Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

Cis peptide bonds in proteins: residues involved, their conformations, interactions and locations.

An analysis of a non-redundant set of protein structures from the Brookhaven Protein Data Bank has been carried out to find out the residue preference, local conformation, hydrogen bonding and other stabilizing interactions involving cis peptide bonds. This has led to a reclassification of turns mediated by cis peptides, and their average geometrical parameters have been evaluated. The interdependence of the side and main-chain torsion angles of proline rings provided an explanation why such rings in cis peptides are found to have the DOWN puckering. A comparison of cis peptides containing proline and non-proline residues show differences in conformation, location in the secondary structure and in relation to the centre of the molecule, and relative accessibilities of residues. Relevance of the results in mutation studies and the cis-trans isomerization during protein folding is discussed.     

A study into the effects of protein binding on nucleotide conformation.

In this study, we examine the effects of binding to protein upon nucleotide conformation, by the comparison of X-ray crystal structures of free and protein-bound nucleotides. A dataset of structurally non-homologous protein-nucleotide complexes was derived from the Brookhaven Protein Data Bank by a novel protocol of dual sequential and structural alignments, and a dataset of native nucleotide structures was obtained from the Cambridge Structural Database. The nucleotide torsion angles and sugar puckers, which describe nucleotide conformation, were analysed in both datasets and compared. Differences between them are described and discussed. Overall, the nucleotides were found to bind in low energy conformations, not significantly different from their 'free' conformations except that they adopted an extended conformation in preference to the 'closed' structure predominantly observed by free nucleotide. The archetypal conformation of a protein-bound nucleotide is derived from these observations.     

The Protein Data Bank: a computer-based archival file for macromolecular structures

The Protein Data Bank is a computer-based archival file for macromolecular structures. The Bank stores in a uniform format atomic co-ordinates and partial bond connectivities, as derived from crystallographic studies. Text included in each data entry gives pertinent information for the structure at hand (e.g. species from which the molecule has been obtained, resolution of diffraction data, literature citations and specifications of secondary structure). In addition to atomic co-ordinates and connectivities, the Protein Data Bank stores structure factors and phases, although these latter data are not placed in any uniform format. Input of data to the Bank and general maintenance functions are carried out at Brookhaven National Laboratory. All data stored in the Bank are available on magnetic tape for public distribution, from Brookhaven (to laboratories in the Americas), Tokyo (Japan), and Cambridge (Europe and worldwide). A master file is maintained at Brookhaven and duplicate copies are stored in Cambridge and Tokyo. In the future, it is hoped to expand the scope of the Protein Data Bank to make available co-ordinates for standard structural types (e.g. α-helix, RNA double-stranded helix) and representative computer programs of utility in the study and interpretation of macromolecular structures.     

Amino acid similarity coefficients for protein modeling and sequence alignment derived from main-chain folding angles

A set of "similarity-parameters" was calculated that reflects the influence of the proteinogenic amino acids on the structure of the protein backbone. The parameters were derived from a detailed analysis of the amino acid specific main-chain torsion angle distributions as they are found in proteins (highly resolved protein structures from the Brookhaven Protein Data Bank). The purpose of these parameters is threefold: (1) they should help in estimating the structural effect of an amino acid substitution during the design of new mutants in protein-engineering; (2) in modeling by homology they should mark places in the protein where changes in the folding are expected; and (3) they should form a scoring matrix in protein sequence alignment superior to identity scoring. The usability of the "structure derived correlation matrix (SCM)" for these purposes is assessed and demonstrated for some examples in the paper.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

TESS: a geometric hashing algorithm for deriving 3D coordinate templates for searching structural databases. Application to enzyme active sites.

It is well established that sequence templates such as those in the PROSITE and PRINTS databases are powerful tools for predicting the biological function and tertiary structure for newly derived protein sequences. The number of X-ray and NMR protein structures is increasing rapidly and it is apparent that a 3D equivalent of the sequence templates is needed. Here, we describe an algorithm called TESS that automatically derives 3D templates from structures deposited in the Brookhaven Protein Data Bank. While a new sequence can be searched for sequence patterns, a new structure can be scanned against these 3D templates to identify functional sites. As examples, 3D templates are derived for enzymes with an O-His-O "catalytic triad" and for the ribonucleases and lysozymes. When these 3D templates are applied to a large data set of nonidentical proteins, several interesting hits are located. This suggests that the development of a 3D template database may help to identify the function of new protein structures, if unknown, as well as to design proteins with specific functions.     

Ensemble modeling of protein disordered states: Experimental restraint contributions and validation

Disordered states of proteins include the biologically functional intrinsically disordered proteins and the unfolded states of normally folded proteins. In recent years, ensemble‐modeling strategies using various experimental measurements as restraints have emerged as powerful means for structurally characterizing disordered states. However, these methods are still in their infancy compared with the structural determination of folded proteins. Here, we have addressed several issues important to ensemble modeling using our ENSEMBLE methodology. First, we assessed how calculating ensembles containing different numbers of conformers affects their structural properties. We find that larger ensembles have very similar properties to smaller ensembles fit to the same experimental restraints, thus allowing a considerable speed improvement in our calculations. In addition, we analyzed the contributions of different experimental restraints to the structural properties of calculated ensembles, enabling us to make recommendations about the experimental measurements that should be made for optimal ensemble modeling. The effects of different restraints, most significantly from chemical shifts, paramagnetic relaxation enhancements and small‐angle X‐ray scattering, but also from other data, underscore the importance of utilizing multiple sources of experimental data. Finally, we validate our ENSEMBLE methodology using both cross‐validation and synthetic experimental restraints calculated from simulated ensembles. Our results suggest that secondary structure and molecular size distribution can generally be modeled very accurately, whereas the accuracy of calculated tertiary structure is dependent on the number of distance restraints used. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

CAP: conformation angles package-displaying the conformation angles of side chains in proteins

SUMMARY: A graphics package has been developed to display all side chain conformation angles of the user selected residue in a given protein structure. The proposed package is incorporated with all the protein structures (solved using X-ray diffraction and NMR spectroscopy) available in the Protein Data Bank. The package displays the multiple conformations adopted by a single amino acid residue whose structure is solved and refined at very high resolution. In addition, it shows the percentage distribution of the side chain conformation angles in different rotameric states. AVAILABILITY: http://144.16.71.146/cap/     

OLDERADO: on-line database of ensemble representatives and domains. On Line Database of Ensemble Representatives And DOmains.

In cases where the structure of a single protein is represented by an ensemble of conformations, there is often a need to determine the common features and to choose a "representative" conformation. This occurs, for example, with structures determined by NMR spectroscopy, analysis of the trajectory from a molecular dynamics simulation, or an ensemble of structures produced by comparative modeling. We reported previously automatic methods for (1) defining the atoms with low spatial variance across an ensemble (i.e., the "core" atoms) and the domains in which these atoms lie, and (2) clustering an ensemble into conformationally related subfamilies. To extend the utility of these methods, we have developed a freely available server on the World Wide Web at http:/(/)neon.chem.le.ac.uk/olderado/. This (1) contains an automatically generated database of representative structures, core atoms, and domains determined for 449 ensembles of NMR-derived protein structures in the Protein Data Bank (PDB) in May 1997, and (2) allows the user to upload a PDB-formatted file containing the coordinates of an ensemble of structures. The server returns in real time: (1) information on the residues constituting domains: (2) the structures that constitute each conformational subfamily; and (3) an interactive java-based three-dimensional viewer to visualise the domains and clusters. Such information is useful, for example, when selecting conformations to be used in comparative modeling and when choosing parts of structures to be used in molecular replacement. Here we describe the OLDERADO server.     

Stereochemical quality of protein structure coordinates.

Methods have been developed to assess the stereochemical quality of any protein structure both globally and locally using various criteria. Several parameters can be derived from the coordinates of a given structure. Global parameters include the distribution of phi, psi and chi 1 torsion angles, and hydrogen bond energies. There are clear correlations between these parameters and resolution; as the resolution improves, the distribution of the parameters becomes more clustered. These features show a broad distribution about ideal values derived from high-resolution structures. Some structures have tightly clustered distributions even at relatively low resolutions, while others show abnormal scatter though the data go to high resolution. Additional indicators of local irregularity include proline phi angles, peptide bond planarities, disulfide bond lengths, and their chi 3 torsion angles. These stereochemical parameters have been used to generate measures of stereochemical quality which provide a simple guide as to the reliability of a structure, in addition to the most important measures, resolution and R-factor. The parameters used in this evaluation are not novel, and are easily calculated from structure coordinates. A program suite is currently being developed which will quickly check a given structure, highlighting unusual stereochemistry and possible errors.     

PACSY, a relational database management system for protein structure and chemical shift analysis

PACSY (Protein structure And Chemical Shift NMR spectroscopY) is a relational database management system that integrates information from the Protein Data Bank, the Biological Magnetic Resonance Data Bank, and the Structural Classification of Proteins database. PACSY provides three-dimensional coordinates and chemical shifts of atoms along with derived information such as torsion angles, solvent accessible surface areas, and hydrophobicity scales. PACSY consists of six relational table types linked to one another for coherence by key identification numbers. Database queries are enabled by advanced search functions supported by an RDBMS server such as MySQL or PostgreSQL. PACSY enables users to search for combinations of information from different database sources in support of their research. Two software packages, PACSY Maker for database creation and PACSY Analyzer for database analysis, are available from http://pacsy.nmrfam.wisc.edu.     

The nature of the turn in omega loops of proteins

An analysis of Omega loops in a nonredundant set of protein structures from the Protein Data Bank has been carried out to determine the nature of the "turn elements" present. Because Omega loops essentially reverse their direction in three-dimensional space, this analysis was made with respect to four turn elements identified as (1) Gly; (2) Pro; (3) a residue with alpha-helical phi,psi angles, termed a helical residue; and (4) a cis peptide. A set of 1079 Omega loops from a set of 680 proteins were used for the analysis. Apart from other criteria that define Omega loops, the selection of an Omega loop from a cluster of loops is based on an exposure index. In this study, analyses have been made with two sets of data: (1) Omega loops arising from a minimum exposure index indicative of a less exposed loop (xmin set) and (2) Omega loops with a maximum exposure index indicative of a relatively exposed loop (xmax set). Overall residue preferences and positional preferences have been examined. Positions of the turn elements for Omega loops of varying length have also been studied. Specific positional preferences are observed for particular turn elements with regard to the length of Omega loops. Analysis in terms of the turn elements can provide guidelines for modeling of loops in proteins. Apart from Pro, which has the natural tendency to form cis peptide bonds, a higher occurrence of non-Pro cis peptide bonds is observed. Torsion angles in Omega loops also indicate the occurrence of a large number of residues with helical phi,psi angles, necessary for the turn in the loop structures.     

Interpreting Dynamically-Averaged Scalar Couplings in Proteins

The experimental determination of scalar three-bond coupling constants represents a powerful method to probe both the structure and dynamics of proteins. The detailed structural interpretation of such coupling constants is usually based on Karplus relationships, which allow the measured couplings to be related to the torsion angles of the molecules. As the measured couplings are sensitive to thermal fluctuations, the parameters in the Karplus relationships are better derived from ensembles representing the distributions of dihedral angles present in solution, rather than from single conformations. We present a method to derive such parameters that uses ensembles of conformations determined through dynamic-ensemble refinement – a method that provides structural ensembles that simultaneously represent both the structure and the associated dynamics of a protein.     

Conformational analysis of protein structures derived from NMR data

A study is presented of the conformational characteristics of NMR-derived protein structures in the Protein Data Bank compared to X-ray structures. Both ensemble and energy-minimized average structures are analyzed. We have addressed the problem using the methods developed for crystal structures by examining the distribution of ?, Ψ, and χ angles as indicators of global conformational irregularity. All these features in NMR structures occur to varying degrees in multiple conformational states. Some measures of local geometry are very tightly constrained by the methods used to generate the structure, e.g., proline ? angles, α-helix ?, Ψ angles, ω angles, and C_α chirality. The more lightly restrained torsion angles do show increasead clustering as the number of overall experimental observations increases. ?, Ψ, and χ₁ angle conformational heterogeneity is strongly correlated with accessibility but shows additional differences which reflect the differing number of observations possible in NMR for the various side chains (e.g., many for Trp, few for Ser). In general, we find that the core is defined to a notional resolution of 2.0 to 2.3 Å. Of real interest is the behavior of surface residues and in particular the side chains where multiple rotameric states in different structures can vary from 10% to 88%. Later generation structures show a much tighter definition which correlates with increasing use of J-coupling information, stereospecific assignments, and heteronumclear techniques. A suite of programs is being developed to address the special needs of NMR-derived structures which will take into account the existence of increased mobility in solution. © 1993 Wiley-Liss, Inc.     

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Ramachandran plot on the web

A graphics package has been developed to display the main chain torsion angles phi, psi (phi, Psi); (Ramachandran angles) in a protein of known structure. In addition, the package calculates the Ramachandran angles at the central residue in the stretch of three amino acids having specified the flanking residue types. The package displays the Ramachandran angles along with a detailed analysis output. This software is incorporated with all the protein structures available in the Protein Databank.