Analysis of secondary structure elements of proteins using indexing techniques

In this paper we present a method for protein structure comparison that is based on indexing. Unlike most methods using indexing, ours does not use invariants of the C_α atoms of the proteins, rather it relies on geometric properties of the secondary structures. Given a set of protein structures, we compute the angles and distances of all the triplets of linear segments associated to the secondary structures of the proteins and use them to build hash tables. The hash tables can be used for fast retrieval of hypotheses of matches of a query protein against the database. We present and analyze the tables obtained for two separate sets of proteins that are representatives of all the folds in the PDB. The tables show an interesting distribution of the triplets of elements, especially if one takes into account that the elements of a triplet are generally not close in space. The majority of the elements are found to belong to two planar regions in the three-dimensional tables. The planar regions can be characterized as those whose corresponding triplets of structures lie on almost parallel planes.