Wavelet based fractal analysis of DNA sequences

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

“…Moreover, some precautions are required when averaging over many sequences in order to improve statistical convergence; in particular some severe criticisms [69,75,83] were raised against the biological significance of Voss study [65,66,67], since his results correspond to averages over complete genebank database categories which are not of equal taxonomic rank. However, beyond these practical problems, there is also a more fundamental theoretical restriction since the measurement of a unique exponent which characterizes the global scaling properties of a sequence fails to resolve multifractality [102], and thus provides very poor information upon the nature of the underlying LRC (if there are any). Actually, it can be shown that for a homogeneous (monofractal) DNA sequence, the scaling exponents estimated with the techniques previously mentioned, can all be expressed as a function of the so-called Hurst or roughness exponent H of the corresponding DNA walk landscape [75,102].…”

“…However, beyond these practical problems, there is also a more fundamental theoretical restriction since the measurement of a unique exponent which characterizes the global scaling properties of a sequence fails to resolve multifractality [102], and thus provides very poor information upon the nature of the underlying LRC (if there are any). Actually, it can be shown that for a homogeneous (monofractal) DNA sequence, the scaling exponents estimated with the techniques previously mentioned, can all be expressed as a function of the so-called Hurst or roughness exponent H of the corresponding DNA walk landscape [75,102]. H = 1/2 corresponds to classical Brownian motion, i.e., uncorrelated random walk.…”

“…There have been some phenomenological attempts to differentiate local patchiness from long-range correlations using 'ad hoc methods' such as the so-called 'min-max method' [64] and the 'detrended fluctuation analysis' [108,109]. Alternatively, the wavelet transform (WT) [110,111,112,113,114] has been proposed as a very powerful technique for fractal analysis of DNA sequences [102,115] (see also Ref. [116] where the WT is used as a tool for visualizing regular patterns in DNA sequences).…”

“…As already experienced in various fields, the WT can be seen as a mathematical microscope that is well suited for characterizing the scaling properties of fractal objects and this even in the presence of some polynomial component [113,117,118,119,120]. By considering analyzing wavelets that make the microscope blind to low frequency trends, one can reveal and quantify the scale invariance properties of DNA walks [102,115,121]. In a previous work, by applying the so-called wavelet transform modulus maxima (WTMM) method [119,120,122] to the analysis of various genomic sequences mainly selected in the human genome, we have found that the fluctuations in the patchy landscapes of both coding and noncoding DNA walks are homogeneous with Gaussian statistics [102,115].…”

“…By considering analyzing wavelets that make the microscope blind to low frequency trends, one can reveal and quantify the scale invariance properties of DNA walks [102,115,121]. In a previous work, by applying the so-called wavelet transform modulus maxima (WTMM) method [119,120,122] to the analysis of various genomic sequences mainly selected in the human genome, we have found that the fluctuations in the patchy landscapes of both coding and noncoding DNA walks are homogeneous with Gaussian statistics [102,115]. The main consequence of this result is the justification of using a single exponent, namely the Hurst or roughness exponent H , to characterize the underlying fractal organization of DNA sequences.…”