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...

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...

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...

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...

Random graph theory is used to model relationships between sequences and secondary structure of RNA molecules. Sequences folding into identical structures form neutral networks which percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value. The networks of...

Success and efficiency of Darwinian evolution is based on the dichotomy of genotype and phenotype: The former is the object under variation whereas the latter constitutes the target of selection. Genotype-phenotype relations are highly complex and hence variation and selection appear...

In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function {\it f(h)},...

Secondary structures of polynucleotides can be view as a certain class of planar vertex-labeled graphs. We construct recursion formulae enumerating various sub-classes of these graphs as well as certain structural elements (sub-graphs). First order asymptotics are derived and their dependence on...

Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of replicator type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems---$n= 2, 3 $, and 4---are discussed and complete...