Implicit and Explicit Representation of Approximated Motifs

PIsanti, Nadia and Soldano, Henry and Carpentier, Mathilde and Pothier, Joel (2005) Implicit and Explicit Representation of Approximated Motifs. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

Detecting repeated 3D protein substructures has become a new crucial frontier in motifs inference. In \cite{cpm} we have suggested a possible solution to this problem by means of a new framework in which the repeated pattern is required to be conserved also in terms of relations between its position pairs. In our application these relations are the distances between $\alpha$-carbons of amino acids in 3D proteins structures, thus leading to a \emph{structural consensus} as well. In this paper we motivate some complexity issues claimed (and assumed, but not proved) in \cite{cpm} concerning inclusion tests between occurrences of repeated motifs. These inclusion tests are performed during the motifs inference in \emph{KMRoverlapR} (presented in \cite{cpm}), but also within other motifs inference tools such as \emph{KMRC} (\cite{kmrc}). These involve alternative representations of motifs, for which we also prove here some interesting properties concerning pattern matching issues. We conclude this contribution with a few tests on cytochrome P450 protein structures.