Graph Theoretic Aspects of Biopolymer Structures

This project is really a collection of different research agenda. The common theme is a coarse grained representation of biopolymers which is conveniently represented as a graph. Examples are the secondary structures of nucleic acids or contact structures of proteins.
Many important RNA molecules contain pseudo-knots, which are excluded explicitly by the definition of secondary structures. Recently we have introduced a generalization that incorporates ``non-nested'' pseudo-knots and a measure of the structural complexity for general contact structures that is related to chromatic number of the associated so-called intersection graphs. For the simplest class of structures beyond secondary structures we have obtained some combinatorial results, for instance upper bounds on the number of possible structures.
Another line of investigation is concerned with cycle bases of contact structures. This is motivated by the fact that the energy model of RNA secondary structure formation is based on the (unique) minimal cycle basis of the secondary structure graphs. Meanwhile, this line of reasearch has developed away from biopolymers, see here.
Yet another topic is the search for good measures of structure distances for different types of biopolymers.