An algebraic representation for tree alignment of RNA pseudoknotted structures

10.7287/peerj.preprints.3327 ◽

2017 ◽

Author(s):

Michela Quadrini ◽

Luca Tesei ◽

Emanuela Merelli ◽

Keyword(s):

Secondary Structures ◽

Algebraic Representation ◽

Structure Comparison ◽

Rna Secondary Structures ◽

Tree Alignment ◽

Ordered Trees ◽

Multiple Context ◽

Alignment Problem ◽

Definition Of ◽

Context Free

The methods proposed in the literature for RNA comparison focus mainly on pseudoknot free structures. The comparison of pseudoknotted structures is still a challenge. In this work, we propose a new algebraic representation of RNA secondary structures based on relations among hairpins in terms of nesting, crossing, and concatenation. Such algebraic representation is obtained from a defined multiple context-free grammar, which maps any kind of RNA secondary structures into extended trees, i.e., ordered trees where internal nodes are labeled with algebraic operators and leaves are labeled with loops. These extended trees permit the definition of the RNA secondary structure comparison as a tree alignment problem.

Download Full-text

BRASERO: A Resource for Benchmarking RNA Secondary Structure Comparison Algorithms

Advances in Bioinformatics ◽

10.1155/2012/893048 ◽

2012 ◽

Vol 2012 ◽

pp. 1-5 ◽

Cited By ~ 6

Author(s):

Julien Allali ◽

Cédric Saule ◽

Cédric Chauve ◽

Yves d’Aubenton-Carafa ◽

Alain Denise ◽

...

Keyword(s):

Noncoding Rna ◽

Fundamental Problem ◽

Pairwise Comparison ◽

Secondary Structures ◽

Software Tools ◽

Structure Comparison ◽

Rna Secondary Structures ◽

Ordered Trees ◽

Synthetic Datasets ◽

Comparison Algorithms

The pairwise comparison of RNA secondary structures is a fundamental problem, with direct application in mining databases for annotating putative noncoding RNA candidates in newly sequenced genomes. An increasing number of software tools are available for comparing RNA secondary structures, based on different models (such as ordered trees or forests, arc annotated sequences, and multilevel trees) and computational principles (edit distance, alignment). We describe here the website BRASERO that offers tools for evaluating such software tools on real and synthetic datasets.

Download Full-text

An efficient seeded tree alignment algorithm for finding the similarity score of two RNA secondary structures

2010 13th International Conference on Computer and Information Technology (ICCIT) ◽

10.1109/iccitechn.2010.5723822 ◽

2010 ◽

Author(s):

Mohammad Shamsur Rahman ◽

Abul Kashem Mia

Keyword(s):

Secondary Structures ◽

Similarity Score ◽

Alignment Algorithm ◽

Rna Secondary Structures ◽

Tree Alignment

Download Full-text

ASYMPTOTICS OF CANONICAL AND SATURATED RNA SECONDARY STRUCTURES

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720009004333 ◽

2009 ◽

Vol 07 (05) ◽

pp. 869-893 ◽

Cited By ~ 11

Author(s):

PETER CLOTE ◽

EVANGELOS KRANAKIS ◽

DANNY KRIZANC ◽

BRUNO SALVY

Keyword(s):

Secondary Structure ◽

Secondary Structures ◽

Expected Number ◽

Greedy Method ◽

Base Pairs ◽

Stem Loop ◽

Rna Secondary Structures ◽

Speed Up ◽

Asymptotic Number ◽

Definition Of

It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is 1.104366 · n-3/2 · 2.618034n. In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures — canonical and saturated structures. Canonical secondary structures are defined to have no lonely (isolated) base pairs. This class of secondary structures was introduced by Bompfünewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up, by proving that the asymptotic number of canonical RNA secondary structures is 2.1614 · n-3/2 · 1.96798n and that the expected number of base pairs in a canonical secondary structure is 0.31724 · n. The asymptotic number of canonical secondary structures was obtained much earlier by Hofacker, Schuster and Stadler using a different method. Saturated secondary structures have the property that no base pairs can be added without violating the definition of secondary structure (i.e. introducing a pseudoknot or base triple). Here we show that the asymptotic number of saturated structures is 1.07427 · n-3/2 · 2.35467n, the asymptotic expected number of base pairs is 0.337361 · n, and the asymptotic number of saturated stem-loop structures is 0.323954 · 1.69562n, in contrast to the number 2n - 2 of (arbitrary) stem-loop structures as classically computed by Stein and Waterman. Finally, we apply the work of Drmota to show that the density of states for [all resp. canonical resp. saturated] secondary structures is asymptotically Gaussian. We introduce a stochastic greedy method to sample random saturated structures, called quasi-random saturated structures, and show that the expected number of base pairs is 0.340633 · n.

Download Full-text

P-DCFOLD OR HOW TO PREDICT ALL KINDS OF PSEUDOKNOTS IN RNA SECONDARY STRUCTURES

International Journal of Artificial Intelligence Tools ◽

10.1142/s021821300500234x ◽

2005 ◽

Vol 14 (05) ◽

pp. 703-716 ◽

Cited By ~ 2

Author(s):

FARIZA TAHI ◽

ENGELEN STEFAN ◽

MIREILLE REGNIER

Keyword(s):

Structure Prediction ◽

Secondary Structure Prediction ◽

Secondary Structures ◽

Divide And Conquer ◽

Comparative Approach ◽

Rna Sequences ◽

Rna Secondary Structure Prediction ◽

Rna Secondary Structures ◽

Knowing That ◽

Definition Of

Pseudoknots play important roles in many RNAs. But for computational reasons, pseudoknots are usually excluded from the definition of RNA secondary structures. Indeed, prediction of pseudoknots increase very highly the complexities in time of the algorithms, knowing that all existing algorithms for RNA secondary structure prediction have complexities at least of O(n3). Some algorithms have been developed for searching pseudoknots, but all of them have very high complexities, and consider generally particular kinds of pseudoknots. We present an algorithm, called P-DCFold based on the comparative approach, for the prediction of RNA secondary structures including all kinds of pseudoknots. The helices are searched recursively using the "Divide and Conquer" approach, searching the helices from the "most significant" to the "less significant". A selected helix subdivide the sequence into two sub-sequences, the internal one and a concatenation of the two externals. This approach is used to search non-interleaved helices and allows to limit the space of searching. To search for pseudoknots, the processing is reiterated. Therefore, each helix of the pseudoknot is selected in a different step. P-DCFold has been applied to several RNA sequences. In less than two seconds, their respective secondary structures, including their pseudoknots, have been recovered very efficiently.

Download Full-text

An Algebraic Representation of RNA Secondary Structures

Journal of Biomolecular Structure and Dynamics ◽

10.1080/07391102.1992.10508663 ◽

1992 ◽

Vol 10 (3) ◽

pp. 465-488 ◽

Cited By ~ 7

Author(s):

Yuri Magarshak ◽

Craig J. Benham

Keyword(s):

Secondary Structures ◽

Algebraic Representation ◽

Rna Secondary Structures

Download Full-text

Counting, Generating, Analyzing and Sampling Tree Alignments

International Journal of Foundations of Computer Science ◽

10.1142/s0129054118420030 ◽

2018 ◽

Vol 29 (05) ◽

pp. 741-767 ◽

Cited By ~ 1

Author(s):

Cedric Chauve ◽

Julien Courtiel ◽

Yann Ponty

Keyword(s):

Probabilistic Analysis ◽

Dynamic Programming Algorithm ◽

Programming Algorithm ◽

Structure Comparison ◽

Tree Alignment ◽

Analytic Combinatorics ◽

Decomposition Scheme ◽

Ordered Trees ◽

Alignment Algorithms ◽

Usual Representation

Pairwise ordered tree alignment are combinatorial objects that appear in important applications, such as RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis. In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees [Formula: see text] and [Formula: see text]. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal alignments.

Download Full-text

Graphical Processing Unit - Supported RNA Secondary Structure Comparison

10.29007/bhsr ◽

2020 ◽

Author(s):

Mutlu Mete ◽

Abdullah Arslan

Keyword(s):

Secondary Structure ◽

Rna Secondary Structure ◽

Secondary Structures ◽

Graphical Processing Unit ◽

Processing Unit ◽

Structure Comparison ◽

Rna Secondary Structures ◽

Large Databases ◽

Graphical Processing ◽

Rna Secondary Structure Comparison

This study is part of our perpetual effort to develop improved RNA secondary structure analysis tools and databases. In this work we present a new Graphical Processing Unit (GPU)-based RNA structural analysis framework that supports fast multiple RNA secondary structure comparison for very large databases. A search-based secondary structure comparison algorithm deployed in RNASSAC website helps bioinformaticians find common RNA substructures from the underlying database. The algorithm performs two levels of binary searches on the database. Its time requirement is affected by the database size. Experiments on the RNASSAC website show that the algorithm takes seconds for a database of 4,666 RNAs. For example, it takes about 4.4 sec for comparing 25 RNAs from this database. In another case, when many non-overlapping common substructures are desired, a heuristic approach requires as long as 85 sec in comparing 40 RNAs from the same database. The comparisons by this sequential algorithm takes at least 50% more time when RNAs are compared from the database of several millions of RNAs. The most recently curated databases already have millions of RNA secondary structures. The improvement in run-time performance of comparison algorithms is necessary. This study present a GPU-based RNA substructure comparison algorithm with which running time for multiple RNA secondary structures remains feasible for large databases. Our new parallel algorithm is 12 times faster than the CPU version (sequential) comparison algorithm of the RNASSAC website. The response time significantly reduces towards development of a realtime RNA comparison web service for bioinformatics community.

Download Full-text