A Seeded Genetic Algorithm for RNA Secondary Structural Prediction with Pseudoknots

This work explores a new approach in using genetic algorithm to predict RNA secondary structures with pseudoknots. Since only a small portion of most RNA structures is comprised of pseudoknots, the majority of structural elements from an optimal pseudoknot-free structure are likely to be part of the true structure. Thus seeding the genetic algorithm with optimal pseudoknot-free structures will more likely lead it to the true structure than a randomly generated population. The genetic algorithm uses the known energy models with an additional augmentation to allow complex pseudoknots. The nearest-neighbor energy model is used in conjunction with Turner’s thermodynamic parameters for pseudoknot-free structures, and the H-type pseudoknot energy estimation for simple pseudoknots. Testing with known pseudoknot sequences from PseudoBase shows that it out performs some of the current popular algorithms

On the combinatorics of sparsification

Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze the sparsification of a particular decomposition rule, $\Lambda^*$, that splits an interval for RNA secondary and pseudoknot structures of fixed topological genus. Essential for quantifying the sparsification is the size of its so called candidate set. We present a combinatorial framework which allows by means of probabilities of irreducible substructures to obtain the expected size of the set of $\Lambda^*$-candidates. We compute these expectations for arc-based energy models via energy-filtered generating functions (GF) for RNA secondary structures as well as RNA pseudoknot structures. For RNA secondary structures we also consider a simplified loop-energy model. This combinatorial analysis is then compared to the expected number of $\Lambda^*$-candidates obtained from folding mfe-structures. In case of the mfe-folding of RNA secondary structures with a simplified loop energy model our results imply that sparsification provides a reduction of time complexity by a constant factor of 91% (theory) versus a 96% reduction (experiment). For the "full" loop-energy model there is a reduction of 98% (experiment).Comment: 27 pages, 12 figure

A Graph Grammar for Modelling RNA Folding

We propose a new approach for modelling the process of RNA folding as a graph transformation guided by the global value of free energy. Since the folding process evolves towards a configuration in which the free energy is minimal, the global behaviour resembles the one of a self-adaptive system. Each RNA configuration is a graph and the evolution of configurations is constrained by precise rules that can be described by a graph grammar.Comment: In Proceedings GaM 2016, arXiv:1612.0105

McGenus: A Monte Carlo algorithm to predict RNA secondary structures with pseudoknots

We present McGenus, an algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. McGenus can treat sequences of up to 1000 bases and performs an advanced stochastic search of their minimum free energy structure allowing for non trivial pseudoknot topologies. Specifically, McGenus employs a multiple Markov chain scheme for minimizing a general scoring function which includes not only free energy contributions for pair stacking, loop penalties, etc. but also a phenomenological penalty for the genus of the pairing graph. The good performance of the stochastic search strategy was successfully validated against TT2NE which uses the same free energy parametrization and performs exhaustive or partially exhaustive structure search, albeit for much shorter sequences (up to 200 bases). Next, the method was applied to other RNA sets, including an extensive tmRNA database, yielding results that are competitive with existing algorithms. Finally, it is shown that McGenus highlights possible limitations in the free energy scoring function. The algorithm is available as a web-server at http://ipht.cea.fr/rna/mcgenus.php .Comment: 6 pages, 1 figur

RNA secondary structure prediction from multi-aligned sequences

It has been well accepted that the RNA secondary structures of most functional non-coding RNAs (ncRNAs) are closely related to their functions and are conserved during evolution. Hence, prediction of conserved secondary structures from evolutionarily related sequences is one important task in RNA bioinformatics; the methods are useful not only to further functional analyses of ncRNAs but also to improve the accuracy of secondary structure predictions and to find novel functional RNAs from the genome. In this review, I focus on common secondary structure prediction from a given aligned RNA sequence, in which one secondary structure whose length is equal to that of the input alignment is predicted. I systematically review and classify existing tools and algorithms for the problem, by utilizing the information employed in the tools and by adopting a unified viewpoint based on maximum expected gain (MEG) estimators. I believe that this classification will allow a deeper understanding of each tool and provide users with useful information for selecting tools for common secondary structure predictions.Comment: A preprint of an invited review manuscript that will be published in a chapter of the book `Methods in Molecular Biology'. Note that this version of the manuscript may differ from the published versio

Algorithms for RNA secondary structure analysis : prediction of pseudoknots and the consensus shapes approach

Reeder J. Algorithms for RNA secondary structure analysis : prediction of pseudoknots and the consensus shapes approach. Bielefeld (Germany): Bielefeld University; 2007.Our understanding of the role of RNA has undergone a major change in the last decade. Once believed to be only a mere carrier of information and structural component of the ribosomal machinery in the advent of the genomic age, it is now clear that RNAs play a much more active role. RNAs can act as regulators and can have catalytic activity - roles previously only attributed to proteins. There is still much speculation in the scientific community as to what extent RNAs are responsible for the complexity in higher organisms which can hardly be explained with only proteins as regulators. In order to investigate the roles of RNA, it is therefore necessary to search for new classes of RNA. For those and already known classes, analyses of their presence in different species of the tree of life will provide further insight about the evolution of biomolecules and especially RNAs. Since RNA function often follows its structure, the need for computer programs for RNA structure prediction is an immanent part of this procedure. The secondary structure of RNA - the level of base pairing - strongly determines the tertiary structure. As the latter is computationally intractable and experimentally expensive to obtain, secondary structure analysis has become an accepted substitute. In this thesis, I present two new algorithms (and a few variations thereof) for the prediction of RNA secondary structures. The first algorithm addresses the problem of predicting a secondary structure from a single sequence including RNA pseudoknots. Pseudoknots have been shown to be functionally relevant in many RNA mediated processes. However, pseudoknots are excluded from considerations by state-of-the-art RNA folding programs for reasons of computational complexity. While folding a sequence of length n into unknotted structures requires O(n^3) time and O(n^2) space, finding the best structure including arbitrary pseudoknots has been proven to be NP-complete. Nevertheless, I demonstrate in this work that certain types of pseudoknots can be included in the folding process with only a moderate increase of computational cost. In analogy to protein coding RNA, where a conserved encoded protein hints at a similar metabolic function, structural conservation in RNA may give clues to RNA function and to finding of RNA genes. However, structure conservation is more complex to deal with computationally than sequence conservation. The method considered to be at least conceptually the ideal approach in this situation is the Sankoff algorithm. It simultaneously aligns two sequences and predicts a common secondary structure. Unfortunately, it is computationally rather expensive - O(n^6) time and O(n^4) space for two sequences, and for more than two sequences it becomes exponential in the number of sequences! Therefore, several heuristic implementations emerged in the last decade trying to make the Sankoff approach practical by introducing pragmatic restrictions on the search space. In this thesis, I propose to redefine the consensus structure prediction problem in a way that does not imply a multiple sequence alignment step. For a family of RNA sequences, my method explicitly and independently enumerates the near-optimal abstract shape space and predicts an abstract shape as the consensus for all sequences. For each sequence, it delivers the thermodynamically best structure which has this shape. The technique of abstract shapes analysis is employed here for a synoptic view of the suboptimal folding space. As the shape space is much smaller than the structure space, and identification of common shapes can be done in linear time (in the number of shapes considered), the method is essentially linear in the number of sequences. Evaluations show that the new method compares favorably with available alternatives

Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics

BACKGROUND: The general problem of RNA secondary structure prediction under the widely used thermodynamic model is known to be NP-complete when the structures considered include arbitrary pseudoknots. For restricted classes of pseudoknots, several polynomial time algorithms have been designed, where the O(n(6))time and O(n(4)) space algorithm by Rivas and Eddy is currently the best available program. RESULTS: We introduce the class of canonical simple recursive pseudoknots and present an algorithm that requires O(n(4)) time and O(n(2)) space to predict the energetically optimal structure of an RNA sequence, possible containing such pseudoknots. Evaluation against a large collection of known pseudoknotted structures shows the adequacy of the canonization approach and our algorithm. CONCLUSIONS: RNA pseudoknots of medium size can now be predicted reliably as well as efficiently by the new algorithm

Discovery of structural and functional features in RNA pseudoknots

An RNA pseudoknot consists of nonnested double-stranded stems connected by single-stranded loops. There is increasing recognition that RNA pseudoknots are one of the most prevalent RNA structures and fulfill a diverse set of biological roles within cells, and there is an expanding rate of studies into RNA pseudoknotted structures as well as increasing allocation of function. These not only produce valuable structural data but also facilitate an understanding of structural and functional characteristics in RNA molecules. PseudoBase is a database providing structural, functional, and sequence data related to RNA pseudoknots. To capture the features of RNA pseudoknots, we present a novel framework using quantitative association rule mining to analyze the pseudoknot data. The derived rules are classified into specified association groups regarding structure, function, and category of RNA pseudoknots. The discovered association rules assist biologists in filtering out significant knowledge of structure-function and structure-category relationships. A brief biological interpretation to the relationships is presented, and their potential correlations with each other are highlighted.<br /