Results 1  10
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158
CONTRAfold: RNA secondary structure prediction without physicsbased models
 Bioinformatics
, 2006
"... doi:10.1093/bioinformatics/btl246 ..."
The language of RNA: A formal grammar that includes pseudoknots
 Bioinformatics
"... Motivation: In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking. Results: Here we show a one ..."
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Cited by 60 (1 self)
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Motivation: In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking. Results: Here we show a onetoone correspondence between that algorithm and a formal transformational grammar. This grammar class encompasses the contextfree grammars and goes beyond to generate pseudoknotted structures. The pseudoknot grammar avoids the use of general contextsensitive rules by introducing a small number of auxiliary symbols used to reorder the strings generated by an otherwise contextfree grammar. This formal representation of the residue correlations in RNA structure is important because it means we can build full probabilistic models of RNA secondary structure, including pseudoknots, and use them to optimally parse sequences in polynomial time. Contact: eddy@genetics.wustl.edu 1 ...
An Iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots
, 2004
"... Motivation: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On ..."
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Cited by 53 (2 self)
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Motivation: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On the other hand, comparative methods are more reliable, but are often done in an ad hoc manner and require expert intervention. Maximum weighted matching, an algorithm for pseudoknot prediction with comparative analysis, suffers from lowprediction accuracy in many cases.
A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences
, 2004
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Exploring the repertoire of rna secondary motifs using graph theory; implications for rna design
 Nucleic Acids Res
, 2003
"... Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for ®nding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a twodimensional graphical representation approach for describing and estimati ..."
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Cited by 39 (9 self)
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Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for ®nding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a twodimensional graphical representation approach for describing and estimating the size of RNA's secondary structural repertoire, including naturally occurring and other possible RNA motifs. We employ tree graphs to describe RNA tree motifs and more general (dual) graphs to describe both RNA tree and pseudoknot motifs. Our estimates of RNA's structural space are vastly smaller than the nucleotide sequence space, suggesting a new avenue for ®nding novel RNAs. Speci®cally our survey shows that known RNA trees and pseudoknots represent only a small subset of all possible motifs, implying that some of the `missing ' motifs may represent novel RNAs. To help pinpoint RNAlike motifs, we show that the motifs of existing functional RNAs are clustered in a narrow range of topological characteristics. We also illustrate the applications of our approach to the design of novel RNAs and automated comparison of RNA structures; we report several occurrences of RNA motifs within larger RNAs. Thus, our graph theory approach to RNA structures has implications for RNA genomics, structure analysis and design.
Partition function and base pairing probabilities of RNA heterodimers
 Algorithms Mol Biol
, 2006
"... Abstract Background: RNA has been recognized as a key player in cellular regulation in recent years. In many cases, noncoding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inte ..."
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Cited by 37 (9 self)
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Abstract Background: RNA has been recognized as a key player in cellular regulation in recent years. In many cases, noncoding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of intermolecular base pairing. The accurate computational treatment of RNARNA binding therefore lies at the heart of target prediction algorithms. Methods: The standard dynamic programming algorithms for computing secondary structures of linear singlestranded RNA molecules are extended to the cofolding of two interacting RNAs. Results: We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures.
Pseudoknots in RNA Secondary Structures
 In RECOMB00: Proceedings of the Fourth Annual International Conference on Computational Molecular Biology
, 1999
"... RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g. as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactory in polynomial time. Most ..."
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Cited by 36 (1 self)
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RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g. as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactory in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots introduce modeling and computational problems. In this paper we consider the problem of predicting RNA secondary structure when certain types of pseudoknots are allowed. We rst present an algorithm that in time O(n 5 ) and space O(n 3 ) predicts the secondary structure of an RNA sequence of length n in a model that allows certain kinds of pseudoknots. We then prove that the general problem of predicting RNA secondary structure containing pseudoknots is NPcomplete for a large class of reasonable models of pseudoknots. 1 Introduction An RNA molecule is a sequence of nucleotides that of...
Thermodynamic analysis of interacting nucleic acid strands
 SIAM Rev
, 2007
"... Abstract. Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary stru ..."
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Cited by 31 (4 self)
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Abstract. Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for singlestranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium basepairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality.
A New Algorithm for RNA Secondary Structure Design
, 2003
"... The function of many RNAs crucially depends on their structure. Therefore, the design of RNA molecules with specific structural properties has many potential applications, e.g.,in the context of investigating the function of biological RNAs, of creating new ribozymes, or of designing artificial RNA ..."
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Cited by 29 (2 self)
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The function of many RNAs crucially depends on their structure. Therefore, the design of RNA molecules with specific structural properties has many potential applications, e.g.,in the context of investigating the function of biological RNAs, of creating new ribozymes, or of designing artificial RNA nanostructures. Here, we present a new algorithm for solving the following RNA secondary structure design problem: Given a secondary structure, find an RNA sequence (if any) that is predicted to fold to that structure. Unlike the (pseudoknotfree) secondary structure prediction problem, this problem appears to be computationally hard. Our new algorithm, "RNA Secondary Structure Designer (RNASSD)", is based on stochastic local search, a prominent general approach for solving hard combinatorial problems. A thorough empirical...
Paradigms for computational nucleic acid design
 Nucleic Acids Res
"... The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCRbased applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensivelyst ..."
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Cited by 26 (3 self)
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The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCRbased applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensivelystudied thermodynamic model, we perform a detailed study of several criteria for designing sequences intended to adopt a target secondary structure. We conclude that superior design methods should explicitly implement both a positive design paradigm (optimize affinity for the target structure) and a negative design paradigm (optimize specificity for the target structure). The commonly used approaches of sequence symmetry minimization and minimum free energy satisfaction primarily implement negative design and can be strengthened by introducing a positive design component. Surprisingly, our findings hold for a wide range of secondary structures and are robust to modest perturbation of the thermodynamic parameters used for evaluating sequence quality, suggesting the feasibility and ongoing utility of a unified approach to nucleic acid design as parameter sets are further refined. Finally, we observe that designing for thermodynamic stability does not determine folding kinetics, emphasizing the opportunity for extending design criteria to target kinetic features of the energy landscape.