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...

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...

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...

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...

Algorithms predicting RNA secondary structures based on different folding criteria---minimum free energy (mfe), kinetic folding (kin), maximum matching (mm)---and different parameter sets are studied systematically. Two base pairing alphabets were used: the binary GC and the natural four-letter...

The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a ``fitness'' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by...

Some global dynamical properties of catalytic networks, in particular permanence, are closely related with a directed graph representing the differential equation. It can be shown that for every directed graph with a Hamiltonian circuit there is a choice of rate constants such that the system is...