Protein motif retrieval through secondary structure spatial co-occurences

The Generalized Hough Transform (GHT) allows to recognize general patterns once defined a model to be recognized, a reference point (RP) rigid with the model, and a mapping rule. This rule establishes the contributions in the parameters space; this space, generally speaking, is given by the parameters of a rigid motion leading to overlap a model item with an equal item detected on the unknown pattern. In this paper we discuss a particular implementation of the GHT applied to structural blocks retrieval into a protein data base. The spatial distribution of rigid arrangement of protein secondary structures (SSs) constitutes the items supporting the contributions. Starting from the co-occurrence of two not necessarily homogeneous SSs (two helices, one helix and one strand, or a β-sheet composed of two or more β-strands parallel or antiparallel) the approach can be generalized easily up to an entire motif composed of a few SSs. The main characteristic of this approach is that even for a simple couple of SSs, the mapping rule is reduced to a single location for the RP for each analogous couple found in the unknown pattern. This reduces very much the contributions (and then the signal-to-noise ratio) on the parameter space and simplifies the implementation and data structure, obviously with the drawback of a more elaborated pre-analysis.