Quantitative organization of the known protein x-ray structures. I. Methods and short-length-scale results

We address herein the problem of delineating the relationships between the known protein structures. In order to study this problem, methods have been developed to represent arbitrarily sized fragments of biopolymer backbone, and to compare distributions of such fragments. These methods are applied to a classification of 123 structures representing the entire set of known x-ray structures. The resulting data are analyzed (on the four-C alpha length scale) to determine both the large-scale organization of the set of known structures (i.e., the relationships between large groups of structures, each comprised of proteins that are structurally related) and its local structure (i.e., the quantitative degree of similarity between any two specific structures). It is shown that the set of structures forms a continuum of structural types, ranging from all-helical to all-sheet/barrel proteins. It is further demonstrated that the density of protein structures is not uniform across this continuum, but rather that structures cluster in certain regions, separated by regions of lower population. The properties of the various regions of the structural space are determined. The existence is demonstrated of strong quantitative correlations between the contents of different types of four-C alpha fragments within protein structures, which imply significant constraints on the types of architecture that can occur in proteins. Analysis of the distribution of structures demonstrates some hitherto unsuspected similarities and suggests that, in some circumstances, neither structural similarity nor sequence homology may be necessary conditions for evolutionary relationship between proteins. It is also suggested that these unsuspected similarities may imply similar folding mechanisms for structures of apparently different global architecture. Cases are also noted in which apparently similar structures may fold by different mechanisms. The connection between structure and dynamic properties is discussed, and a possible role of dynamics in the evolution of protein structures is suggested. The sensitivity of the methods presented herein to anomalies of structure refinement is demonstrated. It is suggested that the present results provide a framework for analyzing experimental results on structural similarity obtained using vibrational circular dichroism spectra, which are sensitive to local backbone structure.     

Piecewise linear approximation of protein structures using the principle of minimum message length

Simple and concise representations of protein-folding patterns provide powerful abstractions for visualizations, comparisons, classifications, searching and aligning structural data. Structures are often abstracted by replacing standard secondary structural features-that is, helices and strands of sheet-by vectors or linear segments. Relying solely on standard secondary structure may result in a significant loss of structural information. Further, traditional methods of simplification crucially depend on the consistency and accuracy of external methods to assign secondary structures to protein coordinate data. Although many methods exist automatically to identify secondary structure, the impreciseness of definitions, along with errors and inconsistencies in experimental structure data, drastically limit their applicability to generate reliable simplified representations, especially for structural comparison. This article introduces a mathematically rigorous algorithm to delineate protein structure using the elegant statistical and inductive inference framework of minimum message length (MML). Our method generates consistent and statistically robust piecewise linear explanations of protein coordinate data, resulting in a powerful and concise representation of the structure. The delineation is completely independent of the approaches of using hydrogen-bonding patterns or inspecting local substructural geometry that the current methods use. Indeed, as is common with applications of the MML criterion, this method is free of parameters and thresholds, in striking contrast to the existing programs which are often beset by them. The analysis of results over a large number of proteins suggests that the method produces consistent delineation of structures that encompasses, among others, the segments corresponding to standard secondary structure. AVAILABILITY: http://www.csse.monash.edu.au/~karun/pmml.     

Structural search and retrieval using a tableau representation of protein folding patterns

Comparison and classification of folding patterns from a database of protein structures is crucial to understand the principles of protein architecture, evolution and function. Current search methods for proteins with similar folding patterns are slow and computationally intensive. The sharp growth in the number of known protein structures poses severe challenges for methods of structural comparison. There is a need for methods that can search the database of structures accurately and rapidly. We provide several methods to search for similar folding patterns using a concise tableau representation of proteins that encodes the relative geometry of secondary structural elements. Our first approach allows the extraction of identical and very closely-related protein folding patterns in constant-time (per hit). Next, we address the hard computational problem of extraction of maximally-similar subtableaux, when comparing two tableaux. We solve the problem using Quadratic and Linear integer programming formulations and demonstrate their power to identify subtle structural similarities, especially when protein structures significantly diverge. Finally, we describe a rapid and accurate method for comparing a query structure against a database of protein domains, TableauSearch. TableauSearch is rapid enough to search the entire structural database in seconds on a standard desktop computer. Our analysis of TableauSearch on many queries shows that the method is very accurate in identifying similarities of folding patterns, even between distantly related proteins. AVAILABILITY: A web server implementing the TableauSearch is available from http://hollywood.bx.psu.edu/TabSearch.     

Description and recognition of regular and distorted secondary structures in proteins using the automated protein structure analysis method

The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in three‐dimensional space and characterizes it by curvature κ and torsion τ as a function of arc length s, was applied on 77 proteins to determine all secondary structural units via specific κ(s) and τ(s) patterns. A total of 533 α‐helices and 644 β‐strands were recognized by APSA, whereas DSSP gives 536 and 651 units, respectively. Kinks and distortions were quantified and the boundaries (entry and exit) of secondary structures were classified. Similarity between proteins can be easily quantified using APSA, as was demonstrated for the roll architecture of proteins ubiquitin and spinach ferridoxin. A twenty‐by‐twenty comparison of all α domains showed that the curvature‐torsion patterns generated by APSA provide an accurate and meaningful similarity measurement for secondary, super secondary, and tertiary protein structure. APSA is shown to accurately reflect the conformation of the backbone effectively reducing three‐dimensional structure information to two‐dimensional representations that are easy to interpret and understand. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Database of homology-derived protein structures and the structural meaning of sequence alignment

The database of known protein three-dimensional structures can be significantly increased by the use of sequence homology, based on the following observations. (1) The database of known sequences, currently at more than 12,000 proteins, is two orders of magnitude larger than the database of known structures. (2) The currently most powerful method of predicting protein structures is model building by homology. (3) Structural homology can be inferred from the level of sequence similarity. (4) The threshold of sequence similarity sufficient for structural homology depends strongly on the length of the alignment. Here, we first quantify the relation between sequence similarity, structure similarity, and alignment length by an exhaustive survey of alignments between proteins of known structure and report a homology threshold curve as a function of alignment length. We then produce a database of homology-derived secondary structure of proteins (HSSP) by aligning to each protein of known structure all sequences deemed homologous on the basis of the threshold curve. For each known protein structure, the derived database contains the aligned sequences, secondary structure, sequence variability, and sequence profile. Tertiary structures of the aligned sequences are implied, but not modeled explicitly. The database effectively increases the number of known protein structures by a factor of five to more than 1800. The results may be useful in assessing the structural significance of matches in sequence database searches, in deriving preferences and patterns for structure prediction, in elucidating the structural role of conserved residues, and in modeling three-dimensional detail by homology.     

Dynameomics: large-scale assessment of native protein flexibility

Structure is only the first step in understanding the interactions and functions of proteins. In this paper, we explore the flexibility of proteins across a broad database of over 250 solvated protein molecular dynamics simulations in water for an aggregate simulation time of approximately 6 micros. These simulations are from our Dynameomics project, and these proteins represent approximately 75% of all known protein structures. We employ principal component analysis of the atomic coordinates over time to determine the primary axis and magnitude of the flexibility of each atom in a simulation. This technique gives us both a database of flexibility for many protein fold families and a compact visual representation of a particular protein's native-state conformational space, neither of which are available using experimental methods alone. These tools allow us to better understand the nature of protein motion and to describe its relationship to other structural and dynamical characteristics. In addition to reporting general properties of protein flexibility and detailing many dynamic motifs, we characterize the relationship between protein native-state flexibility and early events in thermal unfolding and show that flexibility predicts how a protein will begin to unfold. We provide evidence that fold families have conserved flexibility patterns, and family members who deviate from the conserved patterns have very low sequence identity. Finally, we examine novel aspects of highly inflexible loops that are as important to structural integrity as conventional secondary structure. These loops, which are difficult if not impossible to locate without dynamic data, may constitute new structural motifs.     

Contact patterns between helices and strands of sheet define protein folding patterns

Comparing and classifying protein folding patterns allows organizing the known structures and enumerating possible protein structural patterns including those not yet observed. We capture the essence of protein folding patterns in a concise tableau representation based on the order and contact patterns of secondary structures: helices and strands of sheet. The tableaux are intelligible to both humans and computers. They provide a database, derived from the Protein Data Bank, mineable in studies of protein architecture. Using this database, we have: (i) determined statistical properties of secondary structure contacts in an unbiased set of protein domains from ASTRAL, (ii) observed that in 98% of cases, the tableau is a faithful representation of the folding pattern as classified in SCOP, (iii) demonstrated that to a large extent the local structure of proteins indicates their complete folding topology, and (iv) studied the use of the representation for fold identification.     

Non-intertwined binary patterns of hydrophobic/nonhydrophobic amino acids are considerably better markers of regular secondary structures than nonconstrained patterns

Patterns of hydrophobic and hydrophilic residues (binary patterns) play an important role in protein architecture and can be roughly categorized into two classes regarding their preferential participation in α‐helices or β‐strands. However, a single binary pattern can be embedded into different longer patterns carrying opposite structural information and thus cannot be as much informative as expected. Here, we consider conditional binary patterns, or hydrophobic clusters, whose existence is conditioned by the presence of a minimum number of nonhydrophobic residues, called the connectivity distance, that separate two hydrophobic amino acids assumed to belong to two distinct patterns. Conditional binary patterns are distinct from simple ones in that they are not intertwined, i.e., they can not include or be included in other conditional patterns and therefore carry a much more differentiated information, in particular being dramatically better correlated with regular secondary structures (especially β ones). The distribution of these nonintertwined binary patterns in natural proteins was assessed relative to randomness, evidencing the structural bricks that are favored and disfavored by evolutionary selection. Several connectivity distances as well as several hydrophobic alphabets were tested, evidencing the clear superiority of a connectivity distance of 4, which mimics the minimum current length of loops in globular domains, and of the VILFMYW alphabet, selected from structural data (secondary structure propension and Voronoï tesselation), in highlighting fundamental properties of protein folds. Proteins 2003;51:236–244. © 2003 Wiley‐Liss, Inc.     

Amino acid propensities for secondary structures are influenced by the protein structural class

Amino acid propensities for secondary structures were used since the 1970s, when Chou and Fasman evaluated them within datasets of few tens of proteins and developed a method to predict secondary structure of proteins, still in use despite prediction methods having evolved to very different approaches and higher reliability. Propensity for secondary structures represents an intrinsic property of amino acid, and it is used for generating new algorithms and prediction methods, therefore our work has been aimed to investigate what is the best protein dataset to evaluate the amino acid propensities, either larger but not homogeneous or smaller but homogeneous sets, i.e., all-alpha, all-beta, alpha-beta proteins. As a first analysis, we evaluated amino acid propensities for helix, beta-strand, and coil in more than 2000 proteins from the PDBselect dataset. With these propensities, secondary structure predictions performed with a method very similar to that of Chou and Fasman gave us results better than the original one, based on propensities derived from the few tens of X-ray protein structures available in the 1970s. In a refined analysis, we subdivided the PDBselect dataset of proteins in three secondary structural classes, i.e., all-alpha, all-beta, and alpha-beta proteins. For each class, the amino acid propensities for helix, beta-strand, and coil have been calculated and used to predict secondary structure elements for proteins belonging to the same class by using resubstitution and jackknife tests. This second round of predictions further improved the results of the first round. Therefore, amino acid propensities for secondary structures became more reliable depending on the degree of homogeneity of the protein dataset used to evaluate them. Indeed, our results indicate also that all algorithms using propensities for secondary structure can be still improved to obtain better predictive results.     

A substitution matrix for structural alphabet based on structural alignment of homologous proteins and its applications

Analysis of protein structures based on backbone structural patterns known as structural alphabets have been shown to be very useful. Among them, a set of 16 pentapeptide structural motifs known as protein blocks (PBs) has been identified and upon which backbone model of most protein structures can be built. PBs allows simplification of 3D space onto 1D space in the form of sequence of PBs. Here, for the first time, substitution probabilities of PBs in a large number of aligned homologous protein structures have been studied and are expressed as a simplified 16 x 16 substitution matrix. The matrix was validated by benchmarking how well it can align sequences of PBs rather like amino acid alignment to identify structurally equivalent regions in closely or distantly related proteins using dynamic programming approach. The alignment results obtained are very comparable to well established structure comparison methods like DALI and STAMP. Other interesting applications of the matrix have been investigated. We first show that, in variable regions between two superimposed homologous proteins, one can distinguish between local conformational differences and rigid-body displacement of a conserved motif by comparing the PBs and their substitution scores. Second, we demonstrate, with the example of aspartic proteinases, that PBs can be efficiently used to detect the lobe/domain flexibility in the multidomain proteins. Lastly, using protein kinase as an example, we identify regions of conformational variations and rigid body movements in the enzyme as it is changed to the active state from an inactive state.     

Comparative analysis and "expression space" coverage of the production of prokaryotic membrane proteins for structural genomics

Membrane proteins comprise up to one-third of prokaryotic and eukaryotic genomes, but only a very small number of membrane protein structures are known. Membrane proteins are challenging targets for structural biology, primarily due to the difficulty in producing and purifying milligram quantities of these proteins. We are evaluating different methods to produce and purify large numbers of prokaryotic membrane proteins for subsequent structural and functional analysis. Here, we present the comparative expression data for 37 target proteins, all of them secondary transporters, from the mesophilic organism Salmonella typhimurium and the two hyperthermophilic organisms Aquifex aeolicus and Pyrococcus furiosus in three different Escherichia coli expression vectors. In addition, we study the use of Lactococcus lactis as a host for integral membrane protein expression. Overall, 78% of the targets were successfully produced under at least one set of conditions. Analysis of these results allows us to assess the role of different variables in increasing "expression space" coverage for our set of targets. This analysis implies that to maximize the number of nonhomologous targets that are expressed, orthologous targets should be chosen and tested in two vectors with different types of promoters, using C-terminal tags. In addition, E. coli is shown to be a robust host for the expression of prokaryotic transporters, and is superior to L. lactis. These results therefore suggest appropriate strategies for high-throughput heterologous overproduction of membrane proteins.     

Correlation between the structural stability and aggregation propensity of proteins

Protein aggregation, being an outcome of improper protein folding, is largely dependent on the folding kinetics of a protein. Previous studies have reported a positive correlation between the stability of the secondary structural elements of a protein and their rate of folding/unfolding. In this in silico study, the secondary and tertiary structures of proteins a) that form inclusion bodies on overexpression in Escherichia coli, b) that form amyloid fibrils and c) that are soluble on overexpression in E. coli are analyzed for certain features that are known to be associated with structural stability. The study revealed that the soluble proteins seem to have a higher rate of folding (based on contact order) and a lower percentage of exposed hydrophobic residues as compared to the inclusion body forming or amyloidogenic proteins. The soluble proteins also seem to have a more favored helix and strand composition (based on the known secondary structural propensities of amino acids). The secondary structure analyses also reveal that the evolutionary pressure is directed against protein aggregation. This understanding of the positive correlation between structural stability and solubility, along with the other parameters known to influence aggregation, could be exploited in the design of mutations aimed at reducing the aggregation propensity of the proteins.     

Organ-specific properties of cytochromes P-450s21 (steroid 21-hydroxylases) of liver and adrenocortical microsomes

Prothrombin, plasminogen, urokinase- and tissue-type plasminogen activators contain homologous structures known as kringles . The kringles correspond to autonomous structural and folding domains which mediate the binding of these multidomain proteins to other proteins. During evolution the different kringles retained the same gross architecture, the kringle -fold, yet diverged to bind different proteins. We show that the amino acid sequences of the type II structures of the gelatin-binding region of fibronectin are homologous with those of the protease- kringles . Prediction of secondary structures revealed a remarkable agreement in the positions of predicted beta-sheets, suggesting that the folding of kringles and type II structures may also be similar. As a corollary of this finding, the disulphide-bridge pattern of type II structures is shown to be homologous to that in kringles . It is noteworthy that protease- kringles and fibronectin type II structures have similar functions inasmuch as they mediate the binding of multidomain proteins to other proteins. It is proposed that the kringles of proteases and type II structures of fibronectin evolved from a common ancestral protein binding module.     

Decomposing the space of protein quaternary structures with the interface fragment pair library

Background

The physical interactions between proteins constitute the basis of protein quaternary structures. They dominate many biological processes in living cells. Deciphering the structural features of interacting proteins is essential to understand their cellular functions. Similar to the space of protein tertiary structures in which discrete patterns are clearly observed on fold or sub-fold motif levels, it has been found that the space of protein quaternary structures is highly degenerate due to the packing of compact secondary structure elements at interfaces. Therefore, it is necessary to further decompose the protein quaternary structural space into a more local representation.

Results

Here we constructed an interface fragment pair library from the current structure database of protein complexes. After structural-based clustering, we found that more than 90% of these interface fragment pairs can be represented by a limited number of highly abundant motifs. These motifs were further used to guide complex assembly. A large-scale benchmark test shows that the native-like binding is highly likely in the structural ensemble of modeled protein complexes that were built through the library.

Conclusions

Our study therefore presents supportive evidences that the space of protein quaternary structures can be represented by the combination of a small set of secondary-structure-based packing at binding interfaces. Finally, after future improvements such as adding sequence profiles, we expect this new library will be useful to predict structures of unknown protein-protein interactions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0437-4) contains supplementary material, which is available to authorized users.     

Probing protein fold space with a simplified model

We probe the stability and near-native energy landscape of protein fold space using powerful conformational sampling methods together with simple reduced models and statistical potentials. Fold space is represented by a set of 280 protein domains spanning all topological classes and having a wide range of lengths (33-300 residues) amino acid composition and number of secondary structural elements. The degrees of freedom are taken as the loop torsion angles. This choice preserves the native secondary structure but allows the tertiary structure to change. The proteins are represented by three-point per residue, three-dimensional models with statistical potentials derived from a knowledge-based study of known protein structures. When this space is sampled by a combination of parallel tempering and equi-energy Monte Carlo, we find that the three-point model captures the known stability of protein native structures with stable energy basins that are near-native (all α: 4.77 Å, all β: 2.93 Å, α/β: 3.09 Å, α+β: 4.89 Å on average and within 6 Å for 71.41%, 92.85%, 94.29% and 64.28% for all-α, all-β, α/β and α+β, classes, respectively). Denatured structures also occur and these have interesting structural properties that shed light on the different landscape characteristics of α and β folds. We find that α/β proteins with alternating α and β segments (such as the β-barrel) are more stable than proteins in other fold classes.     

Origin and Evolution of Protein Fold Designs Inferred from Phylogenomic Analysis of CATH Domain Structures in Proteomes

The spatial arrangements of secondary structures in proteins, irrespective of their connectivity, depict the overall shape and organization of protein domains. These features have been used in the CATH and SCOP classifications to hierarchically partition fold space and define the architectural make up of proteins. Here we use phylogenomic methods and a census of CATH structures in hundreds of genomes to study the origin and diversification of protein architectures (A) and their associated topologies (T) and superfamilies (H). Phylogenies that describe the evolution of domain structures and proteomes were reconstructed from the structural census and used to generate timelines of domain discovery. Phylogenies of CATH domains at T and H levels of structural abstraction and associated chronologies revealed patterns of reductive evolution, the early rise of Archaea, three epochs in the evolution of the protein world, and patterns of structural sharing between superkingdoms. Phylogenies of proteomes confirmed the early appearance of Archaea. While these findings are in agreement with previous phylogenomic studies based on the SCOP classification, phylogenies unveiled sharing patterns between Archaea and Eukarya that are recent and can explain the canonical bacterial rooting typically recovered from sequence analysis. Phylogenies of CATH domains at A level uncovered general patterns of architectural origin and diversification. The tree of A structures showed that ancient structural designs such as the 3-layer (αβα) sandwich (3.40) or the orthogonal bundle (1.10) are comparatively simpler in their makeup and are involved in basic cellular functions. In contrast, modern structural designs such as prisms, propellers, 2-solenoid, super-roll, clam, trefoil and box are not widely distributed and were probably adopted to perform specialized functions. Our timelines therefore uncover a universal tendency towards protein structural complexity that is remarkable.     

Comparison of protein structural profiles by interactive computer graphics

This paper describes a novel computer graphics tool for predicting protein structures. The method is based on structural profiles; which are plots of hydrophobicity, parameters used for secondary structure prediction, or other residue-specific traits against sequence number. Similar structural profiles can indicate similar tertiary structures, in the absence of sequence homology. The profiles of reference proteins, with known structure, can be used for prediction. In the method presented here, structural profiles are compared by interactive computer graphics, using the program Multiplot. As a test, a structural profile comparison of several proteins known to have similar 3D structures is presented. Comparison of structural profiles detects similar folding of the two domains of rhodanese, which was not easily detected by sequence homology.     

Probing designability via a generalized model of helical bundle geometry

Because the space of folded protein structures is highly degenerate, with recurring secondary and tertiary motifs, methods for representing protein structure in terms of collective physically relevant coordinates are of great interest. By collapsing structural diversity to a handful of parameters, such methods can be used to delineate the space of designable structures (i.e., conformations that can be stabilized with a large number of sequences)—a crucial task for de novo protein design. We first demonstrate this on natural α-helical coiled coils using the Crick parameterization. We show that over 95% of known coiled-coil structures are within  1-Å C_α root mean square deviation of a Crick-ideal backbone. Derived parameters show that natural geometric space of coiled coils is highly restricted and can be represented by “allowed” conformations amidst a potential continuum of conformers. Allowed structures have (1) restricted axial offsets between helices, which differ starkly between parallel and anti-parallel structures; (2) preferred superhelical radii, which depend linearly on the oligomerization state; (3) pronounced radius-dependent a- and d-position amino acid propensities; and (4) discrete angles of rotation of helices about their axes, which are surprisingly independent of oligomerization state or orientation. In all, we estimate the space of designable coiled-coil structures to be reduced at least 160-fold relative to the space of geometrically feasible structures. To extend the benefits of structural parameterization to other systems, we developed a general mathematical framework for parameterizing arbitrary helical structures, which reduces to the Crick parameterization as a special case. The method is successfully validated on a set of non-coiled-coil helical bundles, frequent in channels and transporter proteins, which show significant helix bending but not supercoiling. Programs for coiled-coil parameter fitting and structure generation are provided via a web interface at http://www.gevorggrigoryan.com/cccp/, and code for generalized helical parameterization is available upon request.     

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.     

Exploring an alignment free approach for protein classification and structural class prediction

Alignment free methods based on Chaos Game Representation (CGR), also known as sequence signature approaches, have proven of great interest for DNA sequence analysis. Indeed, they have been successfully applied for sequence comparison, phylogeny, detection of horizontal transfers or extraction of representative motifs in regulation sequences. Transposing such methods to proteins poses several fundamental questions related to representation space dimensionality. Several studies have tackled these points, but none has, so far, brought the application of CGRs to proteins to their fully expected potential. Yet, several studies have shown that techniques based on n-peptide frequencies can be relevant for proteins. Here, we investigate the effectiveness of a strategy based on the CGR approach using a fixed reverse encoding of amino acids into nucleic sequences. We first explore its relevance to protein classification into functional families. We then attempt to apply it to the prediction of protein structural classes. Our results suggest that the reverse encoding approach could be relevant in both cases. We show that it is able to classify functional families of proteins by extracting signatures close to the ProSite patterns. Applied to structural classification, the approach reaches scores of correct classification close to 84%, i.e. close to the scores of related methods in the field. Various optimizations of the approach are still possible, which open the door for future applications.