Characterizing self-similarity in bacteria DNA sequences

In this paper some parametric methods are introduced to characterize the self-similarity of DNA sequences. Compared with Fourier analysis, these methods perform statistically more stably and yield more reliable results. Using these methods, eight whole genomes of bacteria provided by NCBI are analyzed. Long-range correlation properties in the nucleotide density distribution along these DNA sequences are explored. Estimation results show that the long-range correlation structure prevails through the entire molecule of DNA. Higher order statistics through coarse graining reveal that rather than multifractal, there are only monofractal phenomena presented in the sequences. Hence, the nucleotide density distribution can be modeled asymptotically as fractional Gaussian noise. This result points to a new direction for analyzing and understanding the intrinsic structures of DNA sequences.