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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
TT2NE: a novel algorithm to predict RNA secondary structures with pseudoknots
 Nucleic Acids Res
, 2011
"... We present TT2NE, a new algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. TT2NE is guaranteed to find the minimum free energy structure regardless of pseudoknot topology. This unique profic ..."
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We present TT2NE, a new algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. TT2NE is guaranteed to find the minimum free energy structure regardless of pseudoknot topology. This unique proficiency is obtained at the expense of the maximum length of sequences that can be treated, but comparison with stateoftheart algorithms shows that TT2NE significantly improves the quality of predictions. Analysis of TT2NE’s incorrect predictions sheds light on the need to study how sterical constraints limit the range of pseudoknotted structures that can be formed from a given sequence. An implementation of TT2NE on a public server can be found at
Folding 3noncrossing RNA pseudoknot structures
 J. Comput. Biol
"... Abstract. In this paper we present a selfcontained analysis and description of the novel ab initio folding algorithm cross, which generates the minimum free energy (mfe), 3noncrossing, σcanonical RNA structure. Here an RNA structure is 3noncrossing if it does not contain more than three mutually ..."
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Abstract. In this paper we present a selfcontained analysis and description of the novel ab initio folding algorithm cross, which generates the minimum free energy (mfe), 3noncrossing, σcanonical RNA structure. Here an RNA structure is 3noncrossing if it does not contain more than three mutually crossing arcs and σcanonical, if each of its stacks has size greater or equal than σ. Our notion of mfestructure is based on a specific concept of pseudoknots and respective loopbased energy parameters. The algorithm decomposes into three parts: the first is the inductive construction of motifs and shadows, the second is the generation of the skeletatrees rooted in irreducible shadows and the third is the saturation of skeleta via context dependent dynamic programming routines. 1. Introduction and
doi:10.1093/bioinformatics/btq218 Thermodynamics of RNA structures by Wang–Landau sampling
"... Vol. 26 ISMB 2010, pages i278–i286 ..."
McGenus: a Monte Carlo algorithm to predict RNA secondary structures with pseudoknots
 Nucleic Acids Research
, 1900
"... 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 ene ..."
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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 nontrivial pseudoknot topologies. Specifically, McGenus uses a Monte Carlo algorithm with replica exchange 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
Bayesian sampling of evolutionarily conserved RNA secondary structures with pseudoknots
 Bioinformatics
, 2012
"... Motivation: Today many noncoding RNAs are known to play an active role in various important biological processes. Since RNA's functionality is correlated with specic structural motifs that are often conserved in phylogenetically related molecules, computational prediction of RNA structure sho ..."
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Motivation: Today many noncoding RNAs are known to play an active role in various important biological processes. Since RNA's functionality is correlated with specic structural motifs that are often conserved in phylogenetically related molecules, computational prediction of RNA structure should ideally be based on a set of homologous primary structures. But many available RNA secondary structure prediction programs that use sequence alignments do not consider pseudoknots or their estimations consist on a single structure without information on uncertainty. Results: In this paper we present a method that takes advantage of the evolutionary history of a group of aligned RNA sequences for sampling consensus secondary structures, including pseudoknots, according to their approximate posterior probability. We investigate the benet of using evolutionary history and demonstrate the competitiveness of our method compared to similar methods based on RNase P RNA sequences and simulated data.
Fighting against uncertainty: An essential issue in bioinformatics∗
, 2013
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References
"... targets verified by experiments sRNATarBase: A comprehensive database of bacterial sRNA ..."
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targets verified by experiments sRNATarBase: A comprehensive database of bacterial sRNA
On the Page Number of Secondary Structures with Pseudoknots
, 2011
"... Let S denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. {i, j} ∈ S if there is a hydrogen bond between the ith and jth nucleotide. The page number of S, denoted π(S), is the minimum number k such that S can be decomposed into a disjoint union of k second ..."
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Let S denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. {i, j} ∈ S if there is a hydrogen bond between the ith and jth nucleotide. The page number of S, denoted π(S), is the minimum number k such that S can be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NPcomplete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe two greedy algorithms, and show by an example that neither is optimal. We describe an algorithm running in time O(n log n) that produces a decomposition of an RNA structure S on n bases into at most ω(S)·log n disjoint secondary structures, where ω(S) denotes the maximum number of base pairs that may cross a given base pair. It follows that ω(S) ≤ π(S) ≤ ω(S) · log n, where π(S) denotes the page number of S. We give an O(n 3/2) time algorithm for finding a 2page decomposition of bisecondary structures for RNA sequences of size n, and we provide bounds on the expected page number of random structures having pseudoknots.
RESEARCH ARTICLE Open Access Threedimensional modeling of chromatin structure from interaction frequency data using
"... Background: Longrange interactions between regulatory DNA elements such as enhancers, insulators and promoters play an important role in regulating transcription. As chromatin contacts have been found throughout the human genome and in different cell types, spatial transcriptional control is now vi ..."
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Background: Longrange interactions between regulatory DNA elements such as enhancers, insulators and promoters play an important role in regulating transcription. As chromatin contacts have been found throughout the human genome and in different cell types, spatial transcriptional control is now viewed as a general mechanism of gene expression regulation. Chromosome Conformation Capture Carbon Copy (5C) and its variant HiC are techniques used to measure the interaction frequency (IF) between specific regions of the genome. Our goal is to use the IF data generated by these experiments to computationally model and analyze threedimensional chromatin organization. Results: We formulate a probabilistic model linking 5C/HiC data to physical distances and describe a Markov chain Monte Carlo (MCMC) approach called MCMC5C to generate a representative sample from the posterior distribution over structures from IF data. Structures produced from parallel MCMC runs on the same dataset demonstrate that our MCMC method mixes quickly and is able to sample from the posterior distribution of structures and find subclasses of structures. Structural properties (base looping, condensation, and local density) were defined and their distribution measured across the ensembles of structures generated. We applied these methods to a biological model of human myelomonocyte cellular differentiation and identified distinct chromatin conformation