Scaling and hierarchical structures in DNA sequences

A method of analyzing DNA correlation structure is introduced. Density fluctuations of nucleotides are shown to display an extended self-similarity scaling when the scale varies between 100 and 8000 base pairs. The scaling is accurately described by a hierarchical structure model of She and Leveque [Phys. Rev. Lett. 72, 336 (1994)]]. The derived model parameter beta is able to quantify moderately large-scale correlations which exist in a true DNA sequence but are absent in its randomly shuffled sequence and in a simulated model sequence by an evolution model of Hsieh et al. [Phys. Rev. Lett. 90, (2003)]]. Finally, it is shown that beta varies with the evolution category and measures the organizational complexity of the genome.