The Transformation Distance

Evolution operates molecular alterations of two types: punctual mutations, namely insertion, deletion or substitution of one residue, and segment-based modi cations: duplication, displacement, deletion or insertion of a segment of the molecule. Up to now, distance or dissimilarity measures used to compare sequences consider only punctual mutations. To our knowledge, no measure attempts to quantify dissimilarity by assessing segment-based di erences, nor by describing the di erences between two sequences with an edit-script containing such segment operations. Consequently, sequence comparison is often performed on similar parts of the sequences, like structurally or functionally related domains of proteins. Even if they correspond to complete biological entities like whole gene or protein, entire sequences are not compared, or only in case of high similarity. With such restrictions, one forgets some evolutionary meaningful informations written in the molecules.