The fractal structure of the mitochondrial genomes

Multifractal analysis of DNA walks and trails

“…The results for the ECO110K sequence illustrate the bad performance of box-counting when the two sources of systematic errors are present. The aforementioned agreement between the box-counting and the MF-DFA0 methods demonstrates inequivocally that the spurious effects of local trends must be filtered out for a correct account of the fractal or multifractal properties of DNA trails, a procedure that has been ignored in all previous analyses presented in the literature [8,14,15,16,17,18].…”

“…For instance, this easiness of implementation has allowed us to study higherdimensional DNA walks, an awkward task to be carried out using the WTMM method, for several representations proposed in the literature (see, e.g. [8,15,17,18]). As we will show in the sequel, the results were essentially the same as those reported here for the one-dimensional DNA walks.…”

“…Clearly, these spectra are artifacts of the sandbox and box-counting methods which cannot deal adequately with the surface effects. The unjustified dropping of the adjective 'effective' [17,18], led then to the apparent disagreement between the two approaches. These effective multifractal spectra might indeed be an useful tool for comparing random or biological sequences of similar lengths [17], especially if one manages to free them from the local trends effects.…”

“…Moreover, finite-length random walks exhibit an effective multifractal spectrum due mainly to crossover effects between the usually distinct bulk and surface properties of the trail [16]. These caveats, however, have not prevented claims that relatively short (typically 2 × 10 4 bp) mitochondrial DNA genomes have a definite multifractal structure [18]. In Sec.…”

Network clustering coefficient approach to DNA sequence analysis

“…Directly related to the linguistic view is the idea of genomic distance and all the correlation studies between sequences. The scaling methods comprehend the detrended fluctuation, the wavelet analysis, and the fractal and multifractal analysis [2,3]. The search for periodicity, specially 3-bp (base pair), 10-bp, and 200-bp looks for nucleotide periodic repetitions along the sequence [4][5][6][7].…”