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)},...

In many cases fitness landscapes are obtained as particular instances of random fields by assigning a large number of random parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of...

Fitness landscapes are an important concept in molecular evolution since evolutionary adaptation as well as {\it in vitro} selection of biomolecules can be viewed as a hill-climbing-like process. Global features of landscapes can be described by statistical measures such as correlation functions...

We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are extensively probed by analysing the response of the packing...

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...

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...