Analysis of protein sheet topologies by graph theoretical methods.

In order to find rules for the secondary structure prediction of proteins which describe the (sequentially) long-range interactions in sheet structures methods of applied graph theory were used. The so called beta graph which describes the sheet topology was defined for every protein in the Brookhaven Data Bank containing beta sheets. The resemblance of proteins at that topological level is discussed, and four notations and graphic representations of sheets which describe the sequential and topological neighborhoods of the strands were derived. This description level supports the usage of data structures which allow the implementation of efficient algorithms for the analysis and comparison of beta structures in proteins. A computer program for the representation and retrieval of bibliographic data and beta sheet structures was implemented. Some examples for substructure search illustrate the usefulness of the program. Two graphic catalogues were compiled: one contains all beta graphs of PDB proteins and the other all occurring different greek key descriptions.