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Topology and prediction of RNA pseudoknots
 Bioinformatics
"... ABSTRACT Motivation: Several dynamic programming algorithms for predicting RNA structures with pseudoknots have been proposed that differ dramatically from one another in the classes of structures considered. Results: Here we use the natural topological classification of RNA structures in terms of ..."
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ABSTRACT Motivation: Several dynamic programming algorithms for predicting RNA structures with pseudoknots have been proposed that differ dramatically from one another in the classes of structures considered. Results: Here we use the natural topological classification of RNA structures in terms of irreducible components that are embedable in surfaces of fixed genus. We add to the conventional secondary structures four building blocks of genus one in order to construct certain structures of arbitrarily high genus. A corresponding unambiguous multiple context free grammar provides an efficient dynamic programming approach for energy minimization, partition function, and stochastic sampling. It admits a topologydependent parametrization of pseudoknot penalties that increases the sensitivity and positive predictive value of predicted base pairs by 1020% compared to earlier approaches. More general models based on building blocks of higher genus are also discussed. Availability: The source code of gfold is freely available at
PETcofold: predicting conserved interactions and structures of two multiple alignments of RNA sequences
, 2011
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A Combinatorial Framework for Designing (Pseudoknotted) RNA Algorithms
 11TH WORKSHOP ON ALGORITHMS IN BIOINFORMATICS (WABI'11)
, 2011
"... 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, basepair probabilities...) are reformula ..."
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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, basepair 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 fullfledged 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.
On topological RNA interaction structures
, 2012
"... Recently a folding algorithm of topological RNA pseudoknot structures has been presented [24]. This algorithm folds single stranded γstructures, i.e. RNA structures composed by distinct motifs of bounded topological genus. In this paper, we study the two backbone analogue of γstructures: the RNA γ ..."
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Recently a folding algorithm of topological RNA pseudoknot structures has been presented [24]. This algorithm folds single stranded γstructures, i.e. RNA structures composed by distinct motifs of bounded topological genus. In this paper, we study the two backbone analogue of γstructures: the RNA γinteraction structures. These are RNARNA interaction structures that are constructed by a finite number of building blocks over two and one backbone having genus at most γ. Properties of γinteraction structures are of practical interest since they are the targets of topological interaction structure folding algorithms. We show that the generating function of γinteraction structures is algebraic, which implies that the numbers of interaction structures can be computed recursively. We furthermore obtain simple asymptotic formulas for 0 and 1interaction structures. The simplest class are the 0interaction structures, which represent the two backbone analogue of secondary structures.
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"... BIOINFORMATICS Vol. 26 ECCB 2010, pages i460–i466doi:10.1093/bioinformatics/btq372 RactIP: fast and accurate prediction of RNARNA interaction using integer programming ..."
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BIOINFORMATICS Vol. 26 ECCB 2010, pages i460–i466doi:10.1093/bioinformatics/btq372 RactIP: fast and accurate prediction of RNARNA interaction using integer programming
Structural bioinformatics Partition function and base pairing probabilities for RNA–RNA interaction prediction
"... Motivation: The RNA–RNA interaction problem (RIP) consists in finding the energetically optimal structure of two RNA molecules that bind to each other. The standard model allows secondary structures in both partners as well as additional base pairs between the two RNAs subject to certain restriction ..."
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Motivation: The RNA–RNA interaction problem (RIP) consists in finding the energetically optimal structure of two RNA molecules that bind to each other. The standard model allows secondary structures in both partners as well as additional base pairs between the two RNAs subject to certain restrictions that ensure that RIP is solvabale by a polynomial time dynamic programming algorithm. RNA–RNA binding, like RNA folding, is typically not dominated by the ground state structure. Instead, a large ensemble of alternative structures contributes to the interaction thermodynamics. Results: We present here an O(N6) time and O(N4) dynamics programming algorithm for computing the full partition function for RIP which is based on the combinatorial notion of ‘tight structures’. Albeit equivalent to recent work by H. Chitsaz and collaborators, our approach in addition provides a fullfledged computation of the base pairing probabilities, which relies on the notion of a decomposition tree for joint structures. In practise, our implementation is efficient enough to investigate, for instance, the interactions of small bacterial RNAs and their target mRNAs.