Suffix Tree Characterization of Maximal Motifs in Biological Sequences

Finding motifs in biological sequences is one of the most intriguing problems for string algorithms designers as it is necessary to deal with approximations and this complicates the problem. Existing algorithms run in time linear with the input size. Nevertheless, the output size can be very large due to the approximation. This makes the output often unreadable, next to slowing down the inference itself. Since only a subset of the motifs, i.e. the \emph{maximal} motifs, could be enough to give the information of all of them, in this paper, we aim at removing such redundancy. We define notions of maximality that we characterize in the suffix tree data structure. Given that this is used by a whole class of motifs extraction tools, we show how these tools can be modified to include the maximality requirement on the fly without changing the asymptotical complexity

Output-Sensitive Pattern Extraction in Sequences

Genomic Analysis, Plagiarism Detection, Data Mining, Intrusion Detection, Spam Fighting and Time Series Analysis are just some examples of applications where extraction of recurring patterns in sequences of objects is one of the main computational challenges. Several notions of patterns exist, and many share the common idea of strictly specifying some parts of the pattern and to don\u27t care about the remaining parts. Since the number of patterns can be exponential in the length of the sequences, pattern extraction focuses on statistically relevant patterns, where any attempt to further refine or extend them causes a loss of significant information (where the number of occurrences changes). Output-sensitive algorithms have been proposed to enumerate and list these patterns, taking polynomial time O(n^c) per pattern for constant c > 1, which is impractical for massive sequences of very large length n. We address the problem of extracting maximal patterns with at most k don\u27t care symbols and at least q occurrences. Our contribution is to give the first algorithm that attains a stronger notion of output-sensitivity, borrowed from the analysis of data structures: the cost is proportional to the actual number of occurrences of each pattern, which is at most n and practically much smaller than n in real applications, thus avoiding the aforementioned cost of O(n^c) per pattern

Motif Discovery with Compact Approaches - Design and Applications

In the post-genomic era, the ability to predict the behavior, the function, or the structure of biological entities, as well as interactions among them, plays a fundamental role in the discovery of information to help biologists to explain biological mechanisms. In this context, appropriate characterization of the structures under analysis, and the exploitation of combinatorial properties of sequences, are crucial steps towards the development of efficient algorithms and data structures to be able to perform the analysis of biological sequences. Similarity is a fundamental concept in Biology. Several functional and structural properties, and evolutionary mechanisms, can be predicted comparing new elements with already classified elements, or comparing elements with a similar structure of function to infer the common mechanism that is at the basis of the observed similar behavior. Such elements are commonly called motifs. Comparison-based methods for sequence analysis find their application in several biological contexts, such as identification of transcription factor binding sites, finding structural and functional similarities in proteins, and phylogeny. Therefore the development of adequate methodologies for motif discovery is of paramount interests for several fields in computational biology. In motif discovery in biosequences, it is common to assume that statistically significant candidates are those that are likely to hide some biologically significant property. For this purpose all the possible candidates are ranked according to some statistics on words (frequency, over/under representation, etc.). Then they are presented in output for further inspection by a biologist, who identifies the most promising subsequences, and tests them in laboratory to confirm their biological significance. Therefore, when designing algorithms for motif discovery, besides obviously aim at time and space efficiency, particular attention should be devoted to the output representation. In fact, even considering fixed length strings, the size of the candidate set become exponential if exhaustive enumeration is applied. This is already true when only exact matches are considered as candidate occurrences, and worsen if some kind of variability (for example a fixed number of mismatches is allowed). Alternatively, heuristics could be used, however without the warranty of finding the optimal solution. Computational power of nowadays computers can partially reduce these effects, in particular for short length candidates. However, if the size of the output is too big to be analyzed by human inspection the risk is to provide biologists with very fast, but useless tools. A possible solution relies on compact approaches. Compact approaches are based on the partition of the search space into classes. The classes must be designed in such a way that the score used to rank the candidates has a monotone behavior within each class. This allows the identification of a representative of each class, which is the element with the highest score. Consequently, it suffices to compute, and report in output, the score only for the representatives. In fact, we are guaranteed that for each element that has not been ranked there is another one (the representative of the class it belongs to) that is at least equally significant. The final user can then be presented with an output that has the size of the partition, rather than the size of the candidate space, with obvious advantages for the human-based analysis that follows the computer-based filtering of the pattern discovery algorithm. Compact approaches find applications both in searching and discovery frameworks. They can also be applied to several motif models: exact patterns, patterns with given mismatch distribution, patterns with unknown mismatch distribution, profiles (i.e. matrices), and under both i.i.d. and Markov distributions. The purpose of this chapter is to describe the basis of compact approaches, to provide the readers with the conceptual tools for applying compact approaches to the design of their algorithm for biosequence analysis. Moreover, examples of compact approaches that have been successfully developed for several motif models (e.g. exact words, co-occurrences, words with mismatches, etc) will be explained, and experimental results to discuss their power will be presented

Combinatorial RNA Design: Designability and Structure-Approximating Algorithm

In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete characterizations for the structures that can be designed using restricted alphabets. Under a classic four-letter alphabet, we provide a complete characterization of designable structures without unpaired bases. When unpaired bases are allowed, we provide partial characterizations for classes of designable/undesignable structures, and show that the class of designable structures is closed under the stutter operation. Membership of a given structure to any of the classes can be tested in linear time and, for positive instances, a solution can be found in linear time. Finally, we consider a structure-approximating version of the problem that allows to extend bands (helices) and, assuming that the input structure avoids two motifs, we provide a linear-time algorithm that produces a designable structure with at most twice more base pairs than the input structure.Comment: CPM - 26th Annual Symposium on Combinatorial Pattern Matching, Jun 2015, Ischia Island, Italy. LNCS, 201

ModuleOrganizer: detecting modules in families of transposable elements

<p>Abstract</p> <p>Background</p> <p>Most known eukaryotic genomes contain mobile copied elements called transposable elements. In some species, these elements account for the majority of the genome sequence. They have been subject to many mutations and other genomic events (copies, deletions, captures) during transposition. The identification of these transformations remains a difficult issue. The study of families of transposable elements is generally founded on a multiple alignment of their sequences, a critical step that is adapted to transposons containing mostly localized nucleotide mutations. Many transposons that have lost their protein-coding capacity have undergone more complex rearrangements, needing the development of more complex methods in order to characterize the architecture of sequence variations.</p> <p>Results</p> <p>In this study, we introduce the concept of a <it>transposable element module</it>, a flexible motif present in at least two sequences of a family of transposable elements and built on a succession of maximal repeats. The paper proposes an assembly method working on a set of exact maximal repeats of a set of sequences to create such modules. It results in a graphical view of sequences segmented into modules, a representation that allows a flexible analysis of the transformations that have occurred between them. We have chosen as a demonstration data set in depth analysis of the transposable element Foldback in <it>Drosophila melanogaster</it>. Comparison with multiple alignment methods shows that our method is more sensitive for highly variable sequences. The study of this family and the two other families AtREP21 and SIDER2 reveals new copies of very different sizes and various combinations of modules which show the potential of our method.</p> <p>Conclusions</p> <p>ModuleOrganizer is available on the Genouest bioinformatics center at <url>http://moduleorganizer.genouest.org</url></p

Combinatorial RNA Design Designability and Structure-Approximating Algorithm in Watson-Crick and Nussinov-Jacobson Energy Models

We consider the Combinatorial RNA Design problem, a minimal instance of RNA design where one must produce an RNA sequence that adopts a given secondary structure as its minimal free-energy structure. We consider two free-energy models where the contributions of base pairs are additive and independent: the purely combinatorial Watson-Crick model, which only allows equally-contributing A -- U and C -- G base pairs, and the real-valued Nussinov-Jacobson model, which associates arbitrary energies to A -- U, C -- G and G -- U base pairs. We first provide a complete characterization of designable structures using restricted alphabets and, in the four-letter alphabet, provide a complete characterization for designable structures without unpaired bases. When unpaired bases are allowed, we characterize extensive classes of (non-)designable structures, and prove the closure of the set of designable structures under the stutter operation. Membership of a given structure to any of the classes can be tested in $\Theta$(n) time, including the generation of a solution sequence for positive instances. Finally, we consider a structure-approximating relaxation of the design, and provide a $\Theta$(n) algorithm which, given a structure S that avoids two trivially non-designable motifs, transforms S into a designable structure constructively by adding at most one base-pair to each of its stems.Comment: To appea

A computational framework for unsupervised analysis of everyday human activities

In order to make computers proactive and assistive, we must enable them to perceive, learn, and predict what is happening in their surroundings. This presents us with the challenge of formalizing computational models of everyday human activities. For a majority of environments, the structure of the in situ activities is generally not known a priori. This thesis therefore investigates knowledge representations and manipulation techniques that can facilitate learning of such everyday human activities in a minimally supervised manner. A key step towards this end is finding appropriate representations for human activities. We posit that if we chose to describe activities as finite sequences of an appropriate set of events, then the global structure of these activities can be uniquely encoded using their local event sub-sequences. With this perspective at hand, we particularly investigate representations that characterize activities in terms of their fixed and variable length event subsequences. We comparatively analyze these representations in terms of their representational scope, feature cardinality and noise sensitivity. Exploiting such representations, we propose a computational framework to discover the various activity-classes taking place in an environment. We model these activity-classes as maximally similar activity-cliques in a completely connected graph of activities, and describe how to discover them efficiently. Moreover, we propose methods for finding concise characterizations of these discovered activity-classes, both from a holistic as well as a by-parts perspective. Using such characterizations, we present an incremental method to classify a new activity instance to one of the discovered activity-classes, and to automatically detect if it is anomalous with respect to the general characteristics of its membership class. Our results show the efficacy of our framework in a variety of everyday environments.Ph.D.Committee Chair: Aaron Bobick; Committee Member: Charles Isbell; Committee Member: David Hogg; Committee Member: Irfan Essa; Committee Member: James Reh