Scaling properties of coding and non-coding DNA sequences

We study the size distribution of purine and pyrimidine clusters in coding and non-coding DNA sequences. We observe that the cluster-size distribution P(s) follows an exponential decay in coding sequences whereas it follows a power-law decay in non-coding sequences: P(s) similar to s(-1)-(mu), with a power exponent mu = 1.5-1.8. The mean-square displacement sigma(2)(m) is examined via a cluster walk model, with step-size distribution following P(s) and with m denoting the number of clusters covered by the walker. The behaviour of the mean-square displacement is sigma(2)(m) similar to m(2/mu) for non-coding sequences and sigma(2)(m) similar to m for coding sequences. We associate the power-law behaviour in the non-coding with the tendency of large Pu and Py cluster formation which dominate the non-coding. Under this observation the entire DNA sequence may be regarded as a collection of extended non-coding regions interrupted by small coding regions. We recall that this irregular composition of DNA, is of vital importance for the living organisms: Transposable elements and other "parasite" DNA which try to incorporate themselves into the DNA chain most probably intersect the large non-coding regions, thus leaving the organism unaffected, as is well known to biologists.