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 different species, and the evolutionary change in those properties was then investigated. Map patterns of a two-dimensional DNA walk showed that the stretches of exons are significantly shorter than those of introns, suggesting that the evolution of exons is driven by natural selection, whereas that of 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]), medium- (10 to 50 bp) and long-range order (50 to 300 bp) of beta-globin gene sequences could be observed, and power spectral densities of these periodicities were increased with evolution. These results suggest the existence of the internal rules in the occurrence of the synonymous and nonsynonymous substitutions in the sequences, the destabilization of the interaction between 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 increase in the self-similarity (the fractal structure) of DNA sequences with evolution. A general trend of the increase in a 3 bp periodicity with evolution might be functionally related to the CAG trinucleotide repeat diseases such as Huntington chorea, where a marked periodicity of 3 bp could be observed. Fourier transform analysis applied to a DNA sequence offers a great new avenue for extracting information on the evolution of a DNA sequence.