Evolution of the periodicity and the self-similarity in DNA sequence: A Fourier transform analysis

Fourier transform analysis was applied to elucidate the periodical and self -similar properties in the DNA sequences mainly of beta -globin genes in di fferent species, and the evolutionary change in those properties was then i nvestigated. Map patterns of a two-dimensional DNA walk showed that the str etches of exons are significantly shorter than those of introns, suggesting that the evolution of exons is driven by natural selection, whereas that o f introns is generated by unknown internal rules. Using a monomer analysis, we obtained the power spectra of four different bases, A, G, C, and T, in DNA sequences. Periodicities in the short- (2 to 10 base pairs [bp]), mediu m- (10 to 50 bp) and long-range order (50 to 300 bp) of beta -globin gene s equences could be observed, and power spectral densities of these periodici ties were increased with evolution. These results suggest the existence of the internal rules in the occurrence of the synonymous and nonsynonymous su bstitutions in the sequences, the destabilization of the interaction betwee n DNA and histone protein, and the stabilization of the chromatin structure , respectively. Moreover, 1/f(alpha) analysis of the power spectra (log-log plot) in the far long-range region (160 to 16,000 bp) suggested the increa se in the self-similarity (the fractal structure) of DNA sequences with evo lution. A general trend of the increase in a 3 bp periodicity with evolutio n might be functionally related to the CAG trinucleotide repeat diseases su ch as Huntington chorea, where a marked periodicity of 3 bp could be observ ed. Fourier transform analysis applied to a DNA sequence offers a great new avenue for extracting information on the evolution of a DNA sequence.