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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 482 (93 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.
D.: Simple fast algorithms for the editing distance between trees and related problems
 SIAM J. Comput
, 1989
"... Abstract. Ordered labeled trees are trees in which the lefttoright order among siblings is. significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree ..."
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Cited by 315 (10 self)
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Abstract. Ordered labeled trees are trees in which the lefttoright order among siblings is. significant. The distance between two ordered trees is considered to be the weighted number of edit operations (insert, delete, and modify) to transform one tree to another. The problem of approximate tree matching is also considered. Specifically, algorithms are designed to answer the following kinds of questions: 1. What is the distance between two trees? 2. What is the minimum distance between T and T when zero or more subtrees can be removed from T2 3. Let the pruning of a tree at node n mean removing all the descendants of node n. The analogous question for prunings as for subtrees is answered. A dynamic programming algorithm is presented to solve the three questions in sequential time O(I Tll x IT2lxmin (depth ( Tt), leaves ( T)) x min (depth(T2), leaves(T2))) and space O(Ir, x lT21) compared with o(I T,I IT=I x(depth(T)): x (depth(T2))) for the best previous published algorithm due to Tai [J. Assoc. Comput. Mach., 26 (1979), pp. 422433]. Further, the algorithm presented here can be parallelized to give
Matching Hierarchical Structures Using Association Graphs
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453 ..."
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Cited by 172 (26 self)
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this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453
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 81 (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.
Computing the editdistance between unrooted ordered trees
 In Proceedings of the 6th annual European Symposium on Algorithms (ESA
, 1998
"... Abstract. An ordered tree is a tree in which each node’s incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, ..."
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Cited by 81 (0 self)
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Abstract. An ordered tree is a tree in which each node’s incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. WegiveanO(n 3 log n) algorithm to compute the edit distance between two ordered trees. 1
A MemoryEfficient Dynamic Programming Algorithm for Optimal Alignment of a Sequence to an RNA Secondary Structure
, 2002
"... Background: Covariance models (CMs) are probabilistic models of RNA secondary structure, analogous to profile hidden Markov models of linear sequence. The dynamic programming algorithm for aligning a CM to an RNA sequence of length N is O(N³) in memory. This is only practical for small RNAs ..."
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Cited by 78 (6 self)
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Background: Covariance models (CMs) are probabilistic models of RNA secondary structure, analogous to profile hidden Markov models of linear sequence. The dynamic programming algorithm for aligning a CM to an RNA sequence of length N is O(N&sup3;) in memory. This is only practical for small RNAs. Results:...
Analysis of RNA Sequence Structure Maps by Exhaustive Enumeration
, 1996
"... Global relations between RNA sequences and secondary structues are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of all GC and AU sequences with chain lengths up to 30. The technique od tries is used for economic data storage and f ..."
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Cited by 72 (34 self)
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Global relations between RNA sequences and secondary structues are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of all GC and AU sequences with chain lengths up to 30. The technique od tries is used for economic data storage and fast retrieval of information. The computed structural data are evaluated through exhaustive enumeration and used as an exact reference for testing analytical results derived from mathematical models and sampling based of statistical methods. Several new concepts of RNA sequence to secondary structure mappings are investigated, among them the structure of neutral networks (being sets of sequences folding into the same structure), percolation of sequence space by neutral networks, and the principle of shape space covering . The data of exhaustive enumeration are compared to the analytical results of a random graph model that reveals the generic properties of sequence to structure mappings based on some base pairing logic. The differences between the numerical and the analytical results are interpreted in terms of specific biophysical properties of RNA molecules.
Local similarity in RNA secondary structures
, 2003
"... We present a systematic treatment of alignment distance and local similarity algorithms on trees and forests. We build upon the tree alignment algorithm for ordered trees given by Jiang et. al (1995) and extend it to calculate local forest alignments, which is essential for finding local similar reg ..."
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Cited by 72 (2 self)
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We present a systematic treatment of alignment distance and local similarity algorithms on trees and forests. We build upon the tree alignment algorithm for ordered trees given by Jiang et. al (1995) and extend it to calculate local forest alignments, which is essential for finding local similar regions in RNA secondary structures. The time complexity of our algorithm is O(F1  ·F2  ·deg(F1) · deg(F2) · (deg(F1) +deg(F2)) where Fi  is the number of nodes in forest Fi and deg(Fi) is the degree of Fi. We provide carefully engineered dynamic programming implementations using dense, twodimensional tables which considerably reduces the space requirement. We suggest a new representation of RNA secondary structures as forests that allow reasonable scoring of edit operations on RNA secondary structures. The comparison of RNA secondary structures is facilitated by a new visualization technique for RNA secondary structure alignments. Finally, we show how potential regulatory motifs can be discovered solely by their structural preservation, and independent of their sequence conservation and position.
A General Edit Distance between RNA Structures
, 2001
"... Arcannotated sequences are useful in representing the structural information of RNA sequences. ..."
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Cited by 72 (0 self)
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Arcannotated sequences are useful in representing the structural information of RNA sequences.
RNA Folding and Combinatory Landscapes
, 1993
"... In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum free energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structur ..."
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Cited by 71 (29 self)
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In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum free energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable nonscalar "landscape", where a sequence space is mapped into a space of discrete "shapes". We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum free energy structure is found within a small neighborhood of any random sequence. The...