Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

In theory, a polypeptide chain can adopt a vast number of conformations, each corresponding to a set of backbone rotation angles. Many of these conformations are excluded due to steric overlaps. Ramachandran and coworkers were the first to look into this problem by plotting backbone dihedral angles in a two-dimensional plot. The conformational space in the Ramachandran map is further refined by considering the energetic contributions of various non-bonded interactions. Alternatively, the conformation adopted by a polypeptide chain may also be examined by investigating interactions between the residues. Since the Ramachandran map essentially focuses on local interactions (residues closer in sequence), out of interest, we have analyzed the dihedral angle preferences of residues that make non-local interactions (residues far away in sequence and closer in space) in the folded structures of proteins. The non-local interactions have been grouped into different types such as hydrogen bond, van der Waals interactions between hydrophobic groups, ion pairs (salt bridges), and ππ-stacking interactions. The results show the propensity of amino acid residues in proteins forming local and non-local interactions. Our results point to the vital role of different types of non-local interactions and their effect on dihedral angles in forming secondary and tertiary structural elements to adopt their native fold.     

Structural features of transmembrane helices

A total of 160 transmembrane helices of 15 non-homologous high-resolution X-ray protein structures have been analyzed in respect of their structural features. The dihedral angles and hydrogen bonds of the helical sections that span the hydrophobic interior of the lipid bilayer have been investigated. The Ramachandran plot of protein channels and solute transporters exhibit a significant shift Delta (phi- and psi-angles) of Delta mean (+4.5 degrees and -5.4 degrees ), compared to a reference group of 151 alpha-helices of the same average length derived from water-soluble globular proteins. At the C-termini of transmembrane helices structural motifs equivalent to the Gly-caps of helices in globular proteins have been found, with two third of the transmembrane Gly-caps taking up a primary structure that is typically not found at helix termini exposed to a polar solvent. The structural particularities reported here are relevant for the three-dimensional modelling of membrane protein structures.     

Revisiting the Ramachandran plot from a new angle

The pioneering work of Ramachandran and colleagues emphasized the dominance of steric constraints in specifying the structure of polypeptides. The ubiquitous Ramachandran plot of backbone dihedral angles (φ and ψ) defined the allowed regions of conformational space. These predictions were subsequently confirmed in proteins of known structure. Ramachandran and colleagues also investigated the influence of the backbone angle τ on the distribution of allowed φ/ψ combinations. The “bridge region” (φ ≤ 0° and −20° ≤ ψ ≤ 40°) was predicted to be particularly sensitive to the value of τ. Here we present an analysis of the distribution of φ/ψ angles in 850 non-homologous proteins whose structures are known to a resolution of 1.7 Å or less and sidechain B-factor less than 30 Ų. We show that the distribution of φ/ψ angles for all 87,000 residues in these proteins shows the same dependence on τ as predicted by Ramachandran and colleagues. Our results are important because they make clear that steric constraints alone are sufficient to explain the backbone dihedral angle distributions observed in proteins. Contrary to recent suggestions, no additional energetic contributions, such as hydrogen bonding, need be invoked.     

Structural assessment of glycyl mutations in invariantly conserved motifs

Motifs that are evolutionarily conserved in proteins are crucial to their structure and function. In one of our earlier studies, we demonstrated that the conserved motifs occurring invariantly across several organisms could act as structural determinants of the proteins. We observed the abundance of glycyl residues in these invariantly conserved motifs. The role of glycyl residues in highly conserved motifs has not been studied extensively. Thus, it would be interesting to examine the structural perturbations induced by mutation in these conserved glycyl sites. In this work, we selected a representative set of invariant signature (IS) peptides for which both the PDB structure and mutation information was available. We thoroughly analyzed the conformational features of the glycyl sites and their local interactions with the surrounding residues. Using Ramachandran angles, we showed that the glycyl residues occurring in these IS peptides, which have undergone mutation, occurred more often in the L-disallowed as compared with the L-allowed region of the Ramachandran plot. Short range contacts around the mutation site were analyzed to study the steric effects. With the results obtained from our analysis, we hypothesize that any change of activity arising because of such mutations must be attributed to the long-range interaction(s) of the new residue if the glycyl residue in the IS peptide occurred in the L-allowed region of the Ramachandran plot. However, the mutation of those conserved glycyl residues that occurred in the L-disallowed region of the Ramachandran plot might lead to an altered activity of the protein as a result of an altered conformation of the backbone in the immediate vicinity of the glycyl residue, in addition to long range effects arising from the long side chains of the new residue. Thus, the loss of activity because of mutation in the conserved glycyl site might either relate to long range interactions or to local perturbations around the site depending upon the conformational preference of the glycyl residue.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

Studying backbone torsional dynamics of intrinsically disordered proteins using fluorescence depolarization kinetics

Intrinsically disordered proteins (IDPs) do not autonomously adopt a stable unique 3D structure and exist as an ensemble of rapidly interconverting structures. They are characterized by significant conformational plasticity and are associated with several biological functions and dysfunctions. The rapid conformational fluctuation is governed by the backbone segmental dynamics arising due to the dihedral angle fluctuation on the Ramachandran ?–ψ conformational space. We discovered that the intrinsic backbone torsional mobility can be monitored by a sensitive fluorescence readout, namely fluorescence depolarization kinetics, of tryptophan in an archetypal IDP such as α-synuclein. This methodology allows us to map the site-specific torsional mobility in the dihedral space within picosecond-nanosecond time range at a low protein concentration under the native condition. The characteristic timescale of ~?1.4 ns, independent of residue position, represents collective torsional dynamics of dihedral angles (? and ψ) of several residues from tryptophan and is independent of overall global tumbling of the protein. We believe that fluorescence depolarization kinetics methodology will find broad application to study both short-range and long-range correlated motions, internal friction, binding-induced folding, disorder-to-order transition, misfolding and aggregation of IDPs.     

Introduction of a new scheme for classifying β-turns in protein structures

Protein β-turn classification remains an area of ongoing development in structural biology research. While the commonly used nomenclature defining type I, type II and type IV β-turns was introduced in the 1970s and 1980s, refinements of β-turn type definitions have been introduced as recently as 2019 by Dunbrack, Jr and co-workers who expanded the number of β-turn types to 18 (Shapovalov et al, PLOS Computat. Biol., 15, e1006844, 2019). Based on their analysis of 13 030 turns from 1074 ultrahigh resolution (≤1.2 Å) protein structures, they used a new clustering algorithm to expand the definitions used to classify protein β-turns and introduced a new nomenclature system. We recently encountered a specific problem when classifying β-turns in crystal structures of pentapeptide repeat proteins (PRPs) determined in our lab that are largely composed of β-turns that often lie close to, but just outside of, canonical β-turn regions. To address this problem, we devised a new scheme that merges the Klyne-Prelog stereochemistry nomenclature and definitions with the Ramachandran plot. The resulting Klyne-Prelog-modified Ramachandran plot scheme defines 1296 distinct potential β-turn classifications that cover all possible protein β-turn space with a nomenclature that indicates the stereochemistry of i + 1 and i + 2 backbone dihedral angles. The utility of the new classification scheme was illustrated by re-classification of the β-turns in all known protein structures in the PRP superfamily and further assessed using a database of 16 657 high-resolution protein structures (≤1.5 Å) from which 522 776 β-turns were identified and classified.     

ProMode: a database of normal mode analyses on protein molecules with a full-atom model

MOTIVATION: Although information from protein dynamics simulation is important to understand principles of architecture of a protein structure and its function, simulations such as molecular dynamics and Monte Carlo are very CPU-intensive. Although the ability of normal mode analysis (NMA) is limited because of the need for a harmonic approximation on which NMA is based, NMA is adequate to carry out routine analyses on many proteins to compute aspects of the collective motions essential to protein dynamics and function. Furthermore, it is hoped that realistic animations of the protein dynamics can be observed easily without expensive software and hardware, and that the dynamic properties for various proteins can be compared with each other. RESULTS: ProMode, a database collecting NMA results on protein molecules, was constructed. The NMA calculations are performed with a full-atom model, by using dihedral angles as independent variables, faster and more efficiently than the calculations using Cartesian coordinates. In ProMode, an animation of the normal mode vibration is played with a free plug-in, Chime (MDL Information Systems, Inc.). With the full-atom model, the realistic three-dimensional motions at an atomic level are displayed with Chime. The dynamic domains and their mutual screw motions defined from the NMA results are also displayed. Properties for each normal mode vibration and their time averages, e.g. fluctuations of atom positions, fluctuations of dihedral angles and correlations between the atomic motions, are also presented graphically for characterizing the collective motions in more detail. AVAILABILITY: http://promode.socs.waseda.ac.jp     

Dihedral-angle information entropy as a gauge of secondary structure propensity

Protein structural information can be uncovered using an information-theory-based entropy and auxiliary functions by taking advantage of high-quality correlation plots between the dihedral angles around a residue and those between sequential residues. A standard information entropy for a primary sequence has been defined using the values of the probabilities of the most likely dihedral angles along the sequence. The distribution of entropy differences relative to the standard for each protein in a reference set--a sublibrary of the Protein Data Bank at the 90% sequence redundancy level--appears to be nearly Gaussian. It gives rise to an auxiliary checking function whose value signals the extent to which the dihedral angle propensities differ from typical structures. Such deviations can arise either because of incorrect dihedral angle assignments or secondary structural propensities that are atypical of the structures in the reference set. This auxiliary checking function can be readily calculated at the public website, (http://www.d2check.gatech.edu). Its utility is demonstrated here in an analysis displaying differences between experimentally and theoretically derived structures, and in the analysis of structures derived by homology modeling. A comparison of the new measure, D(2)Check, to other checking functions based on backbone conformation-namely, PROCHECK and WHAT_CHECK--is also provided.     

Prediction of Protein Secondary Structure Using Feature Selection and Analysis Approach

The prediction of the secondary structure of a protein from its amino acid sequence is an important step towards the prediction of its three-dimensional structure. However, the accuracy of ab initio secondary structure prediction from sequence is about 80 % currently, which is still far from satisfactory. In this study, we proposed a novel method that uses binomial distribution to optimize tetrapeptide structural words and increment of diversity with quadratic discriminant to perform prediction for protein three-state secondary structure. A benchmark dataset including 2,640 proteins with sequence identity of less than 25 % was used to train and test the proposed method. The results indicate that overall accuracy of 87.8 % was achieved in secondary structure prediction by using ten-fold cross-validation. Moreover, the accuracy of predicted secondary structures ranges from 84 to 89 % at the level of residue. These results suggest that the feature selection technique can detect the optimized tetrapeptide structural words which affect the accuracy of predicted secondary structures.     

Automatic definition of recurrent local structure motifs in proteins

An automatic procedure for defining recurrent folding motifs in proteins of known structure is described. These motifs are formed by short polypeptide fragments of equal size containing between four and seven residues. The method applies a classical clustering algorithm that operates on distances between selected backbone atoms. In one application, we use it to cluster all protein fragments into only four structural classes. This classification is rough considering the observed diversity of local structures, but comparable in homogeneity to the four classes of secondary structure (alpha-helix, beta-strand, turn and coil). Yet, it discriminates between extended and curved coil and distinguishes beta-bulges from beta-strands. In a second application, the clustering procedure is combined with assignment of backbone dihedral angles to allowed regions in the Ramachandran map. This produces an exhaustive repertoire of highly homogeneous families of structural motifs that contains all the beta-hairpins, beta alpha- and alpha beta-loops previously defined by manual procedures, and new structural families of which two examples, a beta alpha-loop and an alpha-helix beginning, are analyzed in detail. The described automatic procedures should be useful in categorizing structure information in proteins, thereby increasing our ability to analyze relations between structure and sequence.     

Support vector machines for prediction of dihedral angle regions

MOTIVATION: Most secondary structure prediction programs target only alpha helix and beta sheet structures and summarize all other structures in the random coil pseudo class. However, such an assignment often ignores existing local ordering in so-called random coil regions. Signatures for such ordering are distinct dihedral angle pattern. For this reason, we propose as an alternative approach to predict directly dihedral regions for each residue as this leads to a higher amount of structural information. RESULTS: We propose a multi-step support vector machine (SVM) procedure, dihedral prediction (DHPRED), to predict the dihedral angle state of residues from sequence. Trained on 20,000 residues our approach leads to dihedral region predictions, that in regions without alpha helices or beta sheets is higher than those from secondary structure prediction programs. AVAILABILITY: DHPRED has been implemented as a web service, which academic researchers can access from our webpage http://www.fz-juelich.de/nic/cbb     

How different are structurally flexible and rigid binding sites? Sequence and structural features discriminating proteins that do and do not undergo conformational change upon ligand binding

Proteins are dynamic molecules and often undergo conformational change upon ligand binding. It is widely accepted that flexible loop regions have a critical functional role in enzymes. Lack of consideration of binding site flexibility has led to failures in predicting protein functions and in successfully docking ligands with protein receptors. Here we address the question: which sequence and structural features distinguish the structurally flexible and rigid binding sites? We analyze high-resolution crystal structures of ligand bound (holo) and free (apo) forms of 41 proteins where no conformational change takes place upon ligand binding, 35 examples with moderate conformational change, and 22 cases where a large conformational change has been observed. We find that the number of residue-residue contacts observed per-residue (contact density) does not distinguish flexible and rigid binding sites, suggesting a role for specific interactions and amino acids in modulating the conformational changes. Examination of hydrogen bonding and hydrophobic interactions reveals that cases that do not undergo conformational change have high polar interactions constituting the binding pockets. Intriguingly, the large, aromatic amino acid tryptophan has a high propensity to occur at the binding sites of examples where a large conformational change has been noted. Further, in large conformational change examples, hydrophobic-hydrophobic, aromatic-aromatic, and hydrophobic-polar residue pair interactions are dominant. Further analysis of the Ramachandran dihedral angles (phi, psi) reveals that the residues adopting disallowed conformations are found in both rigid and flexible cases. More importantly, the binding site residues adopting disallowed conformations clustered narrowly into two specific regions of the L-Ala Ramachandran map. Examination of the dihedral angles changes upon ligand binding shows that the magnitude of phi, psi changes are in general minimal, although some large changes particularly between right-handed alpha-helical and extended conformations are seen. Our work further provides an account of conformational changes in the dihedral angles space. The findings reported here are expected to assist in providing a framework for predicting protein-ligand complexes and for template-based prediction of protein function.     

Fast structure alignment for protein databank searching.

A fast method is described for searching and analyzing the protein structure databank. It uses secondary structure followed by residue matching to compare protein structures and is developed from a previous structural alignment method based on dynamic programming. Linear representations of secondary structures are derived and their features compared to identify equivalent elements in two proteins. The secondary structure alignment then constrains the residue alignment, which compares only residues within aligned secondary structures and with similar buried areas and torsional angles. The initial secondary structure alignment improves accuracy and provides a means of filtering out unrelated proteins before the slower residue alignment stage. It is possible to search or sort the protein structure databank very quickly using just secondary structure comparisons. A search through 720 structures with a probe protein of 10 secondary structures required 1.7 CPU hours on a Sun 4/280. Alternatively, combined secondary structure and residue alignments, with a cutoff on the secondary structure score to remove pairs of unrelated proteins from further analysis, took 10.1 CPU hours. The method was applied in searches on different classes of proteins and to cluster a subset of the databank into structurally related groups. Relationships were consistent with known families of protein structure.     

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.     

Flexible programs for the prediction of average amphipathicity of multiply aligned homologous proteins: application to integral membrane transport proteins

Simple flexible programs (TREEMOMENT and PILEUPMOMENT) are described for depicting the average amphipathicity (hydrophobic moment) along multiply aligned sequences of a family of evolutionarily related proteins. The programs are applicable to any number of aligned sequences and can be set for any desired angle corresponding to a residue repeat unit in a protein secondary structural element such as 100 per residue for an alpha- helix or 180 per residue for a beta-strand. These programs can be used to identify amphipathic regions common to the members of a protein family. The use of these programs is exemplified by showing that some families of integral membrane transport proteins (i.e. permeases of the bacterial phosphotransferase system (PTS) and the anion exchangers of animals) exhibit strikingly amphipathic alpha-helical structures immediately preceding the first hydrophobic transmembrane segment of their membrane-embedded domain(s). Other families, such as the major facilitator superfamily of uniporters, symporters and antiporters, do not exhibit this structural feature. The amphipathic structures in PTS permeases have been implicated in membrane insertion during biogenesis.     

Flexible programs for the prediction of average amphipathicity of multiply aligned homologous proteins: application to integral membrane transport proteins.

Simple flexible programs (TREEMOMENT and PILEUPMOMENT) are described for depicting the average amphipathicity (hydrophobic moment) along multiply aligned sequences of a family of evolutionarily related proteins. The programs are applicable to any number of aligned sequences and can be set for any desired angle corresponding to a residue repeat unit in a protein secondary structural element such as 100 degrees per residue for an alpha-helix or 180 degrees per residue for a beta-strand. These programs can be used to identify amphipathic regions common to the members of a protein family. The use of these programs is exemplified by showing that some families of integral membrane transport proteins (i.e. permeases of the bacterial phosphotransferase system (PTS) and the anion exchangers of animals) exhibit strikingly amphipathic alpha-helical structures immediately preceding the first hydrophobic transmembrane segment of their membrane-embedded domain(s). Other families, such as the major facilitator superfamily of uniporters, symporters and antiporters, do not exhibit this structural feature. The amphipathic structures in PTS permeases have been implicated in membrane insertion during biogenesis.     

Analysis of dihedral angle preferences for alanine and glycine residues in alpha and beta transmembrane regions

For the past 50?years, the Ramachandran map has been used effectively to study the protein structure and folding. However, though extensive analysis has been done on dihedral angle preferences of residues in globular proteins, related studies and reports of membrane proteins are limited. It is of interest to explore the conformational preferences of residues in transmembrane regions of membrane proteins which are involved in several important and diverse biological processes. Hence, in the present work, a systematic comparative computational analysis has been made on dihedral angle preferences of alanine and glycine in alpha and beta transmembrane regions (the two major classes of transmembrane proteins) with the aid of the Ramachandran map. Further, the conformational preferences of residues in transmembrane regions were compared with the non-transmembrane regions. We have extracted cation-pi interacting residues present in transmembrane regions and explored the dihedral angle preferences. From our observations, we reveal the higher percentage of occurrences of glycine in alpha and beta transmembrane regions than other hydrophobic residues. Further, we noted a clear shift in ψ-angle preferences of glycine residues from negative bins in alpha transmembrane regions to positive bins in beta transmembrane regions. Also, cation-pi interacting residues in beta transmembrane regions avoid preferring ψ-angles in the range of ?59° to ?30°. In this article, we insist that the studies on preferences of dihedral angles in transmembrane regions, thorough understanding of structure and folding of transmembrane proteins, can lead to modeling of novel transmembrane regions towards designing membrane proteins.