From Molecular to Biological Structure and Back

A comparative analysis of the topological structure of molecules and molecular biology networks revealed both similarity and differences in the methods used, as well as in the essential features of the two types of systems. Molecular graphs are static and, due to the limitations in atomic valence, show neither power distribution of vertex degrees nor "small-world" properties, which are typical for dynamic evolutionary networks. Areas of mutual benefits from an exchange of methods and ideas are outlined for the two fields. More specifically, chemical graph theory might make use of some new descriptors of network structure. Of interest for quantitative structure-property relationship/quantitative structure-activity relationship and drug design might be the conclusion that descriptors based on distributions of vertex degrees, distances, and subgraphs seem to be more relevant to biological information than the single-number descriptors. The network concepts of centrality, clustering, and cliques provide a basis for similar studies in theoretical chemistry. The need of dynamic theory of molecular topology is advocated.