The fractal characteristics of DNA sequences are studied using the frequency chaos game representation (FCGR) and small-angle scattering (SAS) technique. The FCGR allows representation of the frequencies of occurrence of k-mers (oligonucleotides of length k) in the form of images. The numerically encoded data are then used in a SAS analysis to enhance hidden features in DNA sequences. It is shown that the simulated SAS intensity allows us to obtain the fractal dimensions and scaling factors at various scales. These structural parameters can be used to distinguish unambiguously between the scaling properties of complex hierarchical DNA sequences. The validity of this approach is illustrated on several sequences from: Escherichia coli, Mouse mitochondrion, Homo sapiens mitochondrion and Human cosmid.
Keywords: DNA sequences; chaos game representation; multifractals; small-angle scattering; time series.