Statistical properties and fractals of nucleotide clusters in DNA sequences

Statistical properties of nucleotide clusters in DNA sequences and their fractals are investigated in this paper. The average size of nucleotide clusters in non-coding sequence is larger than that in coding sequence. We investigate the cluster-size distribution P(S) for human chromosomes 21 and 22, and the results are different from previous works. The cluster-size distribution P(S1+S2) with the total size of sequential Pu-cluster and Py-cluster S1+S2 is studied. We observe that P(S1+S2) follows an exponential decay both in coding and non-coding sequences. However, we get different results for human chromosomes 21 and 22. The probability distribution P(S1,S2) of nucleotide clusters with the size of sequential Pu-cluster and Py-cluster S1 and S2 respectively, is also examined. In the meantime, some of the linear correlations are obtained in the double logarithmic plots of the fluctuation F(l) versus nucleotide cluster distance l along the DNA chain. The power spectrums of nucleotide clusters are also discussed, and it is concluded that the curves are flat and hardly changed and the 1/3 frequency is neither observed in coding sequence nor in non-coding sequence. These investigations can provide some insights into the nucleotide clusters of DNA sequences.