Long-range correlation measures for quantifying patchiness: Deviations from uniform power-law scaling in genomic DNA

We introduce and develop new techniques to quantify DNA patchiness, and characteristics of their mosaic structure. These techniques, which involve calculating two functions, α(ℓ) and β(ℓ), measure correlation exponents at length scale ℓ and detect distinct characteristic patch sizes embedded in scale invariant patch size distributions. Using these methods, it is possible to address a number of issues relating to the mosaic structure of genomic DNA. We find several distinct characteristic patch sizes in yeast, human, and prokaryotic sequences. We also find that the distinct patch sizes in all 16 yeast chromosomes are similar.