Statistical analysis of the DNA sequence of human chromosome 22

We study statistical patterns in the DNA sequence of human chromosome 22, the first completely sequenced human chromosome. We find that (i) the $33.4\times {10}^6$ nucleotide long human chromosome exhibits long-range power-law correlations over more than four orders of magnitude, (ii) the entropies $H_n$ of the frequency distribution of oligonucleotides of length n (n-mers) grow sublinearly with increasing n, indicating the presence of higher-order correlations for all of the studied lengths $1<~n<~10,$ and (iii) the generalized entropies $H_n\mathrm{}\left(q\right)\mathrm{}$ of n-mers decrease monotonically with increasing q and the decay of $H_n\mathrm{}\left(q\right)\mathrm{}$ with q becomes steeper with increasing $n<~10,$ indicating that the frequency distribution of oligonucleotides becomes increasingly nonuniform as the length n increases. We investigate to what degree known biological features may explain the observed statistical patterns. We find that (iv) the presence of interspersed repeats may cause the sublinear increase of $H_n$ with n, and that (v) the presence of monomeric tandem repeats as well as the suppression of CG dinucleotides may cause the observed decay of $H_n\mathrm{}\left(q\right)\mathrm{}$ with q.