Fast motif recognition via application of statistical thresholds

Background: Improving the accuracy and efficiency of motif recognition is an important computational challenge that has application to detecting transcription factor binding sites in genomic data. Closely related to motif recognition is the Consensus String decision problem that asks, given a parameter d and a set of ℓ-length strings S = {s1,...,sn}, whether there exists a consensus string that has Hamming distance at most d from any string in S. A set of strings S is pairwise bounded if the Hamming distance between any pair of strings in S is at most 2d. It is trivial to determine whether a set is pairwise bounded, and a set cannot have a consensus string unless it is pairwise bounded. We use Consensus String to determine whether or not a pairwise bounded set has a consensus. Unfortunately, Consensus String is NP-complete. The lack of an efficient method to solve the Consensus String problem has caused it to become a computational bottleneck in MCL-WMR, a motif recognition program capable of solving difficult motif recognition problem instances. Results: We focus on the development of a method for solving Consensus String quickly with a small probability of error. We apply this heuristic to develop a new motif recognition program, sMCL-WMR, which has impressive accuracy and efficiency. We demonstrate the performance of sMCL-WMR in detecting weak motifs in large data sets and in real genomic data sets, and compare the performance to other leading motif recognitio

Detection of subtle variations as consensus motifs

AbstractWe address the problem of detecting consensus motifs, that occur with subtle variations, across multiple sequences. These are usually functional domains in DNA sequences such as transcriptional binding factors or other regulatory sites. The problem in its generality has been considered difficult and various benchmark data serve as the litmus test for different computational methods. We present a method centered around unsupervised combinatorial pattern discovery. The parameters are chosen using a careful statistical analysis of consensus motifs. This method works well on the benchmark data and is general enough to be extended to a scenario where the variation in the consensus motif includes indels (along with mutations). We also present some results on detection of transcription binding factors in human DNA sequences

A Novel Tree Structure for Pattern Matching in Biological Sequences

This dissertation proposes a novel tree structure, Error Tree (ET), to more efficiently solve the Approximate Pattern Matching problem, a fundamental problem in bioinformatics and information retrieval. The problem involves different matching measures such as the Hamming distance, edit distance, and wildcard matching. The input is usually a text of length n over a fixed alphabet of size Σ, a pattern P of length m, and an integer k. The output is those subsequences in the text that are at a distance ≤ k from P by Hamming distance, edit distance, or wildcard matching. An immediate application of the approximate pattern matching is the Planted Motif Search, an important problem in many biological applications such as finding promoters, enhancers, locus control regions, transcription factors, etc. The (l, d)-Planted Motif Search is defined as the following: Given n sequences over an alphabet of size Σ, each of length m, and two integers l and d, find a motif M of length l, where in each sequence there is at least an l-mer (substring of length l) at a Hamming distance of ≤ d from M. Based on the ET structure, our algorithm ET-Motif solves this problem efficiently in time and space. The thesis also discusses how the ET structure may add efficiency when it comes to Genome Assembly and DNA Sequence Compression. Current high-throughput sequencing technologies generate millions or billions of short reads (100-1000 bases) that are sequenced from a genome of millions or billions bases long. The De novo Genome Assembly problem is to assemble the original genome as long and accurate as possible. Although high quality assemblies can be obtained by assembling multiple paired-end libraries with both short and long insert sizes, the latter is costly to generate. Moreover, the recent GAGE-B study showed that a remarkably good assembly quality can be obtained for bacterial genomes by state-of-the-art assemblers run on a single short-insert library with a very high coverage. This thesis introduces a novel Hierarchical Genome Assembly (HGA) method that takes further advantage of such high coverage by independently assembling disjoint subsets of reads, combining assemblies of the subsets, and finally re-assembling the combined contigs along with the original reads. We empirically evaluate this methodology for eight leading assemblers using seven GAGE-B bacterial datasets consisting of 100bp Illumina HiSeq and 250bp Illumina MiSeq reads with coverage ranging from 100x-∼200x. The results show that HGA leads to a significant improvement in the quality of the assembly for all evaluated assemblers and datasets. Still, the problem involves a major step which is overlapping the ends of the reads together and allowing few mismatches (i.e. the approximate matching problem). This requires computing the overlaps between the ends of all-against-all reads. The computation of such overlaps when allowing mismatches is intensive. The ET structure may further speed up this step. Lastly, due to the significant amount of DNA data generated by the Next- Generation-Sequencing machines, there is an increasing need to compress such data to reduce the storage space and transmission time. The Huffman encoding that incorporates DNA sequence characteristics proves to better compress DNA data. Different implementations of Huffman trees, centering on the selection of frequent repeats, are introduced in this thesis. Experimental results demonstrate improvement on the compression ratios for five genomes with lengths ranging from 5Mbp to 50Mbp, compared with the use of a standard Huffman tree algorithm. Hence, the thesis suggests an improvement on all DNA sequence compression algorithms that employ the conventional Huffman encoding. Moreover, approximate repeats can be compressed and further improve the results by encoding the Hamming or edit distance between these repeats. However, computing such distances requires additional costs in both time and space. These costs can be reduced by using the ET structure

Identifying and Disentangling Interleaved Activities of Daily Living from Sensor Data

Activity discovery (AD) refers to the unsupervised extraction of structured activity data from a stream of sensor readings in a real-world or virtual environment. Activity discovery is part of the broader topic of activity recognition, which has potential uses in fields as varied as social work and elder care, psychology and intrusion detection. Since activity recognition datasets are both hard to come by, and very time consuming to label, the development of reliable activity discovery systems could be of significant utility to the researchers and developers working in the field, as well as to the wider machine learning community. This thesis focuses on the investigation of activity discovery systems that can deal with interleaving, which refers to the phenomenon of continuous switching between multiple high-level activities over a short period of time. This is a common characteristic of the real-world datastreams that activity discovery systems have to deal with, but it is one that is unfortunately often left unaddressed in the existing literature. As part of the research presented in this thesis, the fact that activities exist at multiple levels of abstraction is highlighted. A single activity is often a constituent element of a larger, more complex activity, and in turn has constituents of its own that are activities. Thus this investigation necessarily considers activity discovery systems that can find these hierarchies. The primary contribution of this thesis is the development and evaluation of an activity discovery system that is capable of identifying interleaved activities in sequential data. Starting from a baseline system implemented using a topic model, novel approaches are proposed making use of modern language models taken from the field of natural language processing, before moving on to more advanced language modelling that can handle complex, interleaved data. As well as the identification of activities, the thesis also proposes the abstraction of activities into larger, more complex activities. This allows for the construction of hierarchies of activities that more closely reflect the complex inherent structure of activities present in real-world datasets compared to other approaches. The thesis also discusses a number of important issues relating to the evaluation of activity discovery systems, and examines how existing evaluation metrics may at times be misleading. This includes highlighting the existence of differing abstraction issues in activity discovery evaluation, and suggestions for how this problem can be mitigated. Finally, alternative evaluation metrics are investigated. Naturally, this dissertation does not fully solve the problem of activity discovery, and work remains to be done. However, a number of the most pressing issues that affect real-world activity discovery systems are tackled head-on, and show that useful progress can indeed be made on them. This work aims to benefit systems that are as “clean slate as possible, and hence incorporate no domain-specific knowledge. This is perhaps somewhat of an artificial handicap to impose in this problem domain, but it does have the advantage of making this work applicable to as broad a range of domains as possible

Exploring RNA and protein 3D structures by geometric algorithms

Many problems in RNA and protein structures are related with their specific geometric properties. Geometric algorithms can be used to explore the possible solutions of these problems. This dissertation investigates the geometric properties of RNA and protein structures and explores three different ways that geometric algorithms can help to the study of the structures. Determine accurate structures. Accurate details in RNA structures are important for understanding RNA function, but the backbone conformation is difficult to determine and most existing RNA structures show serious steric clashes (greater than or equal to 0.4 A overlap). I developed a program called RNABC (RNA Backbone Correction) that searches for alternative clash-free conformations with acceptable geometry. It rebuilds a suite (unit from sugar to sugar) by anchoring phosphorus and base positions, which are clearest in crystallographic electron density, and reconstructing other atoms using forward kinematics and conjugate gradient methods. Two tests show that RNABC improves backbone conformations for most problem suites in S-motifs and for many of the worst problem suites identified by members of the Richardson lab. Display structure commonalities. Structure alignment commonly uses root mean squared distance (RMSD) to measure the structural similarity. I first extend RMSD to weighted RMSD (wRMSD) for multiple structures and show that using wRMSD with multiplicative weights implies the average is a consensus structure. Although I show that finding the optimal translations and rotations for minimizing wRMSD cannot be decoupled for multiple structures, I develop a near-linear iterative algorithm to converge to a local minimum of wRMSD. Finally I propose a heuristic algorithm to iteratively reassign weights to reduce the effect of outliers and find well-aligned positions that determine structurally conserved regions. Distinguish local structural features. Identifying common motifs (fragments of structures common to a group of molecules) is one way to further our understanding of the structure and function of molecules. I apply a graph database mining technique to identify RNA tertiary motifs. I abstract RNA molecules as labeled graphs, use a frequent subgraph mining algorithm to derive tertiary motifs, and present an iterative structure alignment algorithm to classify tertiary motifs and generate consensus motifs. Tests on ribosomal and transfer RNA families show that this method can identify most known RNA tertiary motifs in these families and suggest candidates for novel tertiary motifs

Combinatorial and Probabilistic Approaches to Motif Recognition

Short substrings of genomic data that are responsible for biological processes, such as gene expression, are referred to as motifs. Motifs with the same function may not entirely match, due to mutation events at a few of the motif positions. Allowing for non-exact occurrences significantly complicates their discovery. Given a number of DNA strings, the motif recognition problem is the task of detecting motif instances in every given sequence without knowledge of the position of the instances or the pattern shared by these substrings. We describe a novel approach to motif recognition, and provide theoretical and experimental results that demonstrate its efficiency and accuracy. Our algorithm, MCL-WMR, builds an edge-weighted graph model of the given motif recognition problem and uses a graph clustering algorithm to quickly determine important subgraphs that need to be searched further for valid motifs. By considering a weighted graph model, we narrow the search dramatically to smaller problems that can be solved with significantly less computation. The Closest String problem is a subproblem of motif recognition, and it is NP-hard. We give a linear-time algorithm for a restricted version of the Closest String problem, and an efficient polynomial-time heuristic that solves the general problem with high probability. We initiate the study of the smoothed complexity of the Closest String problem, which in turn explains our empirical results that demonstrate the great capability of our probabilistic heuristic. Important to this analysis is the introduction of a perturbation model of the Closest String instances within which we provide a probabilistic analysis of our algorithm. The smoothed analysis suggests reasons why a well-known fixed parameter tractable algorithm solves Closest String instances extremely efficiently in practice. Although the Closest String model is robust to the oversampling of strings in the input, it is severely affected by the existence of outliers. We propose a refined model, the Closest String with Outliers problem, to overcome this limitation. A systematic parameterized complexity analysis accompanies the introduction of this problem, providing a surprising insight into the sensitivity of this problem to slightly different parameterizations. Through the application of probabilistic and combinatorial insights into the Closest String problem, we develop sMCL-WMR, a program that is much faster than its predecessor MCL-WMR. We apply and adapt sMCL-WMR and MCL-WMR to analyze the promoter regions of the canola seed-coat. Our results identify important regions of the canola genome that are responsible for specific biological activities. This knowledge may be used in the long-term aim of developing crop varieties with specific biological characteristics, such as being disease-resistant