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- P Schuster, W Fontana, P F Stadler, I L Hofacker
- Proceedings. Biological sciences
- 1994

RNA folding is viewed here as a map assigning secondary structures to sequences. At fixed chain length the number of sequences far exceeds the number of structures. Frequencies of structures are highly non-uniform and follow a generalized form of Zipf's law: we find relatively few common and many rare ones. By using an algorithm for inverse folding, we show… (More)

- W Fontana, P Schuster
- Science
- 1998

To distinguish continuous from discontinuous evolutionary change, a relation of nearness between phenotypes is needed. Such a relation is based on the probability of one phenotype being accessible from another through changes in the genotype. This nearness relation is exemplified by calculating the shape neighborhood of a transfer RNA secondary structure… (More)

- S Wuchty, W Fontana, I L Hofacker, P Schuster
- Biopolymers
- 1999

An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm is particularly fast in the vicinity of the minimum free energy. This enables the efficient approximation of statistical quantities, such as the partition function or measures for structural… (More)

- C Flamm, W Fontana, I L Hofacker, P Schuster
- RNA
- 2000

We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss folding mechanisms and the correlation between the barrier structure of the conformational landscape and the folding kinetics for a number of examples based on… (More)

- W Fontana, P Schuster
- Journal of theoretical biology
- 1998

Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote equivalence classes of genotypes. The definition of neighborhood… (More)

- W Fontana, D A Konings, P F Stadler, P Schuster
- Biopolymers
- 1993

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and… (More)

- C Reidys, P F Stadler, P Schuster
- Bulletin of mathematical biology
- 1997

Random graph theory is used to model and analyse the relationships between sequences and secondary structures of RNA molecules, which are understood as mappings from sequence space into shape space. These maps are non-invertible since there are always many orders of magnitude more sequences than structures. Sequences folding into identical structures form… (More)

- J Hofbauer, P Schuster, K Sigmund
- Journal of theoretical biology
- 1979

In 1974 J. Maynard Smith introduced the fundamental notion of an evolutionarily stable strategy (ESS) in order to explain the evolution of genetically determined social behaviour within a single animal species. If the possible pure strategies for contests within a species are 1,2,. . ., ~1, and if A = (aij) is the payoff matrix, then aij is the payoff for… (More)

- C Reidys, C V Forst, P Schuster
- Bulletin of mathematical biology
- 2001

Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. The mapping is non-invertible since many sequences fold into the same minimum free energy (secondary) structure or shape. The pre-images of this map, called neutral networks, are uniquely associated with the shapes… (More)

- M Tacker, W Fontana, P F Stadler, P Schuster
- European biophysics journal : EBJ
- 1994

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… (More)