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215
The Vienna RNA Secondary Structure Server
 Nucleic Acids Res
, 2003
"... The Vienna RNA secondary structure server provides a web interface to the most frequently used functions of the Vienna RNA software package for the analysis of RNA secondary structures. It currently o#ers prediction of secondary structure from a single sequence, prediction of the consensus secondary ..."
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Cited by 611 (23 self)
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The Vienna RNA secondary structure server provides a web interface to the most frequently used functions of the Vienna RNA software package for the analysis of RNA secondary structures. It currently o#ers prediction of secondary structure from a single sequence, prediction of the consensus secondary structure for a set of aligned sequences, and the design of sequences that will fold into a predefined structure.
PF: Secondary structure prediction for aligned RNA sequences.
 J Mol Biol
, 2002
"... Most functional RNA molecules have characteristic secondary structures that are highly conserved in evolution. Here we present a method for computing the consensus structure of a set aligned RNA sequences taking into account both thermodynamic stability and sequence covariation. Comparison with phy ..."
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Cited by 331 (43 self)
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Most functional RNA molecules have characteristic secondary structures that are highly conserved in evolution. Here we present a method for computing the consensus structure of a set aligned RNA sequences taking into account both thermodynamic stability and sequence covariation. Comparison with phylogenetic structures of rRNAs shows that a reliability of prediction of more than 80% is achieved for only five related sequences. As an application we show that the Early Noduline mRNA contains significant secondary structure that is supported by sequence covariation.
A statistical sampling algorithm for RNA secondary structure prediction
 Nucleic Acids Res
, 2003
"... An RNA molecule, particularly a longchain mRNA, may exist as a population of structures. Furthermore, multiple structures have been demonstrated to play important functional roles. Thus, a representation of the ensemble of probable structures is of interest. We present a statistical algorithm to sa ..."
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Cited by 171 (10 self)
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An RNA molecule, particularly a longchain mRNA, may exist as a population of structures. Furthermore, multiple structures have been demonstrated to play important functional roles. Thus, a representation of the ensemble of probable structures is of interest. We present a statistical algorithm to sample rigorously and exactly from the Boltzmann ensemble of secondary structures. The forward step of the algorithm computes the equilibrium partition functions of RNA secondary structures with recent thermodynamic parameters. Using conditional probabilities computed with the partition functions in a recursive sampling process, the backward step of the algorithm quickly generates a statistically representative
Sfold web server for statistical folding and rational design of nucleic acids
 Nucleic Acids Res
, 2004
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Plasticity, evolvability, and modularity in RNA
 J EXP ZOOL
, 2000
"... RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneou ..."
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Cited by 102 (3 self)
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RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneous and profoundly nonindependent effects of natural selection. Molecular plasticity is viewed here as the capacity of an RNA sequence to assume a variety of energetically favorable shapes by equilibrating among them at constant temperature. Through simulations based on experimental designs, we study the dynamics of a population of RNA molecules that evolve toward a predefined target shape in a constant environment. Each shape in the plastic repertoire of a sequence contributes to the overall fitness of the sequence in proportion to the time the sequence spends in that shape. Plasticity is costly, since the more shapes a sequence can assume, the less time it spends in any one of them. Unsurprisingly, selection leads to a reduction of plasticity (environmental canalization). The most striking observation, however, is the simultaneous slowdown and eventual halting of the evolutionary process. The reduction of plasticity entails genetic canalization, that is, a dramatic loss of variability (and hence a loss of evolvability) to the point of lockin. The causal bridge between environmental canalization and genetic canalization
Abstract shapes of RNA
 Nucleic Acids Res
, 2004
"... The function of a nonproteincoding RNA is often determined by its structure. Since experimental determination of RNA structure is timeconsuming and expensive, its computational prediction is of great interest, and efficient solutions based on thermodynamic parameters are known. Frequently, howeve ..."
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Cited by 65 (13 self)
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The function of a nonproteincoding RNA is often determined by its structure. Since experimental determination of RNA structure is timeconsuming and expensive, its computational prediction is of great interest, and efficient solutions based on thermodynamic parameters are known. Frequently, however, the predicted minimum free energy structures are not the native ones, leading to the necessity of generating suboptimal solutions. While this can be accomplished by a number of programs, the user is often confronted with large outputs of similar structures, although he or she is interested in structures with more fundamentaldifferences,or, inotherwords, with different abstract shapes. Here, we formalize the concept of abstract shapes and introduce their efficient computation. Each shape of an RNA molecule comprises a class of similar structures and has a representative structure of minimal free energy within the class. Shape analysis is implemented in the program RNAshapes. We applied RNAshapes to the prediction of optimal and suboptimal abstract shapes of severalRNAs.For a given energy range, the number of shapes is considerably smaller than the number of structures, and in all cases, the native structures were among the top shape representatives. This demonstrates that the researcher can quickly focus on the structures of interest, without processing up to thousands of nearoptimal solutions. We complement this study with a largescale analysis of the growth behaviour of structure and shape spaces. RNAshapes is available for download and as an online version on the Bielefeld Bioinformatics Server.
Thermodynamics of RNARNA Binding
, 2005
"... Background: Reliable predictions of RNARNA binding energies is crucial e.g. for the understanding on RNAi, microRNAmRNA binding, and antisense interactions. The thermodynamics of such RNARNA interactions can be understood as the sum of two energy contributions: (1) the energy necessary to “open ” ..."
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Cited by 63 (13 self)
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Background: Reliable predictions of RNARNA binding energies is crucial e.g. for the understanding on RNAi, microRNAmRNA binding, and antisense interactions. The thermodynamics of such RNARNA interactions can be understood as the sum of two energy contributions: (1) the energy necessary to “open ” the binding site, and (2) the energy gained from hybridization. Methods: We present an extension of the standard partition function approach to RNA secondary structures that computes the probabilities Pu[i, j] that a sequence interval [i, j] is unpaired. Results: Comparison with experimental data shows that Pu[i, j] can be applied as a significant determinant of local target site accessibility for RNA interference (RNAi). Furthermore, these quantities can be used to rigorously determine binding free energies of short oligomers to large mRNA targets. The resource consumption is comparable to a single partition function computation for the large target molecule. We can show that RNAi efficiency correlates well with the binding energies of siRNAs to their respective mRNA target.
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 52 (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.
Barrier Trees of Degenerate Landscapes
, 2001
"... The heights of energy barriers separating two (macro)states are useful for estimating transition frequencies. In nondegenerate landscapes the decomposition of a landscape into basins surrounding local minima connected by saddle points is straightforward and yields a useful definition of macrostat ..."
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Cited by 52 (28 self)
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The heights of energy barriers separating two (macro)states are useful for estimating transition frequencies. In nondegenerate landscapes the decomposition of a landscape into basins surrounding local minima connected by saddle points is straightforward and yields a useful definition of macrostates. In this work we develop a rigorous concept of barrier trees for degenerate landscapes. We present a program that efficiently computes such barrier trees, and apply it to two well known examples of landscapes. Keywords: Fitness landscape, Potential energy surface, energy barrier, saddle points, degenerate states Dedicated to Peter Schuster on the occasion of his 60th birthday.
P.: A discipline of dynamic programming over sequence data
 Science of Computer Programming
, 2004
"... Abstract. Dynamic programming is a classical programming technique, applicable in a wide variety of domains such as stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing of ambiguous languages, and biosequence analysis. Little methodology has ..."
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Cited by 46 (24 self)
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Abstract. Dynamic programming is a classical programming technique, applicable in a wide variety of domains such as stochastic systems analysis, operations research, combinatorics of discrete structures, flow problems, parsing of ambiguous languages, and biosequence analysis. Little methodology has hitherto been available to guide the design of such algorithms. The matrix recurrences that typically describe a dynamic programming algorithm are difficult to construct, errorprone to implement, and, in nontrivial applications, almost impossible to debug completely. This article introduces a discipline designed to alleviate this problem. We describe an algebraic style of dynamic programming over sequence data. We define its formal framework, based on a combination of grammars and algebras, and including a formalization of Bellman’s Principle. We suggest a language used for algorithm design on a convenient level of abstraction. We outline three ways of implementing this language, including an embedding in a lazy functional language. The workings of the