A simple topological representation of protein structure: implications for new, fast, and robust structural classification

A topological representation of proteins is developed that makes use of two metrics: the Euclidean metric for identifying natural nearest neighboring residues via the Delaunay tessellation in Cartesian space and the distance between residues in sequence space. Using this representation, we introduce a quantitative and computationally inexpensive method for the comparison of protein structural topology. The method ultimately results in a numerical score quantifying the distance between proteins in a heuristically defined topological space. The properties of this scoring scheme are investigated and correlated with the standard Calpha distance root-mean-square deviation measure of protein similarity calculated by rigid body structural alignment. The topological comparison method is shown to have a characteristic dependence on protein conformational differences and secondary structure. This distinctive behavior is also observed in the comparison of proteins within families of structural relatives. The ability of the comparison method to successfully classify proteins into classes, superfamilies, folds, and families that are consistent with standard classification methods, both automated and human-driven, is demonstrated. Furthermore, it is shown that the scoring method allows for a fine-grained classification on the family, protein, and species level that agrees very well with currently established phylogenetic hierarchies. This fine classification is achieved without requiring visual inspection of proteins, sequence analysis, or the use of structural superimposition methods. Implications of the method for a fast, automated, topological hierarchical classification of proteins are discussed.     

Statistics of random protein superpositions: p-values for pairwise structure alignment.

Quantification of statistical significance is essential for the interpretation of protein structural similarity. To address this, a random model for protein structure comparison was developed. Novelty of the model is threefold. First, a sample of random structure comparisons is restricted to molecules of the same size and shape as the superposition of interest. Second, careful selection of the sample and accurate modeling of shape allows approximation of the root mean square deviation (RMSD) distribution of random comparisons with a Nakagami probability density function. Third, through convolution, a second probability density function is obtained that describes the coordinate difference vector projections underlying the random distribution of RMSD. This last feature allows sampling random distributions of not only RMSD, but also any similarity score that depends on difference vector projections, such as GDT_TS score, TM score, and LiveBench 3D score. Probabilities estimated from the method correlate well with common measures of structural similarity, such as the Dali Z-score and the GDT_TS score. As a result, the p-value for a given superposition can be calculated using simple formulae depending on RMSD, radius of gyration, and thinnest molecular dimension. In addition to scoring structural similarity, p-values computed by this method can be applied to evaluation of homology modeling techniques, providing a statistically sound alternative to scores used in reference-independent evaluation of alignment quality.     

Computational analysis of human protein interaction networks

Large amounts of human protein interaction data have been produced by experiments and prediction methods. However, the experimental coverage of the human interactome is still low in contrast to predicted data. To gain insight into the value of publicly available human protein network data, we compared predicted datasets, high-throughput results from yeast two-hybrid screens, and literature-curated protein-protein interactions. This evaluation is not only important for further methodological improvements, but also for increasing the confidence in functional hypotheses derived from predictions. Therefore, we assessed the quality and the potential bias of the different datasets using functional similarity based on the Gene Ontology, structural iPfam domain-domain interactions, likelihood ratios, and topological network parameters. This analysis revealed major differences between predicted datasets, but some of them also scored at least as high as the experimental ones regarding multiple quality measures. Therefore, since only small pair wise overlap between most datasets is observed, they may be combined to enlarge the available human interactome data. For this purpose, we additionally studied the influence of protein length on data quality and the number of disease proteins covered by each dataset. We could further demonstrate that protein interactions predicted by more than one method achieve an elevated reliability.     

Fast similarity search for protein 3D structures using topological pattern matching based on spatial relations

Similarity search for protein 3D structures become complex and computationally expensive due to the fact that the size of protein structure databases continues to grow tremendously. Recently, fast structural similarity search systems have been required to put them into practical use in protein structure classification whilst existing comparison systems do not provide comparison results on time. Our approach uses multi-step processing that composes of a preprocessing step to represent geometry of protein structures with spatial objects, a filter step to generate a small candidate set using approximate topological string matching, and a refinement step to compute a structural alignment. This paper describes the preprocessing and filtering for fast similarity search using the discovery of topological patterns of secondary structure elements based on spatial relations. Our system is fully implemented by using Oracle 8i spatial. We have previously shown that our approach has the advantage of speed of performance compared with other approach such as DALI. This work shows that the discovery of topological relations of secondary structure elements in protein structures by using spatial relations of spatial databases is practical for fast structural similarity search for proteins.     

New benchmark metrics for protein-protein docking methods

With the development of many computational methods that predict the structural models of protein-protein complexes, there is a pressing need to benchmark their performance. As was the case for protein monomers, assessing the quality of models of protein complexes is not straightforward. An effective scoring scheme should be able to detect substructure similarity and estimate its statistical significance. Here, we focus on characterizing the similarity of the interfaces of the complex and introduce two scoring functions. The first, the interfacial Template Modeling score (iTM-score), measures the geometric distance between the interfaces, while the second, the Interface Similarity score (IS-score), evaluates their residue-residue contact similarity in addition to their geometric similarity. We first demonstrate that the IS-score is more suitable for assessing docking models than the iTM-score. The IS-score is then validated in a large-scale benchmark test on 1562 dimeric complexes. Finally, the scoring function is applied to evaluate docking models submitted to the Critical Assessment of Prediction of Interactions (CAPRI) experiments. While the results according to the new scoring scheme are generally consistent with the original CAPRI assessment, the IS-score identifies models whose significance was previously underestimated.     

Secondary structure spatial conformation footprint: a novel method for fast protein structure comparison and classification

Background  

Recently a new class of methods for fast protein structure comparison has emerged. We call the methods in this class projection methods as they rely on a mapping of protein structure into a high-dimensional vector space. Once the mapping is done, the structure comparison is reduced to distance computation between corresponding vectors. As structural similarity is approximated by distance between projections, the success of any projection method depends on how well its mapping function is able to capture the salient features of protein structure. There is no agreement on what constitutes a good projection technique and the three currently known projection methods utilize very different approaches to the mapping construction, both in terms of what structural elements are included and how this information is integrated to produce a vector representation.     

Phyletic relationships of protein structures based on spatial preference of residues

Summary A structure-based scoring matrix MDPRE was derived from amino acid spatial preferences in protein structures. Sequence alignment and evolutionary studies by using MDPRE matrix gave similar results as those from ordinary sequence and structure alignments. It is interesting that a matrix derived from structure data solely could give comparable alignment results, strongly indicating the intimate connection between protein sequences and structures. The branch order and length from this approach were close to those obtained by a structure comparison method. Thus, by applying this structure-based matrix, the trees obtained should reflect evolutionary characteristics of protein structure. This approach takes advantage over a direct structure comparison in that (1) only a sequence and MDPRE matrix are needed, making it simple and widely applicable (especially in the absence of 3-dimensional protein structure data); (2) an established algorithm for sequence alignment and tree building could be employed, providing opportunities for direct comparison between matrices from different methodologies. One of the most striking features of this method is its capability to detect protein structure homologies when the sequence identities are low. This was well reflected in the given examples of the alignment of dinucleotidebinding domains.     

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.     

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.     

Prediction of Protein Function Improving Sequence Remote Alignment Search by a Fuzzy Logic Algorithm

The functional annotation of the new protein sequences represents a major drawback for genomic science. The best way to suggest the function of a protein from its sequence is by finding a related one for which biological information is available. Current alignment algorithms display a list of protein sequence stretches presenting significant similarity to different protein targets, ordered by their respective mathematical scores. However, statistical and biological significance do not always coincide, therefore, the rearrangement of the program output according to more biological characteristics than the mathematical scoring would help functional annotation. A new method that predicts the putative function for the protein integrating the results from the PSI-BLAST program and a fuzzy logic algorithm is described. Several protein sequence characteristics have been checked in their ability to rearrange a PSI-BLAST profile according more to their biological functions. Four of them: amino acid content, matched segment length and hydropathic and flexibility profiles positively contributed, upon being integrated by a fuzzy logic algorithm into a program, BYPASS, to the accurate prediction of the function of a protein from its sequence. Antonio Gómez and Juan Cedano contributed equally to this work.     

Structural relatedness via flow networks in protein sequence space

A novel approach for evaluation of sequence relatedness via a network over the sequence space is presented. This relatedness is quantified by graph theoretical techniques. The graph is perceived as a flow network, and flow algorithms are applied. The number of independent pathways between nodes in the network is shown to reflect structural similarity of corresponding protein fragments. These results provide an appropriate parameter for quantitative estimation of such relatedness, as well as reliability of the prediction. They also demonstrate a new potential for sequence analysis and comparison by means of the flow network in the sequence space.     

Assessing annotation transfer for genomics: quantifying the relations between protein sequence, structure and function through traditional and probabilistic scores

Measuring in a quantitative, statistical sense the degree to which structural and functional information can be "transferred" between pairs of related protein sequences at various levels of similarity is an essential prerequisite for robust genome annotation. To this end, we performed pairwise sequence, structure and function comparisons on approximately 30,000 pairs of protein domains with known structure and function. Our domain pairs, which are constructed according to the SCOP fold classification, range in similarity from just sharing a fold, to being nearly identical. Our results show that traditional scores for sequence and structure similarity have the same basic exponential relationship as observed previously, with structural divergence, measured in RMS, being exponentially related to sequence divergence, measured in percent identity. However, as the scale of our survey is much larger than any previous investigations, our results have greater statistical weight and precision. We have been able to express the relationship of sequence and structure similarity using more "modern scores," such as Smith-Waterman alignment scores and probabilistic P-values for both sequence and structure comparison. These modern scores address some of the problems with traditional scores, such as determining a conserved core and correcting for length dependency; they enable us to phrase the sequence-structure relationship in more precise and accurate terms. We found that the basic exponential sequence-structure relationship is very general: the same essential relationship is found in the different secondary-structure classes and is evident in all the scoring schemes. To relate function to sequence and structure we assigned various levels of functional similarity to the domain pairs, based on a simple functional classification scheme. This scheme was constructed by combining and augmenting annotations in the enzyme and fly functional classifications and comparing subsets of these to the Escherichia coli and yeast classifications. We found sigmoidal relationships between similarity in function and sequence, with clear thresholds for different levels of functional conservation. For pairs of domains that share the same fold, precise function appears to be conserved down to approximately 40 % sequence identity, whereas broad functional class is conserved to approximately 25 %. Interestingly, percent identity is more effective at quantifying functional conservation than the more modern scores (e.g. P-values). Results of all the pairwise comparisons and our combined functional classification scheme for protein structures can be accessed from a web database at http://bioinfo.mbb.yale.edu/alignCopyright 2000 Academic Press.     

Gene ontology improves template selection in comparative protein docking

Structural characterization of protein-protein interactions is essential for our ability to study life processes at the molecular level. Computational modeling of protein complexes (protein docking) is important as the source of their structure and as a way to understand the principles of protein interaction. Rapidly evolving comparative docking approaches utilize target/template similarity metrics, which are often based on the protein structure. Although the structural similarity, generally, yields good performance, other characteristics of the interacting proteins (eg, function, biological process, and localization) may improve the prediction quality, especially in the case of weak target/template structural similarity. For the ranking of a pool of models for each target, we tested scoring functions that quantify similarity of Gene Ontology (GO) terms assigned to target and template proteins in three ontology domains—biological process, molecular function, and cellular component (GO-score). The scoring functions were tested in docking of bound, unbound, and modeled proteins. The results indicate that the combined structural and GO-terms functions improve the scoring, especially in the twilight zone of structural similarity, typical for protein models of limited accuracy.     

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/.     

Pairwise local structural alignment of RNA sequences with sequence similarity less than 40%

MOTIVATION: Searching for non-coding RNA (ncRNA) genes and structural RNA elements (eleRNA) are major challenges in gene finding today as these often are conserved in structure rather than in sequence. Even though the number of available methods is growing, it is still of interest to pairwise detect two genes with low sequence similarity, where the genes are part of a larger genomic region. RESULTS: Here we present such an approach for pairwise local alignment which is based on foldalign and the Sankoff algorithm for simultaneous structural alignment of multiple sequences. We include the ability to conduct mutual scans of two sequences of arbitrary length while searching for common local structural motifs of some maximum length. This drastically reduces the complexity of the algorithm. The scoring scheme includes structural parameters corresponding to those available for free energy as well as for substitution matrices similar to RIBOSUM. The new foldalign implementation is tested on a dataset where the ncRNAs and eleRNAs have sequence similarity <40% and where the ncRNAs and eleRNAs are energetically indistinguishable from the surrounding genomic sequence context. The method is tested in two ways: (1) its ability to find the common structure between the genes only and (2) its ability to locate ncRNAs and eleRNAs in a genomic context. In case (1), it makes sense to compare with methods like Dynalign, and the performances are very similar, but foldalign is substantially faster. The structure prediction performance for a family is typically around 0.7 using Matthews correlation coefficient. In case (2), the algorithm is successful at locating RNA families with an average sensitivity of 0.8 and a positive predictive value of 0.9 using a BLAST-like hit selection scheme. AVAILABILITY: The program is available online at http://foldalign.kvl.dk/     

Combining evolutionary and structural information for local protein structure prediction

We study the effects of various factors in representing and combining evolutionary and structural information for local protein structural prediction based on fragment selection. We prepare databases of fragments from a set of non-redundant protein domains. For each fragment, evolutionary information is derived from homologous sequences and represented as estimated effective counts and frequencies of amino acids (evolutionary frequencies) at each position. Position-specific amino acid preferences called structural frequencies are derived from statistical analysis of discrete local structural environments in database structures. Our method for local structure prediction is based on ranking and selecting database fragments that are most similar to a target fragment. Using secondary structure type as a local structural property, we test our method in a number of settings. The major findings are: (1) the COMPASS-type scoring function for fragment similarity comparison gives better prediction accuracy than three other tested scoring functions for profile-profile comparison. We show that the COMPASS-type scoring function can be derived both in the probabilistic framework and in the framework of statistical potentials. (2) Using the evolutionary frequencies of database fragments gives better prediction accuracy than using structural frequencies. (3) Finer definition of local environments, such as including more side-chain solvent accessibility classes and considering the backbone conformations of neighboring residues, gives increasingly better prediction accuracy using structural frequencies. (4) Combining evolutionary and structural frequencies of database fragments, either in a linear fashion or using a pseudocount mixture formula, results in improvement of prediction accuracy. Combination at the log-odds score level is not as effective as combination at the frequency level. This suggests that there might be better ways of combining sequence and structural information than the commonly used linear combination of log-odds scores. Our method of fragment selection and frequency combination gives reasonable results of secondary structure prediction tested on 56 CASP5 targets (average SOV score 0.77), suggesting that it is a valid method for local protein structure prediction. Mixture of predicted structural frequencies and evolutionary frequencies improve the quality of local profile-to-profile alignment by COMPASS.     

Pure multiple RNA secondary structure alignments: a progressive profile approach

In functional, noncoding RNA, structure is often essential to function. While the full 3D structure is very difficult to determine, the 2D structure of an RNA molecule gives good clues to its 3D structure, and for molecules of moderate length, it can be predicted with good reliability. Structure comparison is, in analogy to sequence comparison, the essential technique to infer related function. We provide a method for computing multiple alignments of RNA secondary structures under the tree alignment model, which is suitable to cluster RNA molecules purely on the structural level, i.e., sequence similarity is not required. We give a systematic generalization of the profile alignment method from strings to trees and forests. We introduce a tree profile representation of RNA secondary structure alignments which allows reasonable scoring in structure comparison. Besides the technical aspects, an RNA profile is a useful data structure to represent multiple structures of RNA sequences. Moreover, we propose a visualization of RNA consensus structures that is enriched by the full sequence information.     

Validation of protein structure models using network similarity score

Accurate structural validation of proteins is of extreme importance in studies like protein structure prediction, analysis of molecular dynamic simulation trajectories and finding subtle changes in very similar structures. The benchmarks for today's structure validation are scoring methods like global distance test‐total structure (GDT‐TS), TM‐score and root mean square deviations (RMSD). However, there is a lack of methods that look at both the protein backbone and side‐chain structures at the global connectivity level and provide information about the differences in connectivity. To address this gap, a graph spectral based method (NSS—network similarity score) which has been recently developed to rigorously compare networks in diverse fields, is adopted to compare protein structures both at the backbone and at the side‐chain noncovalent connectivity levels. In this study, we validate the performance of NSS by investigating protein structures from X‐ray structures, modeling (including CASP models), and molecular dynamics simulations. Further, we systematically identify the local and the global regions of the structures contributing to the difference in NSS, through the components of the score, a feature unique to this spectral based scoring scheme. It is demonstrated that the method can quantify subtle differences in connectivity compared to a reference protein structure and can form a robust basis for protein structure comparison. Additionally, we have also introduced a network‐based method to analyze fluctuations in side chain interactions (edge‐weights) in an ensemble of structures, which can be an useful tool for the analysis of MD trajectories.     

Structural similarity to link sequence space: new potential superfamilies and implications for structural genomics

The current pace of structural biology now means that protein three-dimensional structure can be known before protein function, making methods for assigning homology via structure comparison of growing importance. Previous research has suggested that sequence similarity after structure-based alignment is one of the best discriminators of homology and often functional similarity. Here, we exploit this observation, together with a merger of protein structure and sequence databases, to predict distant homologous relationships. We use the Structural Classification of Proteins (SCOP) database to link sequence alignments from the SMART and Pfam databases. We thus provide new alignments that could not be constructed easily in the absence of known three-dimensional structures. We then extend the method of Murzin (1993b) to assign statistical significance to sequence identities found after structural alignment and thus suggest the best link between diverse sequence families. We find that several distantly related protein sequence families can be linked with confidence, showing the approach to be a means for inferring homologous relationships and thus possible functions when proteins are of known structure but of unknown function. The analysis also finds several new potential superfamilies, where inspection of the associated alignments and superimpositions reveals conservation of unusual structural features or co-location of conserved amino acids and bound substrates. We discuss implications for Structural Genomics initiatives and for improvements to sequence comparison methods.