Pattern matching and pattern discovery algorithms for protein topologies

We describe algorithms for pattern matching and pattern learning in TOPS diagrams (formal descriptions of protein topologies). These problems can be reduced to checking for subgraph isomorphism and finding maximal common subgraphs in a restricted class of ordered graphs. We have developed a subgraph isomorphism algorithm for ordered graphs, which performs well on the given set of data. The maximal common subgraph problem then is solved by repeated subgraph extension and checking for isomorphisms. Despite the apparent inefficiency such approach gives an algorithm with time complexity proportional to the number of graphs in the input set and is still practical on the given set of data. As a result we obtain fast methods which can be used for building a database of protein topological motifs, and for the comparison of a given protein of known secondary structure against a motif database

An optimized TOPS+ comparison method for enhanced TOPS models

This article has been made available through the Brunel Open Access Publishing Fund.Background Although methods based on highly abstract descriptions of protein structures, such as VAST and TOPS, can perform very fast protein structure comparison, the results can lack a high degree of biological significance. Previously we have discussed the basic mechanisms of our novel method for structure comparison based on our TOPS+ model (Topological descriptions of Protein Structures Enhanced with Ligand Information). In this paper we show how these results can be significantly improved using parameter optimization, and we call the resulting optimised TOPS+ method as advanced TOPS+ comparison method i.e. advTOPS+. Results We have developed a TOPS+ string model as an improvement to the TOPS [1-3] graph model by considering loops as secondary structure elements (SSEs) in addition to helices and strands, representing ligands as first class objects, and describing interactions between SSEs, and SSEs and ligands, by incoming and outgoing arcs, annotating SSEs with the interaction direction and type. Benchmarking results of an all-against-all pairwise comparison using a large dataset of 2,620 non-redundant structures from the PDB40 dataset [4] demonstrate the biological significance, in terms of SCOP classification at the superfamily level, of our TOPS+ comparison method. Conclusions Our advanced TOPS+ comparison shows better performance on the PDB40 dataset [4] compared to our basic TOPS+ method, giving 90 percent accuracy for SCOP alpha+beta; a 6 percent increase in accuracy compared to the TOPS and basic TOPS+ methods. It also outperforms the TOPS, basic TOPS+ and SSAP comparison methods on the Chew-Kedem dataset [5], achieving 98 percent accuracy. Software Availability: The TOPS+ comparison server is available at http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/.This article is available through the Brunel Open Access Publishing Fun

Graph theoretic methods for the analysis of structural relationships in biological macromolecules

Subgraph isomorphism and maximum common subgraph isomorphism algorithms from graph theory provide an effective and an efficient way of identifying structural relationships between biological macromolecules. They thus provide a natural complement to the pattern matching algorithms that are used in bioinformatics to identify sequence relationships. Examples are provided of the use of graph theory to analyze proteins for which three-dimensional crystallographic or NMR structures are available, focusing on the use of the Bron-Kerbosch clique detection algorithm to identify common folding motifs and of the Ullmann subgraph isomorphism algorithm to identify patterns of amino acid residues. Our methods are also applicable to other types of biological macromolecule, such as carbohydrate and nucleic acid structures

Risk-Averse Matchings over Uncertain Graph Databases

A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an uncertain, weighted (hyper)graph, how can we efficiently find a (hyper)matching with high expected reward, and low risk? This problem naturally arises in the context of several important applications, such as online dating, kidney exchanges, and team formation. We introduce a novel formulation for finding matchings with maximum expected reward and bounded risk under a general model of uncertain weighted (hyper)graphs that we introduce in this work. Our model generalizes probabilistic models used in prior work, and captures both continuous and discrete probability distributions, thus allowing to handle privacy related applications that inject appropriately distributed noise to (hyper)edge weights. Given that our optimization problem is NP-hard, we turn our attention to designing efficient approximation algorithms. For the case of uncertain weighted graphs, we provide a $\frac{1}{3}$-approximation algorithm, and a $\frac{1}{5}$-approximation algorithm with near optimal run time. For the case of uncertain weighted hypergraphs, we provide a $\Omega(\frac{1}{k})$-approximation algorithm, where $k$ is the rank of the hypergraph (i.e., any hyperedge includes at most $k$ nodes), that runs in almost (modulo log factors) linear time. We complement our theoretical results by testing our approximation algorithms on a wide variety of synthetic experiments, where we observe in a controlled setting interesting findings on the trade-off between reward, and risk. We also provide an application of our formulation for providing recommendations of teams that are likely to collaborate, and have high impact.Comment: 25 page

A data science approach to pattern discovery in complex structures with applications in bioinformatics

Pattern discovery aims to find interesting, non-trivial, implicit, previously unknown and potentially useful patterns in data. This dissertation presents a data science approach for discovering patterns or motifs from complex structures, particularly complex RNA structures. RNA secondary and tertiary structure motifs are very important in biological molecules, which play multiple vital roles in cells. A lot of work has been done on RNA motif annotation. However, pattern discovery in RNA structure is less studied. In the first part of this dissertation, an ab initio algorithm, named DiscoverR, is introduced for pattern discovery in RNA secondary structures. This algorithm works by representing RNA secondary structures as ordered labeled trees and performs tree pattern discovery using a quadratic time dynamic programming algorithm. The algorithm is able to identify and extract the largest common substructures from two RNA molecules of different sizes, without prior knowledge of locations and topologies of these substructures. One application of DiscoverR is to locate the RNA structural elements in genomes. Experimental results show that this tool complements the currently used approaches for mining conserved structural RNAs in the human genome. DiscoverR can also be extended to find repeated regions in an RNA secondary structure. Specifically, this extended method is used to detect structural repeats in the 3\u27-untranslated region of a protein kinase gene

Data-driven network alignment

Biological network alignment (NA) aims to find a node mapping between species' molecular networks that uncovers similar network regions, thus allowing for transfer of functional knowledge between the aligned nodes. However, current NA methods do not end up aligning functionally related nodes. A likely reason is that they assume it is topologically similar nodes that are functionally related. However, we show that this assumption does not hold well. So, a paradigm shift is needed with how the NA problem is approached. We redefine NA as a data-driven framework, TARA (daTA-dRiven network Alignment), which attempts to learn the relationship between topological relatedness and functional relatedness without assuming that topological relatedness corresponds to topological similarity, like traditional NA methods do. TARA trains a classifier to predict whether two nodes from different networks are functionally related based on their network topological patterns. We find that TARA is able to make accurate predictions. TARA then takes each pair of nodes that are predicted as related to be part of an alignment. Like traditional NA methods, TARA uses this alignment for the across-species transfer of functional knowledge. Clearly, TARA as currently implemented uses topological but not protein sequence information for this task. We find that TARA outperforms existing state-of-the-art NA methods that also use topological information, WAVE and SANA, and even outperforms or complements a state-of-the-art NA method that uses both topological and sequence information, PrimAlign. Hence, adding sequence information to TARA, which is our future work, is likely to further improve its performance

TOPS++FATCAT: Fast flexible structural alignment using constraints derived from TOPS+ Strings Model

<p>Abstract</p> <p>Background</p> <p>Protein structure analysis and comparison are major challenges in structural bioinformatics. Despite the existence of many tools and algorithms, very few of them have managed to capture the intuitive understanding of protein structures developed in structural biology, especially in the context of rapid database searches. Such intuitions could help speed up similarity searches and make it easier to understand the results of such analyses.</p> <p>Results</p> <p>We developed a TOPS++FATCAT algorithm that uses an intuitive description of the proteins' structures as captured in the popular TOPS diagrams to limit the search space of the aligned fragment pairs (AFPs) in the flexible alignment of protein structures performed by the FATCAT algorithm. The TOPS++FATCAT algorithm is faster than FATCAT by more than an order of magnitude with a minimal cost in classification and alignment accuracy. For beta-rich proteins its accuracy is better than FATCAT, because the TOPS+ strings models contains important information of the parallel and anti-parallel hydrogen-bond patterns between the beta-strand SSEs (Secondary Structural Elements). We show that the TOPS++FATCAT errors, rare as they are, can be clearly linked to oversimplifications of the TOPS diagrams and can be corrected by the development of more precise secondary structure element definitions.</p> <p>Software Availability</p> <p>The benchmark analysis results and the compressed archive of the TOPS++FATCAT program for Linux platform can be downloaded from the following web site: <url>http://fatcat.burnham.org/TOPS/</url></p> <p>Conclusion</p> <p>TOPS++FATCAT provides FATCAT accuracy and insights into protein structural changes at a speed comparable to sequence alignments, opening up a possibility of interactive protein structure similarity searches.</p