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...

We present a method for approximating a fitness landscapes as a superposition of "elementary" landscapes. Given a correlation function of the landscape in question we show that the relative amplitudes of contributions with P-ary interactions can be computed. We show an application to RNA free...

The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles and W and shorter cycles. It is shown that each minimum cycle basis contains the same number of...

We show that the problem of designing RNA sequences that can fold into multiple stable secondary structures can be transformed into a combinatorial optimization problem that can be solved by means of simple heuristics. Hence it is feasible to design RNA switches with prescribed strucutral...

The theory of autocatalytic binary ligation is reviewed within the context of a rigorously applied Michaelis-Menten quasi-steady-state approximation to obtain explicit analytical results describing time-course data from experiments. A detailed protocol for the step-wise elucidation of a minimal...

Synthesis of random libraries of polynucleotide sequences has become a standard procedure of biotechnology; in combination with amplification methods such as the polymerase chain reaction (PCR) [1] this allows for selection experiments in which large pools of sequences are screened for a...

Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of structure. Two classes of biopolymers, RNA molecules and proteins are considered in detail. A general...

A class of autocatalytic reaction networks based on template dependent ligation and higher order catalysis is analyzed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The over-all dynamics...

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 prediction of the complete matrix of base pairing probabilities was applied to the 3' non-coding region (NCR) of flavivirus genomes. This approach identifies not only well-defined secondary structure elements but also regions of high structural flexibility. Flaviviruses, many of which are...