The RNA folding map, understood as the relationship between sequences and secondary structures or shapes, exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are realized much more...

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...

Understanding the relationship between genotype and phenotype is essential for understanding evolutionary dynamics. RNA is an extremely simple yet highly instructive case: both genotype (sequence) and phenotype (structure) are different aspects of a single molecule. The influence of the generic...

RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype-phenotype map in which concepts like plasticity, evolvability, epistasis and modularity not only can be precisely defined and statistically measured, but reveal simultaneous...

RNA folding is viewed as a map assigning secondary structures to sequences. At fixed chain length the number of sequences exceeds by far the number of structures. Frequencies of structures are highly non-uniform: we find relatively few common and many rare ones. Using an algorithm for inverse...

The formal structure of evolutionary theory is based upon the dynamics of alleles, individuals and populations. As such, the theory must assume the prior existence of these entities. This existence problem was recognized nearly a century ago, when DeVries (1904) stated, ``Natural selection may...

Computer codes for computation and comparison of RNA secondary structures, the {\tt 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...

We develop an abstract chemistry, implemented in a $\lambda$-calculus based modelling platform, and argue that the following features are generic to this particular abstraction of chemistry, hence would be expected to reappear if ``the tape were run twice'': (i) hypercycles of self-reproducing...

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 is exemplified by calculating the shape...

An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm performs particularly well in the vicinity of the minimum free energy. This enables the efficient approximation of statistical...