LaRA 2: parallel and vectorized program for sequence–structure alignment of RNA sequences

Background The function of non-coding RNA sequences is largely determined by their spatial conformation, namely the secondary structure of the molecule, formed by Watson–Crick interactions between nucleotides. Hence, modern RNA alignment algorithms routinely take structural information into account. In order to discover yet unknown RNA families and infer their possible functions, the structural alignment of RNAs is an essential task. This task demands a lot of computational resources, especially for aligning many long sequences, and it therefore requires efficient algorithms that utilize modern hardware when available. A subset of the secondary structures contains overlapping interactions (called pseudoknots), which add additional complexity to the problem and are often ignored in available software. Results We present the SeqAn-based software LaRA 2 that is significantly faster than comparable software for accurate pairwise and multiple alignments of structured RNA sequences. In contrast to other programs our approach can handle arbitrary pseudoknots. As an improved re-implementation of the LaRA tool for structural alignments, LaRA 2 uses multi-threading and vectorization for parallel execution and a new heuristic for computing a lower boundary of the solution. Our algorithmic improvements yield a program that is up to 130 times faster than the previous version. Conclusions With LaRA 2 we provide a tool to analyse large sets of RNA secondary structures in relatively short time, based on structural alignment. The produced alignments can be used to derive structural motifs for the search in genomic databases

A Combinatorial Framework for Designing (Pseudoknotted) RNA Algorithms

We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization, partition function, base-pair probabilities...) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one to conceptually detach the conformation space/energy model -- captured by the hypergraph model -- from the specific application, assuming unambiguity of the decomposition. To ensure the latter property, we propose a new combinatorial methodology based on generating functions. We extend the set of generic applications by proposing an exact algorithm for extracting generalized moments in weighted distribution, generalizing a prior contribution by Miklos and al. Finally, we illustrate our full-fledged programme on three exemplary conformation spaces (secondary structures, Akutsu's simple type pseudoknots and kissing hairpins). This readily gives sets of algorithms that are either novel or have complexity comparable to classic implementations for minimization and Boltzmann ensemble applications of dynamic programming

LaRA 2: parallel and vectorized program for sequence–structure alignment of RNA sequences

Background The function of non-coding RNA sequences is largely determined by their spatial conformation, namely the secondary structure of the molecule, formed by Watson–Crick interactions between nucleotides. Hence, modern RNA alignment algorithms routinely take structural information into account. In order to discover yet unknown RNA families and infer their possible functions, the structural alignment of RNAs is an essential task. This task demands a lot of computational resources, especially for aligning many long sequences, and it therefore requires efficient algorithms that utilize modern hardware when available. A subset of the secondary structures contains overlapping interactions (called pseudoknots), which add additional complexity to the problem and are often ignored in available software. Results We present the SeqAn-based software LaRA 2 that is significantly faster than comparable software for accurate pairwise and multiple alignments of structured RNA sequences. In contrast to other programs our approach can handle arbitrary pseudoknots. As an improved re-implementation of the LaRA tool for structural alignments, LaRA 2 uses multi-threading and vectorization for parallel execution and a new heuristic for computing a lower boundary of the solution. Our algorithmic improvements yield a program that is up to 130 times faster than the previous version. Conclusions With LaRA 2 we provide a tool to analyse large sets of RNA secondary structures in relatively short time, based on structural alignment. The produced alignments can be used to derive structural motifs for the search in genomic databases

Sparsification of RNA structure prediction including pseudoknots

<p>Abstract</p> <p>Background</p> <p>Although many RNA molecules contain pseudoknots, computational prediction of pseudoknotted RNA structure is still in its infancy due to high running time and space consumption implied by the dynamic programming formulations of the problem.</p> <p>Results</p> <p>In this paper, we introduce sparsification to significantly speedup the dynamic programming approaches for pseudoknotted RNA structure prediction, which also lower the space requirements. Although sparsification has been applied to a number of RNA-related structure prediction problems in the past few years, we provide the first application of sparsification to pseudoknotted RNA structure prediction specifically and to handling gapped fragments more generally - which has a much more complex recursive structure than other problems to which sparsification has been applied. We analyse how to sparsify four pseudoknot structure prediction algorithms, among those the most general method available (the Rivas-Eddy algorithm) and the fastest one (Reeder-Giegerich algorithm). In all algorithms the number of "candidate" substructures to be considered is reduced.</p> <p>Conclusions</p> <p>Our experimental results on the sparsified Reeder-Giegerich algorithm suggest a linear speedup over the unsparsified implementation.</p

Sparsification of RNA Structure Prediction Including Pseudoknots

Background: Although many RNA molecules contain pseudoknots, computational prediction of pseudoknottedRNA structure is still in its infancy due to high running time and space consumption implied by the dynamicprogramming formulations of the problem.Results: In this paper, we introduce sparsification to significantly speedup the dynamic programming approachesfor pseudoknotted RNA structure prediction, which also lower the space requirements. Although sparsification hasbeen applied to a number of RNA-related structure prediction problems in the past few years, we provide the firstapplication of sparsification to pseudoknotted RNA structure prediction specifically and to handling gappedfragments more generally - which has a much more complex recursive structure than other problems to whichsparsification has been applied. We analyse how to sparsify four pseudoknot structure prediction algorithms,among those the most general method available (the Rivas-Eddy algorithm) and the fastest one (Reeder-Giegerichalgorithm). In all algorithms the number of “candidate” substructures to be considered is reduced.Conclusions: Our experimental results on the sparsified Reeder-Giegerich algorithm suggest a linear speedup overthe unsparsified implementation

Automated Design of Dynamic Programming Schemes for RNA Folding with Pseudoknots

Despite being a textbook application of dynamic programming (DP) and routine task in RNA structure analysis, RNA secondary structure prediction remains challenging whenever pseudoknots come into play. To circumvent the NP-hardness of energy minimization in realistic energy models, specialized algorithms have been proposed for restricted conformation classes that capture the most frequently observed configurations. While these methods rely on hand-crafted DP schemes, we generalize and fully automatize the design of DP pseudoknot prediction algorithms. We formalize the problem of designing DP algorithms for an (infinite) class of conformations, modeled by (a finite number of) fatgraphs, and automatically build DP schemes minimizing their algorithmic complexity. We propose an algorithm for the problem, based on the tree-decomposition of a well-chosen representative structure, which we simplify and reinterpret as a DP scheme. The algorithm is fixed-parameter tractable for the tree-width tw of the fatgraph, and its output represents a ?(n^{tw+1}) algorithm for predicting the MFE folding of an RNA of length n. Our general framework supports general energy models, partition function computations, recursive substructures and partial folding, and could pave the way for algebraic dynamic programming beyond the context-free case

Dynamic programming based RNA pseudoknot alignment

Pseudoknots are certain structural motifs of RNA molecules. In this thesis we consider the problem of RNA pseudoknot alignment. Most current approaches either discard pseudoknots in order to be efficient or rely on heuristics generating only approximate solutions. This work focuses on dynamic programming based alignment methods and proposes two new approaches for an exact solution of the alignment problem in the presence of pseudoknot structures. The first approach is able to handle arbitrary pseudoknots, however, does not guarantee a polynomial runtime for all instances, due to the NP-hardness of the problem. Nevertheless, an analysis in terms of parameterized complexity shows that the algorithm is fixed parameter tractable for a parameter that is small in practice. The second approach is a general scheme for the alignment of restricted classes of pseudoknots in polynomial time. It is motivated by existing RNA pseudoknot prediction algorithms. We show how to embed seven of those algorithms in a common scheme and present an analogous scheme for the alignment problem, which yields for each of the structure prediction algorithms a corresponding alignment algorithm. The alignment algorithms handle the same class of pseudoknots as the corresponding prediction algorithms and the time and space complexity is only increased by a linear factor, compared to the respective prediction algorithm. Both approaches have been implemented to evaluate their applicability in practice.In dieser Dissertation beschäftige ich mich mit dem Alignment von bestimmten RNA Strukturen, die als Pseudoknoten bezeichnet werden. Da dieses Problem NP-hart ist, berücksichtigen die meisten bisher verfügbaren Alignmentverfahren um effizient zu sein entweder keine Pseudoknoten oder berechnen nur approximierte Lösungen mit Hilfe von Heuristiken. In der vorliegenden Arbeit beschreibe ich zwei neue Verfahren, die mit Hilfe von dynamischer Programmierung eine exakte Lösung für das Alignmentproblem von Pseudoknotenstrukturen berechnen. Das erste Verfahren kann beliebige Pseudoknoten alignieren und hat, da es sich hierbei um ein NPhartes Problem handelt, im allgemeinen keine polynomiell beschränkte Laufzeit. Eine parametrische Komplexitätsanalyse zeigt allerdings, dass der Algorithmus parametrisierbar (fixed parameter tractable) in Bezug auf einen in der Praxis kleinen Parameter ist. Das zweite Verfahren ermöglicht es, unterschiedliche eingeschränkte Klassen von Pseudoknoten in polynomieller Zeit zu alignieren. In einem ersten Schritt zeige ich hierzu, wie man existierende Vorhersagealgorithmen für sieben solcher Klassen in ein gemeinsames Schema einbetten kann. Dann entwickele ich ein analoges Schema für das Alignment von Pseudoknoten, das zu jedem der Vorhersagealgorithmen einen entsprechenden Alignmentalgorithmus mit nur linear erhöhter Speicher- und Zeitkomplexität liefert. Beide Verfahren wurden auch implementiert um die Praxistauglichkeit zu evaluieren

Data mining in computational proteomics and genomics

This dissertation addresses data mining in bioinformatics by investigating two important problems, namely peak detection and structure matching. Peak detection is useful for biological pattern discovery while structure matching finds many applications in clustering and classification. The first part of this dissertation focuses on elastic peak detection in 2D liquid chromatographic mass spectrometry (LC-MS) data used in proteomics research. These data can be modeled as a time series, in which the X-axis represents time points and the Y-axis represents intensity values. A peak occurs in a set of 2D LC-MS data when the sum of the intensity values in a sliding time window exceeds a user-determined threshold. The elastic peak detection problem is to locate all peaks across multiple window sizes of interest in the dataset. A new method, called PeakID, is proposed in this dissertation, which solves the elastic peak detection problem in 2D LC-MS data without yielding any false negative. PeakID employs a novel data structure, called a Shifted Aggregation Tree or AggTree for short, to find the different peaks in the dataset. This method works by first constructing an AggTree in a bottom-up manner from the dataset, and then searching the AggTree for the peaks in a top-down manner. PeakID uses a state-space algorithm to find the topology and structure of an efficient AggTree. Experimental results demonstrate the superiority of the proposed method over other methods on both synthetic and real-world data. The second part of this dissertation focuses on RNA pseudoknot structure matching and alignment. RNA pseudoknot structures play important roles in many genomic processes. Previous methods for comparative pseudoknot analysis mainly focus on simultaneous folding and alignment of RNA sequences. Little work has been done to align two known RNA secondary structures with pseudoknots taking into account both sequence and structure information of the two RNAs. A new method, called RKalign, is proposed in this dissertation for aligning two known RNA secondary structures with pseudoknots. RKalign adopts the partition function methodology to calculate the posterior log-odds scores of the alignments between bases or base pairs of the two RNAs with a dynamic programming algorithm. The posterior log-odds scores are then used to calculate the expected accuracy of an alignment between the RNAs. The goal is to find an optimal alignment with the maximum expected accuracy. RKalign employs a greedy algorithm to achieve this goal. The performance of RKalign is investigated and compared with existing tools for RNA structure alignment. An extension of the proposed method to multiple alignment of pseudoknot structures is also discussed. RKalign is implemented in Java and freely accessible on the Internet. As more and more pseudoknots are revealed, collected and stored in public databases, it is anticipated that a tool like RKalign will play a significant role in data comparison, annotation, analysis, and retrieval in these databases