On the Similarity of DNA Primary Sequences

We consider numerical characterization of graphical representations of DNA primary sequences. In particular we consider graphical representation of DNA of beta-globins of several species, including human, on the basis of the approach of A. Nandy in which nucleic bases are associated with a walk over integral points of a Cartesian x, y-coordinate system. With a so-generated graphical representation of DNA, we associate a distance/distance matrix, the elements of which are given by the quotient of the Euclidean and the graph theoretical distances, that is, through the space and through the bond distances for pairs of bases of graphical representation of DNA. We use eigenvalues of so-constructed matrices to characterize individual DNA sequences. The eigenvalues are used to construct numerical sequences, which are subsequently used for similarity/dissimilarity analysis. The results of such analysis have been compared and combined with similarity tables based on the frequency of occurrence of pairs of bases.