Most functional RNA molecules have characteristic secondary structures that are highly conserved in evolution. Here we present a method for computing the consensus structure of a set aligned RNA sequences taking into account both thermodynamic stability and sequence covariation. Comparison with...

Almost all RNA molecules - and consequently also almost all subsequences of a large RNA molecule - form secondary structures. The presence of secondary structure in itself therefore does not indicate any functional significance. In fact, we may not expect a conserved secondary structure for all...

We present an implementation of McCaskill's algorithm for computing the base pair probabilities of an RNA molecule for massively parallel message passing architectures. The program can be used to routinely fold RNA sequences of more than 10000 nucleotides. Applications to complete viral genomes...

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the...

A principle of stepwise maximization in the economy of the RNA folding process has been previously formulated as the principle of sequential minimization of conformational entropy loss (SMEL). This principle leads to a predictive folding algorithm rooted in an “adiabatic ansatz”. In this...

We investigate the relaxation behavior of complex systems endowed with a rugged free energy landscape from a variational perspective. We focus first on the dynamics in generic ultrametric spaces and then we specialize our generic results to a coarse-grained description of RNA folding, where...

We cast some classes of fitness landscapes as problems in spectral analysis on various Cayley graphs. In particular, landscapes derived from RNA folding are realized on Hamming graphs and analyzed in terms of Walsh transforms; assignment problems are interpreted as functions on the symmetric...

Many properties of organisms show great robustness against mutations. Whether this robustness is an evolved property or intrinsic to genetic systems is by and large unknown. An evolutionary origin of robustness would require a rethinking of key concepts in the field of molecular evolution, such...

We propose a new method for detecting conserved RNA secondary structures in a family of related RNA sequences. Our method is based on a combination of thermodynamic structure prediction and phylogenetic comparison. In contrast to purely phylogenetic methods, our algorithm can be used for small...