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.     

Role of amino acid properties to determine backbone tau(N-Calpha-C') stretching angle in peptides and proteins

The analysis of the basic geometry of amino acid residues of protein structures has demonstrated the invariability of all the bond lengths and bond angles except for tau, the backbone N-Calpha-C' angle. This angle can be widened or contracted significantly from the tetrahedral geometry to accommodate various other strains in the structure. In order to accurately determine the cause for this deviation, a survey is made for the tau angles using the peptide structures and the ultrahigh resolution protein structures. The average deviation of N-Calpha-C' angles from tetrahedral geometry for each amino acid in all the categories were calculated and then correlated with forty-eight physiochemical, energetic and conformational properties of amino acids. Linear and multiple regression analysis were carried out between the amino acid deviation and the 48 properties. This study confirms the deviation of tau angles in both the peptide and protein structures but similar forces do not influence them. The peptide structures are influenced by physical properties whereas as expected the conformational properties influence the protein structures. And it is not any single property that dominates the deviation but the combination of different factors contributes to the tau angle deviation.     

Experimental evidence for the correlation of bond distances in peptide groups detected in ultrahigh-resolution protein structures

The structural analysis of a deamidated derivative of ribonuclease A, determined at 0.87 A resolution, reveals a highly significant negative correlation between CN and CO bond distances in peptide groups. This trend, i.e. the CO bond lengthens when the CN bond shortens, is also found in seven out of eight protein structures, determined at ultrahigh resolution (<0.95 A). In five of them the linear correlation is statistically significant at the 95% confidence level. The present findings are consistent with the traditional view of amide resonance and, although already found in small peptide structures, they represent a new and important result. In fact, in a protein structure the fine details of the peptide geometry are only marginally affected by the crystal field and they are mostly produced by intramolecular and solvent interactions. The analysis of very high-resolution protein structures can reveal subtle information about local electronic features of proteins which may be critical to folding, function or ligand binding.     

On interpretation of protein X‐ray structures: Planarity of the peptide unit

Pauling's mastery of peptide stereochemistry—based on small molecule crystal structures and the theory of chemical bonding—led to his realization that the peptide unit is planar and then to the Pauling–Corey–Branson model of the α‐helix. Similarly, contemporary protein structure refinement is based on experimentally determined diffraction data together with stereochemical restraints. However, even an X‐ray structure at ultra‐high resolution is still an under‐determined model in which the linkage among refinement parameters is complex. Consequently, restrictions imposed on any given parameter can affect the entire structure. Here, we examine recent studies of high resolution protein X‐ray structures, where substantial distortions of the peptide plane are found to be commonplace. Planarity is assessed by the ω‐angle, a dihedral angle determined by the peptide bond (C? N) and its flanking covalent neighbors; for an ideally planar trans peptide, ω = 180°. By using a freely available refinement package, Phenix [Afonine et al. (2012) Acta Cryst. D, 68:352–367], we demonstrate that tightening default restrictions on the ω‐angle can significantly reduce apparent deviations from peptide unit planarity without consequent reduction in reported evaluation metrics (e.g., R‐factors). To be clear, our result does not show that substantial non‐planarity is absent, only that an equivalent alternative model is possible. Resolving this disparity will ultimately require improved understanding of the deformation energy. Meanwhile, we urge inclusion of ω‐angle statistics in new structure reports in order to focus critical attention on the usual practice of assigning default values to ω‐angle constraints during structure refinement. Proteins 2015; 83:1687–1692. © 2015 Wiley Periodicals, Inc.     

Correlation between omega and psi dihedral angles in protein structures

The planarity of the peptide group is one of the fundamental features of protein structure that is described in every chemistry and biochemistry textbook. By surveying a dataset of 163 atomic resolution protein structures we here identify the stereochemical conditions that favor significant deformations of peptide bond planarity. In particular, we demonstrate that the values of the omega dihedral angle are strictly correlated to the values of the adjacent psi angle. This trend is also observed in highly strained states such as those occurring in vicinal disulfide bridges. These findings provide direct evidence for the mutual influence of the geometrical parameters that describe the protein structure.     

Molecular simulation of the effects of alcohols on peptide structure

The effects of alcohols on local protein structure have been simulated using computational approaches and model peptides. Molecular simulations were carried out on a 7-residue peptide created in both an extended conformation and an alpha-helix to explore alcohol-induced changes in peptide structure. It was assumed that alcohols hydrogen bond at peptide carbonyl groups with an optimum geometry and compete with water molecules at these site. Energy minimization of the peptide/alcohol assemblies revealed that alcohols induced a twist in the peptide backbone as a function of (1) the methylene chain length, (2) the hydrogen-bond geometry, (3) halogenation of the molecule, (4) concentration, and (5) the dielectric constant. The rank ordering of the potencies of the alcohols was hexafluoroisopropanol > trifluoroethanol approximately pentanol > butanol > ethanol > methanol. Helix destabilization by cosolvent was measured by examining the hydrogen-bond lengths in peptide structures that resulted from a combination of energy minimization and molecular dynamics simulations. Destabilization was also found to be dependent upon the chemical nature of the alcohol and the hydrogen-bond geometry. The data suggest that alcohols at low concentrations affect protein structure mainly through a combination of hydrogen-bonding and hydrophobic interactions that are influenced by the properties of the solvent.     

Validation of nuclear magnetic resonance structures of proteins and nucleic acids: hydrogen geometry and nomenclature

A statistical analysis is reported of 1,200 of the 1,404 nuclear magnetic resonance (NMR)-derived protein and nucleic acid structures deposited in the Protein Data Bank (PDB) before 1999. Excluded from this analysis were the entries not yet fully validated by the PDB and the more than 100 entries that contained < 95% of the expected hydrogens. The aim was to assess the geometry of the hydrogens in the remaining structures and to provide a check on their nomenclature. Deviations in bond lengths, bond angles, improper dihedral angles, and planarity with respect to estimated values were checked. More than 100 entries showed anomalous protonation states for some of their amino acids. Approximately 250,000 (1.7%) atom names differed from the consensus PDB nomenclature. Most of the inconsistencies are due to swapped prochiral labeling. Large deviations from the expected geometry exist for a considerable number of entries, many of which are average structures. The most common causes for these deviations seem to be poor minimization of average structures and an improper balance between force-field constraints for experimental and holonomic data. Some specific geometric outliers are related to the refinement programs used. A number of recommendations for biomolecular databases, modeling programs, and authors submitting biomolecular structures are given.     

HBAT: a complete package for analysing strong and weak hydrogen bonds in macromolecular crystal structures

The program HBAT is a tool to automate the analysis of potential hydrogen bonds and similar type of weak interactions like halogen bonds and non-canonical interactions in macromolecular structures, available in Brookhaven Protein Database (PDB) file format. HBAT is written using PERL and TK languages. The program generates an MSOFFICE Excel compatible output file for statistical analysis. HBAT identify potential interactions based on geometrical criteria. A series of analysis reports like frequency tables, geometry distribution tables, furcations list are generated. A user friendly GUI offers freedom to select several parameters and options. Graphviz based visualization of hydrogen bond networks in 2D helps to study the cooperativity and anticooperativity geometry in hydrogen bond. HBAT supports post docking interaction analysis between PDB files for any target/receptor (in PDB files) and docked ligands/poses (in SDF). This tool can be implemented in active site interaction analysis, structure based drug design and molecular dynamics simulations.     

Fundamental processes of protein folding: measuring the energetic balance between helix formation and hydrophobic interactions

Theories of protein folding often consider contributions from three fundamental elements: loops, hydrophobic interactions, and secondary structures. The pathway of protein folding, the rate of folding, and the final folded structure should be predictable if the energetic contributions to folding of these fundamental factors were properly understood. alphatalpha is a helix-turn-helix peptide that was developed by de novo design to provide a model system for the study of these important elements of protein folding. Hydrogen exchange experiments were performed on selectively 15N-labeled alphatalpha and used to calculate the stability of hydrogen bonds within the peptide. The resulting pattern of hydrogen bond stability was analyzed using a version of Lifson-Roig model that was extended to include a statistical parameter for tertiary interactions. This parameter, x, represents the additional statistical weight conferred upon a helical state by a tertiary contact. The hydrogen exchange data is most closely fit by the XHC model with an x parameter of 9.25. Thus the statistical weight of a hydrophobic tertiary contact is approximately 5.8x the statistical weight for helix formation by alanine. The value for the x parameter derived from this study should provide a basis for the understanding of the relationship between hydrophobic cluster formation and secondary structure formation during the early stages of protein folding.     

The 1.9 A crystal structure of alanine racemase from Mycobacterium tuberculosis contains a conserved entryway into the active site

We report the crystal structure of alanine racemase from Mycobacterium tuberculosis (Alr(Mtb)) at 1.9 A resolution. In our structure, Alr(Mtb) is found to be a dimer formed by two crystallographically different monomers, each comprising 384 residues. The domain makeup of each monomer is similar to that of Bacillus and Pseudomonas alanine racemases and includes both an alpha/beta-barrel at the N-terminus and a C-terminus primarily made of beta-strands. The hinge angle between these two domains is unique for Alr(Mtb), but the active site geometry is conserved. In Alr(Mtb), the PLP cofactor is covalently bound to the protein via an internal aldimine bond with Lys42. No guest substrate is noted in its active site, although some residual electron density is observed in the enzyme's active site pocket. Analysis of the active site pocket, in the context of other known alanine racemases, allows us to propose the inclusion of conserved residues found at the entrance to the binding pocket as additional targets in ongoing structure-aided drug design efforts. Also, as observed in other alanine racemase structures, PLP adopts a conformation that significantly distorts the planarity of the extended conjugated system between the PLP ring and the internal aldimine bond.     

Systematics in the interaction of metal ions with the main-chain carbonyl group in protein structures

An analysis of the geometry of metal binding by peptide carbonyl groups in proteins is presented. Such metal ions are predominantly calcium in known protein structures. Cations tend to be located in the peptide plane, near the C = O bond direction. This distribution differs from that observed for water molecules bound to carbonyl oxygens. Most metal ions are bound to carbonyl oxygens of peptides in turns or in regions with no regular secondary structure. More infrequent binding interactions occur at the C-terminal end of alpha-helices or at the edges and sides of beta-sheets, where the geometrical preferences of the metal-carbonyl interaction may be satisfied. In many proteins carbonyl groups that are one, two, or three residues apart along the polypeptide chain bind to the same cation; these structures show a limited number of main-chain conformations around the metal center.     

Crystallographic structures of Discosoma red fluorescent protein with immature and mature chromophores: linking peptide bond trans-cis isomerization and acylimine formation in chromophore maturation

The mature self-synthesizing p-hydroxybenzylideneimidazolinone-like fluorophores of Discosoma red fluorescent protein (DsRed) and Aequorea victoria green fluorescent protein (GFP) are extensively studied as powerful biological markers. Yet, the spontaneous formation of these fluorophores by cyclization, oxidation, and dehydration reactions of tripeptides within their protein environment remains incompletely understood. The mature DsRed fluorophore (Gln 66, Tyr 67, and Gly 68) differs from the GFP fluorophore by an acylimine that results in Gln 66 Calpha planar geometry and by a Phe 65-Gln 66 cis peptide bond. DsRed green-to-red maturation includes a green-fluorescing immature chromophore and requires a chromophore peptide bond trans-cis isomerization that is slow and incomplete. To clarify the unique structural chemistry for the individual immature "green" and mature "red" chromophores of DsRed, we report here the determination and analysis of crystal structures for the wild-type protein (1.4 A resolution), the entirely green DsRed K70M mutant protein (1.9 A resolution), and the DsRed designed mutant Q66M (1.9 A resolution), which shows increased red chromophore relative to the wild-type DsRed. Whereas the mature, red-fluorescing chromophore has the expected cis peptide bond and a sp(2)-hybridized Gln 66 Calpha with planar geometry, the crystal structure of the immature green-fluorescing chromophore of DsRed, presented here for the first time, reveals a trans peptide bond and a sp(3)-hybridized Gln 66 Calpha with tetrahedral geometry. These results characterize a GFP-like immature green DsRed chromophore structure, reveal distinct mature and immature chromophore environments, and furthermore provide evidence for the coupling of acylimine formation with trans-cis isomerization.     

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/.     

Structural compromise of disallowed conformations in peptide and protein structures

Using a data set of 454 crystal structures of peptides and 80 crystal structures of non-homologous proteins solved at ultra high resolution of 1.2 A or better we have analyzed the occurrence of disallowed Ramachandran (phi, psi) angles. Out of 1492 and 13508 non-glycyl residues in peptides and proteins respectively 12 and 76 residues in the two datasets adopt clearly disallowed combinations of Ramachandran angles. These examples include a number of conformational points which are far away from any of the allowed regions in the Ramachandran map. According to the Ramachandran map a given (phi, psi) combination is considered disallowed when two non-bonded atoms in a system of two-linked peptide units with ideal geometry are prohibitively proximal in space. However, analysis of the disallowed conformations in peptide and protein structures reveals that none of the observations of disallowed conformations in the crystal structures correspond to a short contact between non-bonded atoms. A further analysis of deviations of bond lengths and angles, from the ideal peptide geometry, at the residue positions of disallowed conformations in the crystal structures suggest that individual bond lengths and angles are all within acceptable limits. Thus, it appears that the rare tolerance of disallowed conformations is possible by gentle and acceptable deviations in a number of bond lengths and angles, from ideal geometry, over a series of bonds resulting in a net gross effect of acceptable non-bonded inter-atomic distances.     

Interaction geometry involving planar groups in protein-protein interfaces

The geometry of interactions of planar residues is nonrandom in protein tertiary structures and gives rise to conventional, as well as nonconventional (X--H...pi, X--H...O, where X = C, N, or O) hydrogen bonds. Whether a similar geometry is maintained when the interaction is across the protein-protein interface is addressed here. The relative geometries of interactions involving planar residues, and the percentage of contacts giving rise to different types of hydrogen bonds are quite similar in protein structures and the biological interfaces formed by protein chains in homodimers and protein-protein heterocomplexes--thus pointing to the similarity of chemical interactions that occurs during protein folding and binding. However, the percentage is considerably smaller in the nonspecific and nonphysiological interfaces that are formed in crystal lattices of monomeric proteins. The C--H...O interaction linking the aromatic and the peptide groups is quite common in protein structures as well as the three types of interfaces. However, as the interfaces formed by crystal contacts are depleted in aromatic residues, the weaker hydrogen bond interactions would contribute less toward their stability.     

Modeling mutations in protein structures

We describe an automated method for the modeling of point mutations in protein structures. The protein is represented by all non-hydrogen atoms. The scoring function consists of several types of physical potential energy terms and homology-derived restraints. The optimization method implements a combination of conjugate gradient minimization and molecular dynamics with simulated annealing. The testing set consists of 717 pairs of known protein structures differing by a single mutation. Twelve variations of the scoring function were tested in three different environments of the mutated residue. The best-performing protocol optimizes all the atoms of the mutated residue, with respect to a scoring function that includes molecular mechanics energy terms for bond distances, angles, dihedral angles, peptide bond planarity, and non-bonded atomic contacts represented by Lennard-Jones potential, dihedral angle restraints derived from the aligned homologous structure, and a statistical potential for non-bonded atomic interactions extracted from a large set of known protein structures. The current method compares favorably with other tested approaches, especially when predicting long and flexible side-chains. In addition to the thoroughness of the conformational search, sampled degrees of freedom, and the scoring function type, the accuracy of the method was also evaluated as a function of the flexibility of the mutated side-chain, the relative volume change of the mutated residue, and its residue type. The results suggest that further improvement is likely to be achieved by concentrating on the improvement of the scoring function, in addition to or instead of increasing the variety of sampled conformations.     

Relaxation of backbone bond geometry improves protein energy landscape modeling

A key issue in macromolecular structure modeling is the granularity of the molecular representation. A fine‐grained representation can approximate the actual structure more accurately, but may require many more degrees of freedom than a coarse‐grained representation and hence make conformational search more challenging. We investigate this tradeoff between the accuracy and the size of protein conformational search space for two frequently used representations: one with fixed bond angles and lengths and one that has full flexibility. We performed large‐scale explorations of the energy landscapes of 82 protein domains under each model, and find that the introduction of bond angle flexibility significantly increases the average energy gap between native and non‐native structures. We also find that incorporating bonded geometry flexibility improves low resolution X‐ray crystallographic refinement. These results suggest that backbone bond angle relaxation makes an important contribution to native structure energetics, that current energy functions are sufficiently accurate to capture the energetic gain associated with subtle deformations from chain ideality, and more speculatively, that backbone geometry distortions occur late in protein folding to optimize packing in the native state.     

Calculation of protein backbone geometry from alpha-carbon coordinates based on peptide-group dipole alignment.

An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C alpha atoms) to an all-atom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the alpha-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model alpha-helical and beta-sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these alpha-helical and beta-sheet structures. Application to the alpha-carbon trace of the backbone of the crystallographic 5PTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C alpha-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of 5PTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.     

Design, synthesis and solution structure of a renin inhibitor. Structural constraints from NOE, and homonuclear and heteronuclear coupling constants combined with distance geometry calculations.

A macrocyclic renin inhibitor was designed using molecular modeling and a model of human renin. The synthesized molecular displayed poor binding affinity. To investigate the reasons for the observed inactivity, the structure of the compound has been studied by NMR spectroscopy and distance geometry. Structural constraints for distance geometry calculations were derived from nuclear Overhauser effects and homonuclear and heteronuclear three bond coupling constants. Homonuclear coupling constants were measured directly from the resolution-enhanced proton spectra and heteronuclear coupling constants were measured from the natural abundance 15N- and 13C-edited TOCSY experiments. One phi angle was determined uniquely by this method and two were reduced to two possible values each. By using a statistical analysis of 400 structures generated with distance geometry, two families of structures were found to be consistent with the NMR data. The solution structures so derived were different from the originally designed structure, including an internal hydrogen bond. This provides a possible explanation for the lack of effectiveness of this compound.