Generalized Lévy-walk model for DNA nucleotide sequences

We propose a generalized L\'evy 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 L\'evy-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 lⱼ) within these correlated sequences. In the generalized L\'evy-walk model, the lⱼ are chosen from a power-law distribution P(lⱼ){∝}lⱼ^-μ. The correlation exponent {α} is related to {μ} through {α}=2-{μ}/2 if 23. The model is consistent with the finding of ``repetitive elements'' of variable length interspersed within noncoding DNA.