Pattern discovery in trees : algorithms and applications to document and scientific data management

Ordered, labeled trees are trees in which each node has a label and the left-to-right order of its children (if it has any) is fixed. Such trees have many applications in vision, pattern recognition, molecular biology and natural language processing. In this dissertation we present algorithms for finding patterns in the ordered labeled trees. Specifically we study the largest approximately common substructure (LACS) problem for such trees. We consider a substructure of a tree T to be a connected subgraph of T. Given two trees T1, T2 and an integer d, the LACS problem is to find a substructure U1 of T1 and a substructure U2 of T2 such that U1 is within distance d of U2 and where there does not exist any other substructure V1 of T1 and V2 of T2 such that V1 and V2 satisfy the distance constraint and the sum of the sizes of V1 and V2 is greater than the sum of the sizes of U1 and U2. The LACS problem is motivated by the studies of document and RNA comparison. We consider two types of distance measures: the general edit distance and a restricted edit distance originated from Selkow. We present dynamic programming algorithms to solve the LACS problem based on the two distance measures. The algorithms run as fast as the best known algorithms for computing the distance of two trees when the distance allowed in the common substructures is a constant independent of the input trees. To demonstrate the utility of our algorithms, we discuss their applications to discovering motifs in multiple RNA secondary structures. Such an application shows an example of scientific data mining. We represent an RNA secondary structure by an ordered labeled tree based on a previously proposed scheme. The patterns in the trees are substructures that can differ in both substitutions and deletions/insertions of nodes of the trees. Our techniques incorporate approximate tree matching algorithms and novel heuristics for discovery and optimization. Experimental results obtained by running these algorithms on both generated data and RNA secondary structures show the good performance of the algorithms. It is shown that the optimization heuristics speed up the discovery algorithm by a factor of 10. Moreover, our optimized approach is 100,000 times faster than the brute force method. Finally we implement our techniques into a graphic toolbox that enables users to find repeated substructures in an RNA secondary structure as well as frequently occurring patterns in multiple RNA secondary structures pertaining to rhinovirus obtained from the National Cancer Institute. The system is implemented in C programming language and X windows and is fully operational on SUN workstations

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

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

Multiple structural alignment for distantly related all b structures using TOPS pattern discovery and simulated annealing

Topsalign is a method that will structurally align diverse protein structures, for example, structural alignment of protein superfolds. All proteins within a superfold share the same fold but often have very low sequence identity and different biological and biochemical functions. There is often signi®cant structural diversity around the common scaffold of secondary structure elements of the fold. Topsalign uses topological descriptions of proteins. A pattern discovery algorithm identi®es equivalent secondary structure elements between a set of proteins and these are used to produce an initial multiple structure alignment. Simulated annealing is used to optimize the alignment. The output of Topsalign is a multiple structure-based sequence alignment and a 3D superposition of the structures. This method has been tested on three superfolds: the b jelly roll, TIM (a/b) barrel and the OB fold. Topsalign outperforms established methods on very diverse structures. Despite the pattern discovery working only on b strand secondary structure elements, Topsalign is shown to align TIM (a/b) barrel superfamilies, which contain both a helices and b strands

A new procedure to analyze RNA non-branching structures

RNA structure prediction and structural motifs analysis are challenging tasks in the investigation of RNA function. We propose a novel procedure to detect structural motifs shared between two RNAs (a reference and a target). In particular, we developed two core modules: (i) nbRSSP_extractor, to assign a unique structure to the reference RNA encoded by a set of non-branching structures; (ii) SSD_finder, to detect structural motifs that the target RNA shares with the reference, by means of a new score function that rewards the relative distance of the target non-branching structures compared to the reference ones. We integrated these algorithms with already existing software to reach a coherent pipeline able to perform the following two main tasks: prediction of RNA structures (integration of RNALfold and nbRSSP_extractor) and search for chains of matches (integration of Structator and SSD_finder)

Time Series Data Mining Algorithms for Identifying Short RNA in Arabidopsis thaliana

The class of molecules called short RNAs (sRNAs) are known to play a key role in gene regulation. Th are typically sequences of nucleotides between 21-25 nucleotides in length. They are known to play a key role in gene regulation. The identification, clustering and classification of sRNA has recently become the focus of much research activity. The basic problem involves detecting regions of interest on the chromosome where the pattern of candidate matches is somehow unusual. Currently, there are no published algorithms for detecting regions of interest, and the unpublished methods that we are aware of involve bespoke rule based systems designed for a specific organism. Work in this very new field has understandably focused on the outcomes rather than the methods used to obtain the results. In this paper we propose two generic approaches that place the specific biological problem in the wider context of time series data mining problems. Both methods are based on treating the occurrences on a chromosome, or “hit count” data, as a time series, then running a sliding window along a chromosome and measuring unusualness. This formulation means we can treat finding unusual areas of candidate RNA activity as a variety of time series anomaly detection problem. The first set of approaches is model based. We specify a null hypothesis distribution for not being a sRNA, then estimate the p-values along the chromosome. The second approach is instance based. We identify some typical shapes from known sRNA, then use dynamic time warping and fourier trans-form based distance to measure how closely the candidate series matches. We demonstrate that these methods can find known sRNA on Arabidopsis thaliana chromosomes and illustrate the benefits of the added information provided by these algorithms

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

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