Fractal Analysis of DNA Sequences Using Frequency Chaos Game Representation and Small-Angle Scattering

Abstract

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.

Polarization- and CGR-based binary representations as identifiers of the nucleotide sequences in bioinformatics

“…Для некоторых нуклеотидных последовательностей подобная пространственная неоднородность позволяет говорить о «фрактальности» CGR отображения, в определенном смысле аналогичной, например, классическому ковру Серпинского. В качестве примера можно сослаться на работу [34], наглядно иллюстрирующую фрактальный характер CGR отображений большой длины (порядка нескольких сотен тысяч нуклеотидов).…”

Polarization- and Chaos-Game-Based Fingerprinting of Molecular Targets of Listeria Monocytogenes Vaccine and Fully Virulent Strains

“…When comparing the pair of sequences, the distance matrix of their complete CGR graphs must be calculated [55]. The CGR-based approaches have been successfully used even for interspecific discrimination of different bacterial and viral species including those that could not be classified by the traditional multiple sequence alignment methods based on the whole genome nucleotide sequences [60], particularly, when only incomplete genomic sequences are available [13]. However, a single-target gene analysis with smaller numbers of mismatches may be less fortunate.…”

“…Jeffrey in 1990 [8]. Since that time, the CGR technique has been successfully used to analyze and visualize various nucleotide sequences many times (see, e.g., [9][10][11][12][13]). It should be noted that the general problem when using polyline and dot-based displaying techniques (including the CGR technique) for nucleotide sequences is the low level of their representations of relatively short fragments of nucleotide sequences (those with several hundred to several thousand bases).…”

Multifractal Detrended Fluctuation Analysis of Phonocardiogram signal and classification using Support Vector Machine

“…The core of MFDFA is to get beyond different constraints or limitations of the "detrended fluctuation analysis (DFA)" technique and its ability to give satisfactory results in time analysis. It has received great interest from researchers in all fields;in Stock Market Indexes [3], Human Brain Activity [4], earthquakes [5], human gait [6] and speech [7], heart rate variability [8],financial time series [9], DNA sequences [10],geoelectrical signals [11],Fish Sound Characterization [12], the DC-ring microgrid protection scheme based on PV-wind [13], air flow signals [14] and It has been applied in the current studies on Study of infant cry signals in normal and pathological case [15] Characterization of carbonate platform bathymetry [16],Multifractal Analysis and correlation structure of Bridsong [17],Stability Analysis in micro milling [18] and another domains. For PCG signals, using this method, researchers, physicians and clinicians made a qualitative leap from the conventional study of PCG represented by extracting frequency, energy, and Entropy to discover new features of PCG that are more accurate, precise and clearer.…”