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...

Numerical estimates for the number of local optima of p-spin Hamiltonians with p=3,4,5, and 6 are reported. The data can be explained by means of a simple estimate in terms of the "correlation length" of the Hamiltonian.

Two-connected outerplanar graphs have a unique minimal cycle basis with length $2|E|-|V|$. They are the only Hamiltonian graphs with a cycle basis of this length.

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...

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...

A particular class of ordinary differential equations (ODE) describing catalyzed, template-induced, and erroneous replication is investigated. The ODEs can be split into a replicator part accounting for the correct replication and a mutation term accounting for all miscopying processes. The set...

The dynamics of a network of autocatalytically replicating species in a continuously stirred tank reactor can be described by a replicator equation in the limit of small flux rates.