Characterization of DNA primary sequences based on the average distances between bases

We outline numerical characterization of DNA primary sequence based on calc ulation of the average distance between pairs of nucleic acid bases. This l eads to a representation of DNA by a condensed 4 x 4 symmetrical matrix, th e elements of which give the average separation between pair of bases X, Y in DNA (X, Y = A, C, G, T). As an invariant of choice we consider the leadi ng eigenvalue of the derived 4 x 4 matrix. Additional structurally related invariants were obtained by constructing additional "higher order" 4 x 4 ma trices derived from the initial 4 x 4 matrix by raising its elements to hig her powers. Suitably normalized leading eigenvalue of these matrices offer a novel characterization of DNA primary sequences, referred to as "DNA prof iles". The approach is illustrated on exon 1 of human beta -globin gene.