LB3D: a protein three-dimensional substructure search program based on the lower bound of a root mean square deviation value

Searching for protein structure-function relationships using three-dimensional (3D) structural coordinates represents a fundamental approach for determining the function of proteins with unknown functions. Since protein structure databases are rapidly growing in size, the development of a fast search method to find similar protein substructures by comparison of protein 3D structures is essential. In this article, we present a novel protein 3D structure search method to find all substructures with root mean square deviations (RMSDs) to the query structure that are lower than a given threshold value. Our new algorithm runs in O(m + N/m(0.5)) time, after O(N log N) preprocessing, where N is the database size and m is the query length. The new method is 1.8-41.6 times faster than the practically best known O(N) algorithm, according to computational experiments using a huge database (i.e., >20,000,000 C-alpha coordinates).     

Searching for three-dimensional secondary structural patterns in proteins with ProSMoS

MOTIVATION: Many evolutionarily distant, but functionally meaningful links between proteins come to light through comparison of spatial structures. Most programs that assess structural similarity compare two proteins to each other and find regions in common between them. Structural classification experts look for a particular structural motif instead. Programs base similarity scores on superposition or closeness of either Cartesian coordinates or inter-residue contacts. Experts pay more attention to the general orientation of the main chain and mutual spatial arrangement of secondary structural elements. There is a need for a computational tool to find proteins with the same secondary structures, topological connections and spatial architecture, regardless of subtle differences in 3D coordinates. RESULTS: We developed ProSMoS--a Protein Structure Motif Search program that emulates an expert. Starting from a spatial structure, the program uses previously delineated secondary structural elements. A meta-matrix of interactions between the elements (parallel or antiparallel) minding handedness of connections (left or right) and other features (e.g. element lengths and hydrogen bonds) is constructed prior to or during the searches. All structures are reduced to such meta-matrices that contain just enough information to define a protein fold, but this definition remains very general and deviations in 3D coordinates are tolerated. User supplies a meta-matrix for a structural motif of interest, and ProSMoS finds all proteins in the protein data bank (PDB) that match the meta-matrix. ProSMoS performance is compared to other programs and is illustrated on a beta-Grasp motif. A brief analysis of all beta-Grasp-containing proteins is presented. Program availability: ProSMoS is freely available for non-commercial use from ftp://iole.swmed.edu/pub/ProSMoS.     

Predicting common foldings of homologous RNAs.

A new approach is proposed for determining common RNA secondary structures within a set of homologous RNAs. The approach is a combination of phylogenetic and thermodynamic methods which is based on the prediction of optimal and suboptimal secondary structures, topological similarity searches and phylogenetic comparative analysis. The optimal and suboptimal RNA secondary structures are predicted by energy minimization. Structural comparison of the predicted RNA secondary structures is used to find conserved structures that are topologically similar in all these homologous RNAs. The validity of the conserved structural elements found is then checked by phylogenetic comparison of the sequences. This procedure is used to predict common structures of ribonuclease P (RNAase P) RNAs.     

The ups and downs of protein topology; rapid comparison of protein structure

Protein topology can be described at different levels. At the most fundamental level, it is a sequence of secondary structure elements (a "primary topology string"). Searching predicted primary topology strings against a library of strings from known protein structures is the basis of some protein fold recognition methods. Here a method known as TOPSCAN is presented for rapid comparison of protein structures. Rather than a simple two-letter alphabet (encoding strand and helix), more complex alphabets are used encoding direction, proximity, accessibility and length of secondary elements and loops in addition to secondary structure. Comparisons are made between the structural information content of primary topology strings and encodings which contain additional information ("secondary topology strings"). The algorithm is extremely fast, with a scan of a large domain against a library of more than 2000 secondary structure strings completing in approximately 30 s. Analysis of protein fold similarity using TOPSCAN at primary and secondary topology levels is presented.     

Analysis of topological and nontopological structural similarities in the PDB: New examples with old structures

We have developed a new method and program, SARF2, for fast comparison of protein structures, which can detect topological as well as nontopological similarities. The method searches for large ensembles of secondary structure elements, which are mutually compatible in two proteins. These ensembles consist of small fragments of C^α-trace, similarly arranged in three-dimensional space in two proteins, but not necessarily equally-ordered along the polypeptide chains. The program SARF2 is available for everyone through the World-Wide Web (WWW). We have performed an exhaustive pairwise comparison of all the entries from a recent issue of the Protein Data Bank (PDB) and report here on the results of an automated hierarchical cluster analysis. In addition, we report on several new cases of significant structural resemblance between proteins. To this end, a new definition of the significance of structural similarity is introduced, which effectively distinguishes the biologically meaningful equivalences from those occurring by chance. Analyzing the distribution of sequence similarity in significant structural matches, we show that sequence similarity as low as 20% in structurally-prealigned proteins can be a strong indication for the biological relevance of structural similarity. © 1996 Wiley-Liss, Inc.     

Angle-distance image matching techniques for protein structure comparison

Proteins that contain similar structural elements often have analogous functions regardless of the degree of sequence similarity or structure connectivity in space. In general, protein structure comparison (PSC) provides a straightforward methodology for biologists to determine critical aspects of structure and function. Here, we developed a novel PSC technique based on angle-distance image (A-D image) transformation and matching, which is independent of sequence similarity and connectivity of secondary structure elements (SSEs). An A-D image is constructed by utilizing protein secondary structure information. According to various types of SSEs, the mutual SSE pairs of the query protein are classified into three different types of sub-images. Subsequently, corresponding sub-images between query and target protein structures are compared using modified cross-correlation approaches to identify the similarity of various patterns. Structural relationships among proteins are displayed by hierarchical clustering trees, which facilitate the establishment of the evolutionary relationships between structure and function of various proteins.Four standard testing datasets and one newly created dataset were used to evaluate the proposed method. The results demonstrate that proteins from these five datasets can be categorized in conformity with their spatial distribution of SSEs. Moreover, for proteins with low sequence identity that share high structure similarity, the proposed algorithms are an efficient and effective method for structural comparison.     

A new topological method to measure protein structure similarity

A method for the quantitative evaluation of structural similarity between protein pairs is developed that makes use of a Delaunay-based topological mapping. The result of the mapping is a three-dimensional array which is representative of the global structural topology and whose elements can be used to construe an integral scoring scheme. This scoring scheme was tested for its dependence on the protein length difference in a pairwise comparison, its ability to provide a reasonable means for structural similarity comparison within a family of structural neighbors of similar length, and its sensitivity to the differences in protein conformation. It is shown that such a topological evaluation of similarity is capable of providing insight into these points of interest. Protein structure comparison using the method is computationally efficient and the topological scores, although providing different information about protein similarity, correlate well with the distance root-mean-square deviation values calculated by rigid-body structural alignment.     

Protein structural similarity search by Ramachandran codes

Background  

Protein structural data has increased exponentially, such that fast and accurate tools are necessary to access structure similarity search. To improve the search speed, several methods have been designed to reduce three-dimensional protein structures to one-dimensional text strings that are then analyzed by traditional sequence alignment methods; however, the accuracy is usually sacrificed and the speed is still unable to match sequence similarity search tools. Here, we aimed to improve the linear encoding methodology and develop efficient search tools that can rapidly retrieve structural homologs from large protein databases.     

Identification of conserved regulatory RNA structures in prokaryotic metabolic pathway genes

A combination of algorithms to search RNA sequence for the potential for secondary structure formation, and search large numbers of sequences for structural similarity, were used to search the 5'UTRs of annotated genes in the Escherichia coli genome for regulatory RNA structures. Using this approach, similar RNA structures that regulate genes in the thiamin metabolic pathway were identified. In addition, several putative regulatory structures were discovered upstream of genes involved in other metabolic pathways including glycerol metabolism and ethanol fermentation. The results demonstrate that this computational approach is a powerful tool for discovery of important RNA structures within prokaryotic organisms.     

Prediction of protein coarse contact maps

Prediction of topological representations of proteins that are geometrically invariants can contribute towards the solution of fundamental open problems in structural genomics like folding. In this paper we focus on coarse grained protein contact maps, a representation that describes the spatial neighborhood relation between secondary structure elements such as helices, beta sheets, and random coils. Our methodology is based on searching the graph space. The search algorithm is guided by an adaptive evaluation function computed by a specialized noncausal recursive connectionist architecture. The neural network is trained using candidate graphs generated during examples of successful searches. Our results demonstrate the viability of the approach for predicting coarse contact maps.     

Protein structure similarity from principle component correlation analysis

Background  

Owing to rapid expansion of protein structure databases in recent years, methods of structure comparison are becoming increasingly effective and important in revealing novel information on functional properties of proteins and their roles in the grand scheme of evolutionary biology. Currently, the structural similarity between two proteins is measured by the root-mean-square-deviation (RMSD) in their best-superimposed atomic coordinates. RMSD is the golden rule of measuring structural similarity when the structures are nearly identical; it, however, fails to detect the higher order topological similarities in proteins evolved into different shapes. We propose new algorithms for extracting geometrical invariants of proteins that can be effectively used to identify homologous protein structures or topologies in order to quantify both close and remote structural similarities.     

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.     

Assessment of the probabilities for evolutionary structural changes in protein folds

MOTIVATION: The evolution of protein sequences can be described by a stepwise process, where each step involves changes of a few amino acids. In a similar manner, the evolution of protein folds can be at least partially described by an analogous process, where each step involves comparatively simple changes affecting few secondary structure elements. A number of such evolution steps, justified by biologically confirmed examples, have previously been proposed by other researchers. However, unlike the situation with sequences, as far as we know there have been no attempts to estimate the comparative probabilities for different kinds of such structural changes. RESULTS: We have tried to assess the comparative probabilities for a number of known structural changes, and to relate the probabilities of such changes with the distance between protein sequences. We have formalized these structural changes using a topological representation of structures (TOPS), and have developed an algorithm for measuring structural distances that involve few evolutionary steps. The probabilities of structural changes then were estimated on the basis of all-against-all comparisons of the sequence and structure of protein domains from the CATH-95 representative set. The results obtained are reasonably consistent for a number of different data subsets and permit the identification of several 'most popular' types of evolutionary changes in protein structure. The results also suggest that alterations in protein structure are more likely to occur when the sequence similarity is >10% (the average similarity being approximately 6% for the data sets employed in this study), and that the distribution of probabilities of structural changes is fairly uniform within the interval of 15-50% sequence similarity. AVAILABILITY: The algorithms have been implemented on the Windows operating system in C++ and using the Borland Visual Component Library. The source code is available on request from the first author. The data sets used for this study (representative sets of protein domains, matrices of sequence similarities and structural distances) are available on http://bioinf.mii.lu.lv/epsrc_project/struct_ev.html.     

MAMMOTH (matching molecular models obtained from theory): an automated method for model comparison

Advances in structural genomics and protein structure prediction require the design of automatic, fast, objective, and well benchmarked methods capable of comparing and assessing the similarity of low-resolution three-dimensional structures, via experimental or theoretical approaches. Here, a new method for sequence-independent structural alignment is presented that allows comparison of an experimental protein structure with an arbitrary low-resolution protein tertiary model. The heuristic algorithm is given and then used to show that it can describe random structural alignments of proteins with different folds with good accuracy by an extreme value distribution. From this observation, a structural similarity score between two proteins or two different conformations of the same protein is derived from the likelihood of obtaining a given structural alignment by chance. The performance of the derived score is then compared with well established, consensus manual-based scores and data sets. We found that the new approach correlates better than other tools with the gold standard provided by a human evaluator. Timings indicate that the algorithm is fast enough for routine use with large databases of protein models. Overall, our results indicate that the new program (MAMMOTH) will be a good tool for protein structure comparisons in structural genomics applications. MAMMOTH is available from our web site at http://physbio.mssm.edu/~ortizg/.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

Diversity of functions of proteins with internal symmetry in spatial arrangement of secondary structural elements.

We carry out a systematic analysis of the correlation between similarity of protein three-dimensional structures and their evolutionary relationships. The structural similarity is quantitatively identified by an all-against-all comparison of the spatial arrangement of secondary structural elements in nonredundant 967 representative proteins, and the evolutionary relationship is judged according to the definition of superfamily in the SCOP database. We find the following symmetry rule: a protein pair that has similar folds but belong to different superfamilies has (with a very rare exception) certain internal symmetry in its common similar folds. Possible reasons behind the symmetry rule are discussed.     

Flexible secondary structure based protein structure comparison applied to the detection of circular permutation.

We present a novel method for structural comparison of protein structures. The approach consists of two main phases: 1) an initial search phase where, starting from aligned pairs of secondary structure elements, the space of 3D transformations is searched for similarities and 2) a subsequent refinement phase where interim solutions are subjected to parallel, local, iterative dynamic programming in the areas of possible improvement. The proposed method combines dynamic programming for finding alignments but does not restrict solutions to be sequential. In addition, to deal with the problem of nonuniqueness of optimal similarities, we introduce a consensus scoring method in selecting the preferred similarity and provide a list of top-ranked solutions. The method, called FASE (flexible alignment of secondary structure elements), was tested on well-known data and various standard problems from the literature. The results show that FASE is able to find remote and weak similarities consistently using a reasonable run time. The method was tested (using the SCOP database) on its ability to discriminate interfold pairs from intrafold pairs at the level of the best existing methods. The method was then applied to the problem of finding circular permutations in proteins.     

Within the twilight zone: a sensitive profile-profile comparison tool based on information theory

This paper presents a novel approach to profile-profile comparison. The method compares two input profiles (like those that are generated by PSI-BLAST) and assigns a similarity score to assess their statistical similarity. Our profile-profile comparison tool, which allows for gaps, can be used to detect weak similarities between protein families. It has also been optimized to produce alignments that are in very good agreement with structural alignments. Tests show that the profile-profile alignments are indeed highly correlated with similarities between secondary structure elements and tertiary structure. Exhaustive evaluations show that our method is significantly more sensitive in detecting distant homologies than the popular profile-based search programs PSI-BLAST and IMPALA. The relative improvement is the same order of magnitude as the improvement of PSI-BLAST relative to BLAST. Our new tool often detects similarities that fall within the twilight zone of sequence similarity.