GENERALIZED LEVY-WALK MODEL FOR DNA NUCLEOTIDE-SEQUENCES

We propose a generalized Levy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Levy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length l(j)) within these correlated sequences. In the generalized Levy-walk model, the l(j) are chosen from a power-law distribution P(l(j)) is-proportional-to l(j)-u. The correlation exponent alpha is related to mu through alpha = 2 - mu/2 if 2 < mu < 3. The model is consistent with the finding of ''repetitive elements'' of variable length interspersed within noncoding DNA.