Poincaré recurrences and multifractal properties of genomic sequences

Abstract

We propose the return times spectra as a tool to analyze the genomic sequences. The spectra discriminate between regular, chaotic and mixed dynamical systems since generally their decay follows respectively an exponential law, a power law or is a linear combination of them. The analysis of words of n bases from a DNA sequence exhibits the same exponential behavior for the coding and noncoding component. The multifractal analysis shows a definite difference, which suggests a less uniform structure for the noncoding part.

Poincaré recurrences of DNA sequences

“…Surprisingly, this powerful tool of dynamical systems has not been applied for detailed statistical studies of the DNA sequence, which also can be viewed as a symbolic trajectory. There have been only a few earlier attempts going in this direction including researchers in dynamical systems [11] and bioinformatics [12][13][14]. However, in [11] only short recurrence times with t 4 have been considered and it was concluded that the probability of recurrences decays exponentially.…”

“…The comparison with random data sequences and the known results for dynamical maps [5][6][7][8][9][10] allowed us to establish new, interesting features for the Poincaré recurrences of the DNA sequence. Our approach allowed to analyze the recurrences with time t being by five to six orders of magnitude larger than those reached in [11][12][13][14]. For the Homo sapiens (HS) database we performed statistical analysis for 1.5 × 10 10 base pairs (bp).…”

“…There have been only a few earlier attempts going in this direction including researchers in dynamical systems [11] and bioinformatics [12][13][14]. However, in [11] only short recurrence times with t ≤ 4 have been considered and it was concluded that the probability of recurrences decays exponentially. The studies in bioinformatics were not aware about the concept of Poincaré recurrences but their approach had certain links with them aiming to use digital signal representations of genomic data [12].…”

Multifractality in arterial pulse

“…Multifractal studies have been undertaken in other domains such as DNA sequences [18], turbulence [5], day and night heart rate characteristics [17], alterations with disease and aging [7]. In this study, we have confined our scope to extract only the multifractality present in the pulse waveforms.…”

Characterization of DNA methylation as a function of biological complexity via dinucleotide inter-distances

“…Thereafter, much effort has been devoted to the analysis of symbolic trajectories in very different contexts: stochastic processes [21], biological data [22] and literary texts [23], to mention just a few. These tools have been applied to genomics in different forms for about the last 10 years [24,25], becoming nowadays rather common, e.g. for the reconstruction of the phylogenetic tree [18,19], for the detection of CpG islands [26] and for the characterization of long-range correlations in DNA [27].…”