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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.
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 79 (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.
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.
Landscapes  Complex Optimization Problems and Biopolymer Structures
 Computers Chem
, 1993
"... The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical ..."
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Cited by 31 (16 self)
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The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical measures like number of optima, lengths of walks, and correlation functions. The evolution of a quasispecies on such landscapes exhibits three dynamical regimes depending on the replication fidelity: Above the "localization threshold" the population is centered around a (local) optimum. Between localization and "dispersion threshold" the population is still centered around a consensus sequence, which, however, changes in time. For very large mutation rates the population spreads in sequence space like a gas. The critical mutation rates separating the three domains depend strongly on characteristics properties of the fitness landscapes. Statistical characteristics of RNA landscapes are acces...
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 ...
Discrete Models of Biopolymers
, 2000
"... Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the sequencestructure relationships. We review the combinatorics of nucleic acid secondary structures as wel ..."
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Cited by 14 (5 self)
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Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the sequencestructure relationships. We review the combinatorics of nucleic acid secondary structures as well as lattice models of proteins, and show how properties such as the existence of extended neutral networks or shape space covering can be explained on this basis.
RNA Secondary Structures: A Tractable Model of Biopolymer Folding
 Approach to Biopolymers and Protein Folding
, 1998
"... RNA secondary structures provide a suitable model system for studying the thermodynamics and kinetics of biopolymer folding. In contrast to models of protein folding of comparable complexity, the ground state structure as well as most thermodynamic quantities of interest, such as partition function ..."
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Cited by 9 (1 self)
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RNA secondary structures provide a suitable model system for studying the thermodynamics and kinetics of biopolymer folding. In contrast to models of protein folding of comparable complexity, the ground state structure as well as most thermodynamic quantities of interest, such as partition function and density of states can be calculated by efficient algorithms in polynomial time. For small RNA molecules, up to as few hundred bases, the kinetics of folding can be studied in Monte Carlo type simulations. As an example application, we consider the effect of modified bases in tRNA molecules.
Exact Folding Dynamics of RNA Secondary Structures
"... Barrier trees consisting of local minima and their connecting saddle points imply a natural coarsegraining for the description of the energy landscape of RNA secondary structures. Here we show that, based on this approach, it is possible to predict the folding behavior of RNA molecules by numerical ..."
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Cited by 9 (4 self)
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Barrier trees consisting of local minima and their connecting saddle points imply a natural coarsegraining for the description of the energy landscape of RNA secondary structures. Here we show that, based on this approach, it is possible to predict the folding behavior of RNA molecules by numerical integration. Comparison with stochastic folding simulations shows reasonable agreement of the resulting folding dynamics and a drastic increase in computational efficiency that makes it possible to investigate the folding dynamics of RNA of at least tRNA size. Our approach is readily applicable to bistable RNA molecules and promises to facilitate studies on the dynamic behavior of RNA switches.
The GS (Genetic Selection) Principle
 Front. Biosci. 2009
"... 3. Where selection must occur 4. The requirements of selection ..."
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Cited by 4 (1 self)
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3. Where selection must occur 4. The requirements of selection