Graphical and numerical representations of DNA sequences: statistical aspects of similarity

New approaches aiming at a detailed similarity/dissimilarity analysis of DNA sequences are formulated. Several corrections that enrich the information which may be derived from the alignment methods are proposed. The corrections take into account the distributions along the sequences of the aligned bases (neglected in the standard alignment methods). As a consequence, different aspects of similarity, as for example asymmetry of the gene structure, may be studied either using new similarity measures associated with four-component spectral representation of the DNA sequences or using alignment methods with corrections introduced in this paper. The corrections to the alignment methods and the statistical distribution moment-based descriptors derived from the four-component spectral representation of the DNA sequences are applied to similarity/dissimilarity studies of β-globin gene across species. The studies are supplemented by detailed similarity studies for histones H1 and H4 coding sequences. The data are described according to the latest version of the EMBL database. The work is supplemented by a concise review of the state-of-art graphical representations of DNA sequences.