Rescaled range and transition matrix analysis of DNA sequences

In this paper we treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping DNA sequences to integer sequences, followed by R/S analysis of the model and computation of the Hurst exponents. Second, we consider transition between the four kinds of bases within DNA. The transition matrix analysis of DNA sequences shows that some measures of complexity based on transition proportion matrix are of interest. The main results are: 1) Hexon > Hintron for virus. But Hintron > Hexon for the species which have the shape of cell except for drosophila. 2) For Virus, E. coli, yeast, drosophila, mouse and human, measures H of transition proportion matrix of exon is larger than that of intron, and measures λ, D, C, D̃ and C̃ of transition proportion matrix of intron are larger than that of exon. 3) Regarding the evolution, we find that when the species goes higher in grade, the measures D, C, D̃ and C̃ of exon become larger, the measure H of exon becomes lesser except for yeast. Hence for species of higher grade, the transition rate among the four kinds of bases goes further from the equilibrium.