino acids beyond the Cα configuration

Based on a CSD search, a meta‐analysis of 1179 structures of 19 natural amino acids H₃NC_αH(R)C′(O)O and their derivatives H₃NC_αH(R)C′(O)O(H/R/M), protonated, esterified, or coordinated at the carboxylic group, shows that the chirality chain with its two steps, established in the preceding paper for alanine, can be extended to natural amino acids. High diastereoselectivities are observed in the induction from the L configuration at C_α to the ?ψ and +ψ conformations, which in turn distort the planar carboxylic group C_αC′(O_cis)O_trans to asymmetric flat tetrahedra, showing that the chirality chain is an integral part of natural amino acids.