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Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package)
"... Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and bas ..."
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Cited by 473 (90 self)
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Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities. An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment. All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.
Landscapes and Their Correlation Functions
, 1996
"... Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive const ..."
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Cited by 89 (15 self)
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Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive constant) eigenfuctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.
Generic Properties of Combinatory Maps  Neutral Networks of RNA Secondary Structures
, 1995
"... Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of any ..."
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Cited by 80 (36 self)
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Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of any two different structures almost touch each other, and sequences folding into almost all "common" structures can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared with data obtained by folding large samples of RNA sequences. Differences are explained in terms of RNA molecular structures. 1.
Evolutionary Dynamics and Optimization  Neutral Networks as ModelLandscapes for RNA SecondaryStructure FoldingLandscapes
, 1995
"... We view the folding of RNAsequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure s). By interpreting the secondary structure as biological i ..."
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Cited by 26 (6 self)
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We view the folding of RNAsequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure s). By interpreting the secondary structure as biological information we can formulate the so called Error Threshold of Shapes as an extension of Eigen's et al. concept of an error threshold in the single peak landscape [5]. Analogue to the approach of Derrida & Peliti [3] for a flat landscape we investigate the spatial distribution of the population on the neutral network. On the one hand this model of a single shape landscape allows the derivation of analytical results, on the other hand the concept gives rise to study various scenarios by means of simulations, e.g. the interaction of two different networks [29]. It turns out that the intersection of two sets of compatible sequences (with respect to the pair of secondary structures) plays a key role in the search for "fitter" secondary structures.
Neutral Networks in Protein Space  A Computational Study Based on KnowledgeBased Potentials of Mean Force
, 1997
"... Background: Protein space is explored by means of an inverse folding procedure that makes use of knowledgebased potentials of mean force. Results: Computer simulations indicate that amino acid sequences folding into a common shape are distributed homogeneously forming extended percolating networks ..."
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Cited by 25 (14 self)
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Background: Protein space is explored by means of an inverse folding procedure that makes use of knowledgebased potentials of mean force. Results: Computer simulations indicate that amino acid sequences folding into a common shape are distributed homogeneously forming extended percolating networks that span the entire sequence space. Conclusions: The existence of very long neutral paths on all examined protein structures, indicates the existence of neutral networks percolating protein space. The same qualitative results were obtained for some, but not all, restricted amino acid alphabets. In this respect, the sequencestructure map of proteins seems to be very similar to the nucleic acid case.
RNA Structures with PseudoKnots  GraphTheoretical and Combinatorial Properties
, 1997
"... Secondary structures of nucleic acids are a particularly interesting class of contact structures. Many important RNA molecules contain pseudoknots, which are excluded explicitly by the definition of secondary structures. We propose here a generalization of secondary structures that incorporates "non ..."
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Cited by 24 (7 self)
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Secondary structures of nucleic acids are a particularly interesting class of contact structures. Many important RNA molecules contain pseudoknots, which are excluded explicitly by the definition of secondary structures. We propose here a generalization of secondary structures that incorporates "nonnested" pseudoknots. We also introduce a measure for the complexity of more general contact structures in terms of the chromatic number of their intersection graph. We show that RNA structures without nested pseudoknots form a special class of planar graphs. Upper bounds on their number are derived, showing that there are fewer different structures than sequences. 1. Introduction Presumably the most important problem and the greatest challenge in present day theoretical biophysics is deciphering the code that transforms sequences of biopolymers into spatial molecular structures. A sequence is properly visualized as a string of symbols which together with the environment encodes the molecul...
Combinatorics of RNA structures with pseudoknots. Bull.Math.Biol
 Bull.Math.Biol
, 2007
"... Abstract. In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all knoncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate pseudoknot structures over circular RNA. For 3noncrossing ..."
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Cited by 20 (15 self)
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Abstract. In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all knoncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate pseudoknot structures over circular RNA. For 3noncrossing RNA structures and RNA secondary structures we present a novel 4term recursion formula and a 2term recursion, respectively. Furthermore we enumerate for arbitrary k all knoncrossing, restricted RNA structures i.e. knoncrossing RNA structures without 2arcs i.e. arcs of the form (i, i + 2), for 1 ≤ i ≤ n − 2. 1.
Molecular Insights into Evolution of Phenotypes
, 2000
"... re analyzed for RNA secondary structures. Optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of an uninterrupted series of phenotypes from ..."
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Cited by 20 (8 self)
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re analyzed for RNA secondary structures. Optimization of molecular properties in populations is modeled in silico through replication and mutation in a flow reactor. The approach towards a predefined structure is monitored and reconstructed in terms of an uninterrupted series of phenotypes from initial stucture to target, called relay series. We give a novel definition of continuity in evolution which identifies discontinuities as major changes in molecular phenotypes. Evolutionary Dynamics  Exploring the Interplay of Accident, Selection, Neutrality, and Function Edited by J. P. Crutchfield and P. Schuster, Oxford Univ. Press 1 2 Evolution of Phenotypes 1 GENOTYPES AND PHENOTYPES Evolutionary optimization in asexually multiplying populations follows Darwin 's principle and is determined by the interplay of two processes which exert counteracting influences on genetic heterogeneity: (i) Mutations increase di
RNA Structures with Pseudoknots
, 1997
"... i Abstract Secondary structures of nucleic acids are a particularly interesting class of contact structures. Many important RNA molecules,however contain pseudoknots, which are excluded explicitly by the definition of secondary structures. We propose here a generalization of secondary structures th ..."
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Cited by 18 (1 self)
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i Abstract Secondary structures of nucleic acids are a particularly interesting class of contact structures. Many important RNA molecules,however contain pseudoknots, which are excluded explicitly by the definition of secondary structures. We propose here a generalization of secondary structures that incorporates "nonnested" pseudoknots. We also introduce a measure for the complexity of more general contact structures in terms of the chromatic number of their intersection graph. We show that RNA structures without nested pseudoknots form a special class of planar graphs, the so called "bisecondary structures". Upper bounds on their number are derived, showing that there are fewer different structures than sequences. An energy function capable of dealing with bisecondary structures was implemented into a generalized kinetic folding algorithm. Sterical hindrances involved in pseudoknot formation are taken into account with the help of two simplifications: stacked regions are viewed ...