Generalized Lévy-walk model for DNA nucleotide sequences

We propose a generalized Lévy 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 α. The generalized Lévy-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 ${\mathit{l}}_{\mathit{j}}$) within these correlated sequences. In the generalized Lévy-walk model, the ${\mathit{l}}_{\mathit{j}}$ are chosen from a power-law distribution P(${\mathit{l}}_{\mathit{j}}$)∝${\mathit{l}}_{\mathit{j}}^{\mathrm{-}\mathrm{\mu }}$. The correlation exponent α is related to μ through α=2-μ/2 if 2<μ<3. The model is consistent with the finding of ‘‘repetitive elements’’ of variable length interspersed within noncoding DNA.