Automated assignment of SCOP and CATH protein structure classifications from FSSP scores

Impact of structure space continuity on protein fold classification

Protein structure classification hierarchically clusters domain structures based on structure and/or sequence similarities and plays important roles in the study of protein structure-function relationship and protein evolution. Among many classifications, SCOP and CATH are widely viewed as the gold standards. Fold classification is of special interest because this is the lowest level of classification that does not depend on protein sequence similarity. The current fold classifications such as those in SCOP and CATH are controversial because they implicitly assume that folds are discrete islands in the structure space, whereas increasing evidence suggests significant similarities among folds and supports a continuous fold space. Although this problem is widely recognized, its impact on fold classification has not been quantitatively evaluated. Here we develop a likelihood method to classify a domain into the existing folds of CATH or SCOP using both query-fold structure similarities and within-fold structure heterogeneities. The new classification differs from the original classification for 3.4-12% of domains, depending on factors such as the structure similarity score and original classification scheme used. Because these factors differ for different biological purposes, our results indicate that the importance of considering structure space continuity in fold classification depends on the specific question asked.

Touring protein space with Matt

Using the Matt structure alignment program, we take a tour of protein space, producing a hierarchical clustering scheme that divides protein structural domains into clusters based on geometric dissimilarity. While it was known that purely structural, geometric, distance-based measures of structural similarity, such as Dali/FSSP, could largely replicate hand-curated schemes such as SCOP at the family level, it was an open question as to whether any such scheme could approximate SCOP at the more distant superfamily and fold levels. We partially answer this question in the affirmative, by designing a clustering scheme based on Matt that approximately matches SCOP at the superfamily level, and demonstrates qualitative differences in performance between Matt and DaliLite. Implications for the debate over the organization of protein fold space are discussed. Based on our clustering of protein space, we introduce the Mattbench benchmark set, a new collection of structural alignments useful for testing sequence aligners on more distantly homologous proteins.

DECISION TREE BASED INFORMATION INTEGRATION FOR AUTOMATED PROTEIN CLASSIFICATION

We propose a novel technique for automatically generating the SCOP classification of a protein structure with high accuracy. We achieve accurate classification by combining the decisions of multiple methods using the consensus of a committee (or an ensemble) classifier. Our technique, based on decision trees, is rooted in machine learning which shows that by judicially employing component classifiers, an ensemble classifier can be constructed to outperform its components. We use two sequence- and three structure-comparison tools as component classifiers. Given a protein structure and using the joint hypothesis, we first determine if the protein belongs to an existing category (family, superfamily, fold) in the SCOP hierarchy. For the proteins that are predicted as members of the existing categories, we compute their family-, superfamily-, andfold-level classifications using the consensus classifier. We show that we can significantly improve the classification accuracy compared to the individual component classifiers. In particular, we achieve error rates that are 3–12 times less than the individual classifiers' error rates at the family level, 1.5–4.5 times less at the superfamily level, and 1.1–2.4 times less at the fold level.

An Algebro-topological description of protein domain structure

The space of possible protein structures appears vast and continuous, and the relationship between primary, secondary and tertiary structure levels is complex. Protein structure comparison and classification is therefore a difficult but important task since structure is a determinant for molecular interaction and function. We introduce a novel mathematical abstraction based on geometric topology to describe protein domain structure. Using the locations of the backbone atoms and the hydrogen bonds, we build a combinatorial object – a so-called fatgraph. The description is discrete yet gives rise to a 2-dimensional mathematical surface. Thus, each protein domain corresponds to a particular mathematical surface with characteristic topological invariants, such as the genus (number of holes) and the number of boundary components. Both invariants are global fatgraph features reflecting the interconnectivity of the domain by hydrogen bonds. We introduce the notion of robust variables, that is variables that are robust towards minor changes in the structure/fatgraph, and show that the genus and the number of boundary components are robust. Further, we invesigate the distribution of different fatgraph variables and show how only four variables are capable of distinguishing different folds. We use local (secondary) and global (tertiary) fatgraph features to describe domain structures and illustrate that they are useful for classification of domains in CATH. In addition, we combine our method with two other methods thereby using primary, secondary, and tertiary structure information, and show that we can identify a large percentage of new and unclassified structures in CATH.

Fast and automated functional classification with MED-SuMo: an application on purine-binding proteins

Ligand-protein interactions are essential for biological processes, and precise characterization of protein binding sites is crucial to understand protein functions. MED-SuMo is a powerful technology to localize similar local regions on protein surfaces. Its heuristic is based on a 3D representation of macromolecules using specific surface chemical features associating chemical characteristics with geometrical properties. MED-SMA is an automated and fast method to classify binding sites. It is based on MED-SuMo technology, which builds a similarity graph, and it uses the Markov Clustering algorithm. Purine binding sites are well studied as drug targets. Here, purine binding sites of the Protein DataBank (PDB) are classified. Proteins potentially inhibited or activated through the same mechanism are gathered. Results are analyzed according to PROSITE annotations and to carefully refined functional annotations extracted from the PDB. As expected, binding sites associated with related mechanisms are gathered, for example, the Small GTPases. Nevertheless, protein kinases from different Kinome families are also found together, for example, Aurora-A and CDK2 proteins which are inhibited by the same drugs. Representative examples of different clusters are presented. The effectiveness of the MED-SMA approach is demonstrated as it gathers binding sites of proteins with similar structure-activity relationships. Moreover, an efficient new protocol associates structures absent of cocrystallized ligands to the purine clusters enabling those structures to be associated with a specific binding mechanism. Applications of this classification by binding mode similarity include target-based drug design and prediction of cross-reactivity and therefore potential toxic side effects.

The CATH database

The CATH database provides hierarchical classification of protein domains based on their folding patterns. Domains are obtained from protein structures deposited in the Protein Data Bank and both domain identification and subsequent classification use manual as well as automated procedures. The accompanying website http://www.cathdb.info provides an easy-to-use entry to the classification, allowing for both browsing and downloading of data. Here, we give a brief review of the database, its corresponding website and some related tools.

A structure-centric view of protein evolution, design, and adaptation

Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent in the indispensability of proteins for living cells is the fact that a given protein can adopt a specific three-dimensional shape that is specified solely by the protein's sequence of amino acids. Over the past several decades, structural biologists have demonstrated that the array of structures that proteins may adopt is quite astounding, and this has lead to a strong interest in understanding how protein structures change and evolve over time. In this review we consider a large body of recent work that attempts to illuminate this structure-centric picture of protein evolution. Much of this work has focused on the question of how completely new protein structures (i.e., new folds or topologies) are discovered by protein sequences as they evolve. Pursuant to this question of structural innovation has been a desire to describe and understand the observation that certain types of protein structures are far more abundant than others and how this uneven distribution of proteins implicates on the process through which new shapes are discovered. We consider a number of theoretical models that have been successful at explaining this heterogeneity in protein populations and discuss the increasing amount of evidence that indicates that the process of structural evolution involves the divergence of protein sequences and structures from one another. We also consider the topic of protein designability, which concerns itself with understanding how a protein's structure influences the number of sequences that can fold successfully into that structure. Understanding and quantifying the relationship between the physical feature of a structure and its designability has been a long-standing goal of the study of protein structure and evolution, and we discuss a number of recent advances that have yielded a promising answer to this question. Finally, we review the relatively new field of protein structural phylogeny, an area of study in which information about the distribution of protein structures among different organisms is used to reconstruct the evolutionary relationships between them. Taken together, the work that we review presents an increasingly coherent picture of how these unique polymers have evolved over the course of life on Earth.

Clustering algorithms for detecting functional modules in protein interaction networks

Protein-Protein Interaction (PPI) networks are believed to be important sources of information related to biological processes and complex metabolic functions of the cell. When studying the workings of a biological cell, it is useful to be able to detect known and predict still undiscovered protein complexes within the cell's PPI networks. Such predictions may be used as an inexpensive tool to direct biological experiments. The increasing amount of available PPI data necessitate a fast, accurate approach to biological complex identification. Because of its importance in the studies of protein interaction network, there are different models and algorithms in identifying functional modules in PPI networks. In this paper, we review some representative algorithms, focusing on the algorithms underlying the approaches and how the algorithms relate to each other. In particular, a comparison is given based on the property of the algorithms. Since the PPI network is noisy and still incomplete, some methods which consider other additional properties for preprocessing and purifying of PPI data are presented. We also give a discussion about the functional annotation and validation of protein complexes. Finally, new progress and future research directions are discussed from the computational viewpoint.

Cross-over between discrete and continuous protein structure space: insights into automatic classification and networks of protein structures

Structural classifications of proteins assume the existence of the fold, which is an intrinsic equivalence class of protein domains. Here, we test in which conditions such an equivalence class is compatible with objective similarity measures. We base our analysis on the transitive property of the equivalence relationship, requiring that similarity of A with B and B with C implies that A and C are also similar. Divergent gene evolution leads us to expect that the transitive property should approximately hold. However, if protein domains are a combination of recurrent short polypeptide fragments, as proposed by several authors, then similarity of partial fragments may violate the transitive property, favouring the continuous view of the protein structure space. We propose a measure to quantify the violations of the transitive property when a clustering algorithm joins elements into clusters, and we find out that such violations present a well defined and detectable cross-over point, from an approximately transitive regime at high structure similarity to a regime with large transitivity violations and large differences in length at low similarity. We argue that protein structure space is discrete and hierarchic classification is justified up to this cross-over point, whereas at lower similarities the structure space is continuous and it should be represented as a network. We have tested the qualitative behaviour of this measure, varying all the choices involved in the automatic classification procedure, i.e., domain decomposition, alignment algorithm, similarity score, and clustering algorithm, and we have found out that this behaviour is quite robust. The final classification depends on the chosen algorithms. We used the values of the clustering coefficient and the transitivity violations to select the optimal choices among those that we tested. Interestingly, this criterion also favours the agreement between automatic and expert classifications. As a domain set, we have selected a consensus set of 2,890 domains decomposed very similarly in SCOP and CATH. As an alignment algorithm, we used a global version of MAMMOTH developed in our group, which is both rapid and accurate. As a similarity measure, we used the size-normalized contact overlap, and as a clustering algorithm, we used average linkage. The resulting automatic classification at the cross-over point was more consistent than expert ones with respect to the structure similarity measure, with 86% of the clusters corresponding to subsets of either SCOP or CATH superfamilies and fewer than 5% containing domains in distinct folds according to both SCOP and CATH. Almost 15% of SCOP superfamilies and 10% of CATH superfamilies were split, consistent with the notion of fold change in protein evolution. These results were qualitatively robust for all choices that we tested, although we did not try to use alignment algorithms developed by other groups. Folds defined in SCOP and CATH would be completely joined in the regime of large transitivity violations where clustering is more arbitrary. Consistently, the agreement between SCOP and CATH at fold level was lower than their agreement with the automatic classification obtained using as a clustering algorithm, respectively, average linkage (for SCOP) or single linkage (for CATH). The networks representing significant evolutionary and structural relationships between clusters beyond the cross-over point may allow us to perform evolutionary, structural, or functional analyses beyond the limits of classification schemes. These networks and the underlying clusters are available at http://ub.cbm.uam.es/research/ProtNet.php

Making order of the fast-growing information on proteins is essential for gaining evolutionary and functional knowledge. The most successful approaches to this task are based on classifications of protein structures, such as SCOP and CATH, which assume a discrete view of the protein structure space as a collection of separated equivalence classes (folds). However, several authors proposed that protein domains should be regarded as assemblies of polypeptide fragments, which implies that the protein–structure space is continuous. Here, we assess these views of domain space through the concept of transitivity; i.e., we test whether structure similarity of A with B and B with C implies that A and C are similar, as required for consistent classification. We find that the domain space is approximately transitive and discrete at high similarity and continuous at low similarity, where transitivity is severely violated. Comparing our classification at the cross-over similarity with CATH and SCOP, we find that they join proteins at low similarity where classification is inconsistent. Part of this discrepancy is due to structural divergence of homologous domains, which are forced to be in a single cluster in CATH and SCOP. Structural and evolutionary relationships between consistent clusters are represented as a network in our approach, going beyond current protein classification schemes. We conjecture that our results are related to a change of evolutionary regime, from uniparental divergent evolution for highly related domains to assembly of large fragments for which the classical tree representation is unsuitable.

Towards an automatic classification of protein structural domains based on structural similarity

Background

Formal classification of a large collection of protein structures aids the understanding of evolutionary relationships among them. Classifications involving manual steps, such as SCOP and CATH, face the challenge of increasing volume of available structures. Automatic methods such as FSSP or Dali Domain Dictionary, yield divergent classifications, for reasons not yet fully investigated. One possible reason is that the pairwise similarity scores used in automatic classification do not adequately reflect the judgments made in manual classification. Another possibility is the difference between manual and automatic classification procedures. We explore the degree to which these two factors might affect the final classification.

Results

We use DALI, SHEBA and VAST pairwise scores on the SCOP C class domains, to investigate a variety of hierarchical clustering procedures. The constructed dendrogram is cut in a variety of ways to produce a partition, which is compared to the SCOP fold classification.

Ward's method dendrograms led to partitions closest to the SCOP fold classification. Dendrogram- or tree-cutting strategies fell into four categories according to the similarity of resulting partitions to the SCOP fold partition. Two strategies which optimize similarity to SCOP, gave an average of 72% true positives rate (TPR), at a 1% false positive rate. Cutting the largest size cluster at each step gave an average of 61% TPR which was one of the best strategies not making use of prior knowledge of SCOP. Cutting the longest branch at each step produced one of the worst strategies.

We also developed a method to detect irreducible differences between the best possible automatic partitions and SCOP, regardless of the cutting strategy. These differences are substantial. Visual examination of hard-to-classify proteins confirms our previous finding, that global structural similarity of domains is not the only criterion used in the SCOP classification.

Conclusion

Different clustering procedures give rise to different levels of agreement between automatic and manual protein classifications. None of the tested procedures completely eliminates the divergence between automatic and manual protein classifications. Achieving full agreement between these two approaches would apparently require additional information.

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.

Results

We propose a new linear encoding method, SARST (Structural similarity search Aided by Ramachandran Sequential Transformation). SARST transforms protein structures into text strings through a Ramachandran map organized by nearest-neighbor clustering and uses a regenerative approach to produce substitution matrices. Then, classical sequence similarity search methods can be applied to the structural similarity search. Its accuracy is similar to Combinatorial Extension (CE) and works over 243,000 times faster, searching 34,000 proteins in 0.34 sec with a 3.2-GHz CPU. SARST provides statistically meaningful expectation values to assess the retrieved information. It has been implemented into a web service and a stand-alone Java program that is able to run on many different platforms.

Conclusion

As a database search method, SARST can rapidly distinguish high from low similarities and efficiently retrieve homologous structures. It demonstrates that the easily accessible linear encoding methodology has the potential to serve as a foundation for efficient protein structural similarity search tools. These search tools are supposed applicable to automated and high-throughput functional annotations or predictions for the ever increasing number of published protein structures in this post-genomic era.

A framework for protein structure classification and identification of novel protein structures

Background

Protein structure classification plays a central role in understanding the function of a protein molecule with respect to all known proteins in a structure database. With the rapid increase in the number of new protein structures, the need for automated and accurate methods for protein classification is increasingly important.

Results

In this paper we present a unified framework for protein structure classification and identification of novel protein structures. The framework consists of a set of components for comparing, classifying, and clustering protein structures. These components allow us to accurately classify proteins into known folds, to detect new protein folds, and to provide a way of clustering the new folds. In our evaluation with SCOP 1.69, our method correctly classifies 86.0%, 87.7%, and 90.5% of new domains at family, superfamily, and fold levels. Furthermore, for protein domains that belong to new domain families, our method is able to produce clusters that closely correspond to the new families in SCOP 1.69. As a result, our method can also be used to suggest new classification groups that contain novel folds.

Conclusion

We have developed a method called proCC for automatically classifying and clustering domains. The method is effective in classifying new domains and suggesting new domain families, and it is also very efficient. A web site offering access to proCC is freely available at

Statistics of knots, geometry of conformations, and evolution of proteins

Like shoelaces, the backbones of proteins may get entangled and form knots. However, only a few knots in native proteins have been identified so far. To more quantitatively assess the rarity of knots in proteins, we make an explicit comparison between the knotting probabilities in native proteins and in random compact loops. We identify knots in proteins statistically, applying the mathematics of knot invariants to the loops obtained by complementing the protein backbone with an ensemble of random closures, and assigning a certain knot type to a given protein if and only if this knot dominates the closure statistics (which tells us that the knot is determined by the protein and not by a particular method of closure). We also examine the local fractal or geometrical properties of proteins via computational measurements of the end-to-end distance and the degree of interpenetration of its subchains. Although we did identify some rather complex knots, we show that native conformations of proteins have statistically fewer knots than random compact loops, and that the local geometrical properties, such as the crumpled character of the conformations at a certain range of scales, are consistent with the rarity of knots. From these, we may conclude that the known "protein universe" (set of native conformations) avoids knots. However, the precise reason for this is unknown--for instance, if knots were removed by evolution due to their unfavorable effect on protein folding or function or due to some other unidentified property of protein evolution.

ROC and confusion analysis of structure comparison methods identify the main causes of divergence from manual protein classification

Background

Current classification of protein folds are based, ultimately, on visual inspection of similarities. Previous attempts to use computerized structure comparison methods show only partial agreement with curated databases, but have failed to provide detailed statistical and structural analysis of the causes of these divergences.

Results

We construct a map of similarities/dissimilarities among manually defined protein folds, using a score cutoff value determined by means of the Receiver Operating Characteristics curve. It identifies folds which appear to overlap or to be "confused" with each other by two distinct similarity measures. It also identifies folds which appear inhomogeneous in that they contain apparently dissimilar domains, as measured by both similarity measures. At a low (1%) false positive rate, 25 to 38% of domain pairs in the same SCOP folds do not appear similar. Our results suggest either that some of these folds are defined using criteria other than purely structural consideration or that the similarity measures used do not recognize some relevant aspects of structural similarity in certain cases. Specifically, variations of the "common core" of some folds are severe enough to defeat attempts to automatically detect structural similarity and/or to lead to false detection of similarity between domains in distinct folds. Structures in some folds vary greatly in size because they contain varying numbers of a repeating unit, while similarity scores are quite sensitive to size differences. Structures in different folds may contain similar substructures, which produce false positives. Finally, the common core within a structure may be too small relative to the entire structure, to be recognized as the basis of similarity to another.

Conclusion

A detailed analysis of the entire available protein fold space by two automated similarity methods reveals the extent and the nature of the divergence between the automatically determined similarity/dissimilarity and the manual fold type classifications. Some of the observed divergences can probably be addressed with better structure comparison methods and better automatic, intelligent classification procedures. Others may be intrinsic to the problem, suggesting a continuous rather than discrete protein fold space.

Automated protein classification using consensus decision

We propose a novel technique for automatically generating the SCOP classification of a protein structure with high accuracy. High accuracy is achieved by combining the decisions of multiple methods using the consensus of a committee (or an ensemble) classifier. Our technique is rooted in machine learning which shows that by judicially employing component classifiers, an ensemble classifier can be constructed to outperform its components. We use two sequence- and three structure-comparison tools as component classifiers. Given a protein structure, using the joint hypothesis, we first determine if the protein belongs to an existing category (family, superfamily, fold) in the SCOP hierarchy. For the proteins that are predicted as members of the existing categories, we compute their family-, superfamily-, and fold-level classifications using the consensus classifier. We show that we can significantly improve the classification accuracy compared to the individual component classifiers. In particular, we achieve error rates that are 3-12 times less than the individual classifiers' error rates at the family level, 1.5-4.5 times less at the superfamily level, and 1.1-2.4 times less at the fold level.

Super paramagnetic clustering of protein sequences

Background

Detection of sequence homologues represents a challenging task that is important for the discovery of protein families and the reliable application of automatic annotation methods. The presence of domains in protein families of diverse function, inhomogeneity and different sizes of protein families create considerable difficulties for the application of published clustering methods.

Results

Our work analyses the Super Paramagnetic Clustering (SPC) and its extension, global SPC (gSPC) algorithm. These algorithms cluster input data based on a method that is analogous to the treatment of an inhomogeneous ferromagnet in physics. For the SwissProt and SCOP databases we show that the gSPC improves the specificity and sensitivity of clustering over the original SPC and Markov Cluster algorithm (TRIBE-MCL) up to 30%. The three algorithms provided similar results for the MIPS FunCat 1.3 annotation of four bacterial genomes, Bacillus subtilis, Helicobacter pylori, Listeria innocua and Listeria monocytogenes. However, the gSPC covered about 12% more sequences compared to the other methods. The SPC algorithm was programmed in house using C++ and it is available at . The FunCat annotation is available at .

Conclusion

The gSPC calculated to a higher accuracy or covered a larger number of sequences than the TRIBE-MCL algorithm. Thus it is a useful approach for automatic detection of protein families and unsupervised annotation of full genomes.

When proteome meets genome: the alpha helix and the beta strand of proteins are eschewed by mRNA splice junctions and may define the minimal indivisible modules of protein architecture

The significance of the intron-exon structure of genes is a mystery. As eukaryotic proteins are made up of modular functional domains, each exon was suspected to encode some form of module; however, the definition of a module remained vague. Comparison of pre-mRNA splice junctions with the three-dimensional architecture of its protein product from different eukaryotes revealed that the junctions were far less likely to occur inside the alpha-helices and beta-strands of proteins than within the more flexible linker regions ('turns' and 'loops') connecting them. The splice junctions were equally distributed in the different types of linkers and throughout the linker sequence, although a slight preference for the central region of the linker was observed. The avoidance of the alpha-helix and the beta-strand by splice junctions suggests the existence of a selection pressure against their disruption, perhaps underscoring the investment made by nature in building these intricate secondary structures. A corollary is that the helix and the strand are the smallest integral architectural units of a protein and represent the minimal modules in the evolution of protein structure. These results should find use in comparative genomics, designing of cloning strategies, and in the mutual verification of genome sequences with protein structures.

4SCOPmap: automated assignment of protein structures to evolutionary superfamilies

Background

Inference of remote homology between proteins is very challenging and remains a prerogative of an expert. Thus a significant drawback to the use of evolutionary-based protein structure classifications is the difficulty in assigning new proteins to unique positions in the classification scheme with automatic methods. To address this issue, we have developed an algorithm to map protein domains to an existing structural classification scheme and have applied it to the SCOP database.

Results

The general strategy employed by this algorithm is to combine the results of several existing sequence and structure comparison tools applied to a query protein of known structure in order to find the homologs already classified in SCOP database and thus determine classification assignments. The algorithm is able to map domains within newly solved structures to the appropriate SCOP superfamily level with ~95% accuracy. Examples of correctly mapped remote homologs are discussed. The algorithm is also capable of identifying potential evolutionary relationships not specified in the SCOP database, thus helping to make it better. The strategy of the mapping algorithm is not limited to SCOP and can be applied to any other evolutionary-based classification scheme as well. SCOPmap is available for download.

Conclusion

The SCOPmap program is useful for assigning domains in newly solved structures to appropriate superfamilies and for identifying evolutionary links between different superfamilies.

A consensus view of fold space: combining SCOP, CATH, and the Dali Domain Dictionary

We have determined consensus protein-fold classifications on the basis of three classification methods, SCOP, CATH, and Dali. These classifications make use of different methods of defining and categorizing protein folds that lead to different views of protein-fold space. Pairwise comparisons of domains on the basis of their fold classifications show that much of the disagreement between the classification systems is due to differing domain definitions rather than assigning the same domain to different folds. However, there are significant differences in the fold assignments between the three systems. These remaining differences can be explained primarily in terms of the breadth of the fold classifications. Many structures may be defined as having one fold in one system, whereas far fewer are defined as having the analogous fold in another system. By comparing these folds for a nonredundant set of proteins, the consensus method breaks up broad fold classifications and combines restrictive fold classifications into metafolds, creating, in effect, an averaged view of fold space. This averaged view requires that the structural similarities between proteins having the same metafold be recognized by multiple classification systems. Thus, the consensus map is useful for researchers looking for fold similarities that are relatively independent of the method used to compare proteins. The 30 most populated metafolds, representing the folds of about half of a nonredundant subset of the PDB, are presented here. The full list of metafolds is presented on the Web.

Quantifying structure-function uncertainty: a graph theoretical exploration into the origins and limitations of protein annotation

Since the advent of investigations into structural genomics, research has focused on correctly identifying domain boundaries, as well as domain similarities and differences in the context of their evolutionary relationships. As the science of structural genomics ramps up adding more and more information into the databanks, questions about the accuracy and completeness of our classification and annotation systems appear on the forefront of this research. A central question of paramount importance is how structural similarity relates to functional similarity. Here, we begin to rigorously and quantitatively answer these questions by first exploring the consensus between the most common protein domain structure annotation databases CATH, SCOP and FSSP. Each of these databases explores the evolutionary relationships between protein domains using a combination of automatic and manual, structural and functional, continuous and discrete similarity measures. In order to examine the issue of consensus thoroughly, we build a generalized graph out of each of these databases and hierarchically cluster these graphs at interval thresholds. We then employ a distance measure to find regions of greatest overlap. Using this procedure we were able not only to enumerate the level of consensus between the different annotation systems, but also to define the graph-theoretical origins behind the annotation schema of class, family and superfamily by observing that the same thresholds that define the best consensus regions between FSSP, SCOP and CATH correspond to distinct, non-random phase-transitions in the structure comparison graph itself. To investigate the correspondence in divergence between structure and function further, we introduce a measure of functional entropy that calculates divergence in function space. First, we use this measure to calculate the general correlation between structural homology and functional proximity. We extend this analysis further by quantitatively calculating the average amount of functional information gained from our understanding of structural distance and the corollary inherent uncertainty that represents the theoretical limit of our ability to infer function from structural similarity. Finally we show how our measure of functional "entropy" translates into a more intuitive concept of functional annotation into similarity EC classes.

Computing a New Family of Shape Descriptors for Protein Structures

The large-scale 3D structure of a protein can be represented by the polygonal curve through the carbon alpha atoms of the protein backbone. We introduce an algorithm for computing the average number of times that a given configuration of crossings on such polygonal curves is seen, the average being taken over all directions in space. Hereby, we introduce a new family of global geometric measures of protein structures, which we compare with the so-called generalized Gauss integrals.

Protein complexes and functional modules in molecular networks

Proteins, nucleic acids, and small molecules form a dense network of molecular interactions in a cell. Molecules are nodes of this network, and the interactions between them are edges. The architecture of molecular networks can reveal important principles of cellular organization and function, similarly to the way that protein structure tells us about the function and organization of a protein. Computational analysis of molecular networks has been primarily concerned with node degree [Wagner, A. & Fell, D. A. (2001) Proc. R. Soc. London Ser. B 268, 1803-1810; Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N. & Barabasi, A. L. (2000) Nature 407, 651-654] or degree correlation [Maslov, S. & Sneppen, K. (2002) Science 296, 910-913], and hence focused on single/two-body properties of these networks. Here, by analyzing the multibody structure of the network of protein-protein interactions, we discovered molecular modules that are densely connected within themselves but sparsely connected with the rest of the network. Comparison with experimental data and functional annotation of genes showed two types of modules: (i) protein complexes (splicing machinery, transcription factors, etc.) and (ii) dynamic functional units (signaling cascades, cell-cycle regulation, etc.). Discovered modules are highly statistically significant, as is evident from comparison with random graphs, and are robust to noise in the data. Our results provide strong support for the network modularity principle introduced by Hartwell et al. [Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. (1999) Nature 402, C47-C52], suggesting that found modules constitute the "building blocks" of molecular networks.

Expanding protein universe and its origin from the biological Big Bang

The bottom-up approach to understanding the evolution of organisms is by studying molecular evolution. With the large number of protein structures identified in the past decades, we have discovered peculiar patterns that nature imprints on protein structural space in the course of evolution. In particular, we have discovered that the universe of protein structures is organized hierarchically into a scale-free network. By understanding the cause of these patterns, we attempt to glance at the very origin of life.