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 Ca 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.
