Automatic classification of protein structures relying on similarities between alignments

ABSTRACT: BACKGROUND: Identification of protein structural cores requires isolation of sets of proteins all sharing a same subset of structural motifs. In the context of ever growing number of available 3D protein structures, standard and automatic clustering algorithms require adaptations so as to allow for efficient identification of such sets of proteins. RESULTS: When considering a pair of 3D structures, they are stated as similar or not according to the local similarities of their matching substructures in a structural alignment. This binary relation can be represented in a graph of similarities where a node represents a 3D protein structure and an edge states that two 3D protein structures are similar. Therefore, the classification of proteins into structural families can be viewed as graph clustering task. Unfortunately, because such a graph encodes only pairwise similarity information, clustering algorithms may group in the same cluster a subset of 3D structures that do not share a common substructure. To overcome this drawback we first define a ternary similarity on a triple of 3D structures as a constraint to be satisfied by the graph of similarities. Such a ternary constraint takes into account similarities between pairwise alignments, so as to ensure that the three involved protein structures do have some common substructure. We propose hereunder a modification algorithm that eliminates edges from the original graph of similarities and outputs a reduced graph in which no ternary constraints are violated. Our proposition is then first to build a graph of similarities, then to reduce the graph according to the modification algorithm, and finally to apply to the reduced graph a standard graph clustering algorithm. We applied this method to ASTRAL-40 non-redundant protein domains, identifying significant pairwise similarities with Yakusa, a program devised for rapid 3D structure alignments. CONCLUSIONS: We show that filtering similarities prior to standard graph based clustering process by applying ternary similarity constraints i) improves the separation of proteins of different classes and consequently ii) improves the classification quality of standard graph based clustering algorithms according to the reference classification SCOP.     

Mining frequent stem patterns from unaligned RNA sequences

MOTIVATION: In detection of non-coding RNAs, it is often necessary to identify the secondary structure motifs from a set of putative RNA sequences. Most of the existing algorithms aim to provide the best motif or few good motifs, but biologists often need to inspect all the possible motifs thoroughly. RESULTS: Our method RNAmine employs a graph theoretic representation of RNA sequences and detects all the possible motifs exhaustively using a graph mining algorithm. The motif detection problem boils down to finding frequently appearing patterns in a set of directed and labeled graphs. In the tasks of common secondary structure prediction and local motif detection from long sequences, our method performed favorably both in accuracy and in efficiency with the state-of-the-art methods such as CMFinder. AVAILABILITY: The software is available upon request.     

Use of techniques derived from graph theory to compare secondary structure motifs in proteins

A substructure matching algorithm is described that can be used for the automatic identification of secondary structural motifs in three-dimensional protein structures from the Protein Data Bank. The proteins and motifs are stored for searching as labelled graphs, with the nodes of a graph corresponding to linear representations of helices and strands and the edges to the inter-line angles and distances. A modification of Ullman's subgraph isomorphism algorithm is described that can be used to search these graph representations. Tests with patterns from the protein structure literature demonstrate both the efficiency and the effectiveness of the search procedure, which has been implemented in FORTRAN 77 on a MicroVAX-II system, coupled to the molecular fitting program FRODO on an Evans and Sutherland PS300 graphics system.     

MotifCut: regulatory motifs finding with maximum density subgraphs

MOTIVATION: DNA motif finding is one of the core problems in computational biology, for which several probabilistic and discrete approaches have been developed. Most existing methods formulate motif finding as an intractable optimization problem and rely either on expectation maximization (EM) or on local heuristic searches. Another challenge is the choice of motif model: simpler models such as the position-specific scoring matrix (PSSM) impose biologically unrealistic assumptions such as independence of the motif positions, while more involved models are harder to parametrize and learn. RESULTS: We present MotifCut, a graph-theoretic approach to motif finding leading to a convex optimization problem with a polynomial time solution. We build a graph where the vertices represent all k-mers in the input sequences, and edges represent pairwise k-mer similarity. In this graph, we search for a motif as the maximum density subgraph, which is a set of k-mers that exhibit a large number of pairwise similarities. Our formulation does not make strong assumptions regarding the structure of the motif and in practice both motifs that fit well the PSSM model, and those that exhibit strong dependencies between position pairs are found as dense subgraphs. We benchmark MotifCut on both synthetic and real yeast motifs, and find that it compares favorably to existing popular methods. The ability of MotifCut to detect motifs appears to scale well with increasing input size. Moreover, the motifs we discover are different from those discovered by the other methods. AVAILABILITY: MotifCut server and other materials can be found at motifcut.stanford.edu.     

Database of structural motifs in proteins

SUMMARY: The database of structural motifs in proteins (DSMP) contains data relevant to helices, beta-turns, gamma-turns, beta-hairpins, psi-loops, beta-alpha-beta motifs, beta-sheets, beta-strands and disulphide bridges extracted from all proteins in the Protein Data Bank primarily using the PROMOTIF program and implemented as a web-based network service using the SRS. The data corresponding to the structural motifs includes; sequence, position in polypeptide chain, geometry, type, unique code, keywords and resolution of crystal structure. This data is available for a representative data set of 1028 protein chains and also for all 10 213 proteins in the Protein Data Bank. The three-dimensional coordinates for all structural motifs (except sheet and disulphide bridge) are also available for the representative data set. Using features in SRS, DSMP can be queried to extract information from one or more structural motifs that may be useful for sequence-structure analysis, prediction, modelling or design. AVAILABILITY: http://www. cdfd.org.in/dsmp.html     

RAG: RNA-As-Graphs database--concepts, analysis, and features

MOTIVATION: Understanding RNA's structural diversity is vital for identifying novel RNA structures and pursuing RNA genomics initiatives. By classifying RNA secondary motifs based on correlations between conserved RNA secondary structures and functional properties, we offer an avenue for predicting novel motifs. Although several RNA databases exist, no comprehensive schemes are available for cataloguing the range and diversity of RNA's structural repertoire. RESULTS: Our RNA-As-Graphs (RAG) database describes and ranks all mathematically possible (including existing and candidate) RNA secondary motifs on the basis of graphical enumeration techniques. We represent RNA secondary structures as two-dimensional graphs (networks), specifying the connectivity between RNA secondary structural elements, such as loops, bulges, stems and junctions. We archive RNA tree motifs as 'tree graphs' and other RNAs, including pseudoknots, as general 'dual graphs'. All RNA motifs are catalogued by graph vertex number (a measure of sequence length) and ranked by topological complexity. The RAG inventory immediately suggests candidates for novel RNA motifs, either naturally occurring or synthetic, and thereby might stimulate the prediction and design of novel RNA motifs. AVAILABILITY: The database is accessible on the web at http://monod.biomath.nyu.edu/rna     

Identification of novel RNA design candidates by clustering the extended RNA-As-Graphs library

BackgroundWe re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications.MethodsClustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into ‘existing’ or hypothetical, and the latter into, ‘RNA-like’ or ‘non RNA-like’ topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups.ResultsThe unsupervised PAM and K-means clustering approaches correctly classify 72–77% of all existing graph topologies and 75–82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%.ConclusionsUsing linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach.General significanceOur updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.     

Fast and accurate protein substructure searching with simulated annealing and GPUs

Background  

Searching a database of protein structures for matches to a query structure, or occurrences of a structural motif, is an important task in structural biology and bioinformatics. While there are many existing methods for structural similarity searching, faster and more accurate approaches are still required, and few current methods are capable of substructure (motif) searching.     

SAGA: a subgraph matching tool for biological graphs

MOTIVATION: With the rapid increase in the availability of biological graph datasets, there is a growing need for effective and efficient graph querying methods. Due to the noisy and incomplete characteristics of these datasets, exact graph matching methods have limited use and approximate graph matching methods are required. Unfortunately, existing graph matching methods are too restrictive as they only allow exact or near exact graph matching. This paper presents a novel approximate graph matching technique called SAGA. This technique employs a flexible model for computing graph similarity, which allows for node gaps, node mismatches and graph structural differences. SAGA employs an indexing technique that allows it to efficiently evaluate queries even against large graph datasets. RESULTS: SAGA has been used to query biological pathways and literature datasets, which has revealed interesting similarities between distinct pathways that cannot be found by existing methods. These matches associate seemingly unrelated biological processes, connect studies in different sub-areas of biomedical research and thus pose hypotheses for new discoveries. SAGA is also orders of magnitude faster than existing methods. AVAILABILITY: SAGA can be accessed freely via the web at http://www.eecs.umich.edu/saga. Binaries are also freely available at this website.     

RNAMotifContrast: a method to discover and visualize RNA structural motif subfamilies

Understanding the 3D structural properties of RNAs will play a critical role in identifying their functional characteristics and designing new RNAs for RNA-based therapeutics and nanotechnology. While several existing computational methods can help in the analysis of RNA properties by recognizing structural motifs, they do not provide the means to compare and contrast those motifs extensively. We have developed a new method, RNAMotifContrast, which focuses on analyzing the similarities and variations of RNA structural motif characteristics. In this method, a graph is formed to represent the similarities among motifs, and a new traversal algorithm is applied to generate visualizations of their structural properties. Analyzing the structural features among motifs, we have recognized and generalized the concept of motif subfamilies. To asses its effectiveness, we have applied RNAMotifContrast on a dataset of known RNA structural motif families. From the results, we observed that the derived subfamilies possess unique structural variations while holding standard features of the families. Overall, the visualization approach of this method presents a new perspective to observe the relation among motifs more closely, and the discovered subfamilies provide opportunities to achieve valuable insights into RNA’s diverse roles.     

Automated multiple structure alignment and detection of a common substructural motif

While a number of approaches have been geared toward multiple sequence alignments, to date there have been very few approaches to multiple structure alignment and detection of a recurring substructural motif. Among these, none performs both multiple structure comparison and motif detection simultaneously. Further, none considers all structures at the same time, rather than initiating from pairwise molecular comparisons. We present such a multiple structural alignment algorithm. Given an ensemble of protein structures, the algorithm automatically finds the largest common substructure (core) of C(alpha) atoms that appears in all the molecules in the ensemble. The detection of the core and the structural alignment are done simultaneously. Additional structural alignments also are obtained and are ranked by the sizes of the substructural motifs, which are present in the entire ensemble. The method is based on the geometric hashing paradigm. As in our previous structural comparison algorithms, it compares the structures in an amino acid sequence order-independent way, and hence the resulting alignment is unaffected by insertions, deletions and protein chain directionality. As such, it can be applied to protein surfaces, protein-protein interfaces and protein cores to find the optimally, and suboptimally spatially recurring substructural motifs. There is no predefinition of the motif. We describe the algorithm, demonstrating its efficiency. In particular, we present a range of results for several protein ensembles, with different folds and belonging to the same, or to different, families. Since the algorithm treats molecules as collections of points in three-dimensional space, it can also be applied to other molecules, such as RNA, or drugs.     

RNAMotifScanX: a graph alignment approach for RNA structural motif identification

RNA structural motifs are recurrent three-dimensional (3D) components found in the RNA architecture. These RNA structural motifs play important structural or functional roles and usually exhibit highly conserved 3D geometries and base-interaction patterns. Analysis of the RNA 3D structures and elucidation of their molecular functions heavily rely on efficient and accurate identification of these motifs. However, efficient RNA structural motif search tools are lacking due to the high complexity of these motifs. In this work, we present RNAMotifScanX, a motif search tool based on a base-interaction graph alignment algorithm. This novel algorithm enables automatic identification of both partially and fully matched motif instances. RNAMotifScanX considers noncanonical base-pairing interactions, base-stacking interactions, and sequence conservation of the motifs, which leads to significantly improved sensitivity and specificity as compared with other state-of-the-art search tools. RNAMotifScanX also adopts a carefully designed branch-and-bound technique, which enables ultra-fast search of large kink-turn motifs against a 23S rRNA. The software package RNAMotifScanX is implemented using GNU C++, and is freely available from http://genome.ucf.edu/RNAMotifScanX.     

Comparing graph representations of protein structure for mining family-specific residue-based packing motifs.

We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; second, using Delaunay tessellation; and third, using the recently developed almost-Delaunay edges. For a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, subgraph mining typically identifies several hundred common subgraphs corresponding to spatial motifs that are frequently found in proteins in the family but rarely found outside of it. We find that some of the large motifs map onto known functional regions in two protein families explored in this study, i.e., serine proteases and kinases. We find that graphs based on almost-Delaunay edges significantly reduce the number of edges in the graph representation and hence present computational advantage, yet the patterns extracted from such graphs have a biological interpretation approximately equivalent to that of those extracted from distance based graphs.     

Protein evolution within a structural space

Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural “space” might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analogous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.     

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.     

SING: Subgraph search In Non-homogeneous Graphs

Background  

Finding the subgraphs of a graph database that are isomorphic to a given query graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism is a computationally hard problem, indexing techniques have been intensively exploited to speed up the process. Such systems filter out those graphs which cannot contain the query, and apply a subgraph isomorphism algorithm to each residual candidate graph. The applicability of such systems is limited to databases of small graphs, because their filtering power degrades on large graphs.     

Minimotif Miner: a tool for investigating protein function

In addition to large domains, many short motifs mediate functional post-translational modification of proteins as well as protein-protein interactions and protein trafficking functions. We have constructed a motif database comprising 312 unique motifs and a web-based tool for identifying motifs in proteins. Functional motifs predicted by MnM can be ranked by several approaches, and we validated these scores by analyzing thousands of confirmed examples and by confirming prediction of previously unidentified 14-3-3 motifs in EFF-1.     

Analysis of structural motifs of proteins using sets of codes, describing local structures]

An amino acid sequence pattern conserved among a family of proteins is called motif. It is usually related to the specific function of the family. On the other hand, functions of proteins are achieved by their 3D structures. Specific local structures, called structural motifs, are considered related to their functions. However, searching for common structural motifs in different proteins is much more difficult than for common sequence motifs. We are attempting in this study to convert the information about the structural motifs into a set of one-dimensional digital strings, i.e., a set of codes, to compare them more easily by computer and to investigate their relationship to functions more quantitatively. By applying the Delaunay tessellation to a 3D structure of a protein, we can assign each local structure to a unique code that is defined so as to reflect its structural feature. Since a structural motif is defined as a set of the local structures in this paper, the structural motif is represented by a set of the codes. In order to examine the ability of the set of the codes to distinguish differences among the sets of local structures with a given PROSITE pattern that contain both true and false positives, we clustered them by introducing a similarity measure among the set of the codes. The obtained clustering shows a good agreement with other results by direct structural comparison methods such as a superposition method. The structural motifs in homologous proteins are also properly clustered according to their sources. These results suggest that the structural motifs can be well characterized by these sets of the codes, and that the method can be utilized in comparing structural motifs and relating them with function.     

Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design

Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for finding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a two-dimensional graphical representation approach for describing and estimating the size of RNA’s secondary structural repertoire, including naturally occurring and other possible RNA motifs. We employ tree graphs to describe RNA tree motifs and more general (dual) graphs to describe both RNA tree and pseudoknot motifs. Our estimates of RNA’s structural space are vastly smaller than the nucleotide sequence space, suggesting a new avenue for finding novel RNAs. Specifically our survey shows that known RNA trees and pseudoknots represent only a small subset of all possible motifs, implying that some of the ‘missing’ motifs may represent novel RNAs. To help pinpoint RNA-like motifs, we show that the motifs of existing functional RNAs are clustered in a narrow range of topological characteristics. We also illustrate the applications of our approach to the design of novel RNAs and automated comparison of RNA structures; we report several occurrences of RNA motifs within larger RNAs. Thus, our graph theory approach to RNA structures has implications for RNA genomics, structure analysis and design.