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BASES OF MOTIFS FOR GENERATING REPEATED PATTERNS WITH WILD CARDS structuring such input. Yet, it appeared clear also to any computational biologist working with motifs as patterns that there was further structure to be extracted from the set of motifs found, even when such a set is huge. Furthermore, such a structure could reflect some additional biological information, thus providing additional motivation for inferring it. Doing this is generally addressed by means of clustering, or even by attempting to bring together the two types of motif models (PSSMs and patterns).
Indeed, variability may be considered part of their function. Such variability translates itself into changes in the motif, mostly substitutions, that do not affect the biological function. Two main schools of thought on how to define motifs in biology have coexisted for years, each valid in its own way. The first works with a statistical representation of motifs, usually given in the form of what is called in the literature a PSSM (“Position Specific Scoring Matrix” , , ,  or a profile which is one type of PSSM).
In particular, we consider a promising idea that was recently proposed, which attempted to avoid the combinatorial explosion in the number of motifs by means of a generator set for the motifs. Instead of exhibiting a complete list of motifs satisfying some input constraints, what is produced is a basis of such motifs from which all the other ones can be generated. We study the computational cost of determining such a basis of repeated motifs with wild cards in a sequence. We give new upper and lower bounds on such a cost, introducing a notion of basis that is provably contained in (and, thus, smaller) than previously defined ones.
IEEE Transactions on Computational Biology and Bioinformatics (January-March)