SCALING PROPERTIES OF CODING AND NONCODING DNA-SEQUENCES

We study the size distribution of purine and pyrimidine clusters in co ding and non-coding DNA sequences. We observe that the cluster-size di stribution P(s) follows an exponential decay in coding sequences where as 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 dis placement sigma(2)(m) is examined via a cluster walk model, with step- size distribution following P(s) and with m denoting the number of clu sters covered by the walker. The behaviour of the mean-square displace ment is sigma(2)(m) similar to m(2/mu) for non-coding sequences and si gma(2)(m) similar to m for coding sequences. We associate the power-la w behaviour in the non-coding with the tendency of large Pu and Py clu ster formation which dominate the non-coding. Under this observation t he entire DNA sequence may be regarded as a collection of extended non -coding regions interrupted by small coding regions. We recall that th is 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.