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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 ..."
Abstract

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.
Statistics of RNA Melting Kinetics
, 1993
"... We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that assigns structure dependent overall rate constants of melting (or refolding) to a sequence. This induces a "landscape" ..."
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Cited by 32 (13 self)
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We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that assigns structure dependent overall rate constants of melting (or refolding) to a sequence. This induces a "landscape" of reaction rates, or activation energies, over the space of sequences with fixed length. We study the distribution and the correlation structure of these activation energies. 1. Introduction Single stranded RNA sequences fold into complex threedimensional structures. A tractable, yet reasonable, model for the map from sequences to structures considers a more coarse grained level of resolution known as the secondary structure. The secondary structure is a list of base pairs such that no pairings occur between bases located in different loop regions. Algorithms based on empirical energy data have been developed to compute the minimum free energy secondary structure of an RNA sequence (Zuker...
Approximate Scaling Properties of RNA Free Energy Landscapes
, 1996
"... RNA free energy landscapes are analyzed by means of "timeseries" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the st ..."
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Cited by 6 (2 self)
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RNA free energy landscapes are analyzed by means of "timeseries" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "timeseries". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and selfaffine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately selfaffine on time scales up to approximately the correlation length. We present an empirical relation between the correlation parameter ae of the AR(1) model and the exponents characterizing selfaffinity. Key Words RNA Folding  Excursion Sets  Fractal Landscape ...