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Abstract: A new version of DNA walks, where nucleotides are regarded unequal in their contribution to a walk is introduced, which allows us to study thoroughly the “fine structure” of nucleotide sequences. The approach is based on the assumption that nucleotides have an inner abstract characteristic, the determinative degree, which reflects genetic code phenomenological properties and is adjusted to nucleotides physical properties. We consider each codon position independently, which gives three separate walks characterized by different angles and lengths, and that such an object is called triander which reflects the “strength” of branch. A general method for identifying DNA sequence “by triander” which can be treated as a unique “genogram” (or “gene passport”) is proposed. The two- and three-dimensional trianders are considered. The difference of sequences fine structure in genes and the intergenic space is shown. A clear triplet signal in coding sequences was found which is absent in the intergenic space and is independent from the sequence length. This paper presents the topological classification of trianders which can allow us to provide a detailed working out signatures of functionally different genomic regions.

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