Wavelet based fractal analysis of DNA sequences

Abstract The fractal scaling properties of DNA sequences are analyzed using the wavelet transform. Mapping nucleotide sequences onto a “DNA walk” produces fractal landscapes that can be studied quantitatively by applying the so-called wavelet transform modulus maxima method. This method provides a natural generalization of the classical box-counting techniques to fractal signals, the wavelets playing the role of “generalized oscillating boxes”. From the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima, this method allows us to determine the singularity spectrum of the considered signal and thereby to achieve a complete multifractal analysis. Moreover, by considering analyzing wavelets that make the “wavelet transform microscope” blind to “patches” of different nucleotide composition that are observed in genomic sequences, we demonstrate and quantify the existence of long-range correlations in the noncoding regions. Although the fluctuations in the patchy landscape of the DNA walks reconstructed from both noncoding and (protein) coding regions are found homogeneous with Gaussian statistics, our wavelet-based analysis allows us to discriminate unambiguously between the fluctuations of the former which behave like fractional Brownian motions, from those of the latter which cannot be distinguished from uncorrelated random Brownian walks. We discuss the robustness of these results with respect to various legitimate codings of the DNA sequences. Finally, we comment about the possible understanding of the origin of the observed long-range correlations in noncoding DNA sequences in terms of the nonequilibrium dynamical processes that produce the “isochore structre of the genome”.