A two-dimensional modified Lévy-walk model for the DNA sequences

A two-dimensional modified Lévy-walk model for the DNA sequences with only three parameters is proposed. This model is applied to simulate real DNA sequence data of the Saccharomyces cerevisiae genome. DNA sequences are converted into one- and two-dimensional random walk mappings for statistical study. Satisfactory statistical results are obtained when 16 chromosomes in the genome are all analyzed and compared to the model sequence data. Measurements on the root-mean-square deviations are in good agreement when real sequences and model sequences are compared. Lévy type statistics plays a major role in generating “long-range correlation” phenomena. Power values α=0.64-0.68 are obtained for the power law F(l)∼lα where F(l) is the root-mean-square deviation at step size l. The same model is applied to sequences of some other species. Fair agreement is also obtained.