Reconstructing phylogeny from the multifractal spectrum of mitochondrial DNA

Multifractal perturbations to multiplicative cascades promote multifractal nonlinearity with asymmetric spectra

Biological and psychological processes have been conceptualized as emerging from intricate multiplicative interactions among component processes across various spatial and temporal scales. Among the statistical models employed to approximate these intricate nonlinear interactions across scales, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, several fundamental questions persist concerning the proper interpretations of multifractal evidence of nonlinear cross-scale interactivity. Does multifractal spectrum width depend on multiplicative interactions, constituent noise processes participating in those interactions, or both? We conducted numerical simulations of cascade time series featuring component noise processes characterizing a range of nonlinear temporal correlations: nonlinearly multifractal, linearly multifractal (obtained via the iterative amplitude adjusted wavelet transform of nonlinearly multifractal), phase-randomized linearity (obtained via the iterative amplitude adjustment Fourier transform of nonlinearly multifractal), and phase and amplitude randomized (obtained via shuffling of nonlinearly multifractal). Our findings show that the multiplicative interactions coordinate with the nonlinear temporal correlations of noise components to dictate emergent multifractal properties. Multiplicative cascades with stronger nonlinear temporal correlations make multifractal spectra more asymmetric with wider left sides. However, when considering multifractal spectral differences between the original and surrogate time series, even multiplicative cascades produce multifractality greater than in surrogate time series, even with linearized multifractal noise components. In contrast, additivity among component processes leads to a linear outcome. These findings provide a robust framework for generating multifractal expectations for biological and psychological models in which cascade dynamics flow from one part of an organism to another.

Hardware Accelerator for the Multifractal Analysis of DNA Sequences

The multifractal analysis has allowed to quantify the genetic variability and non-linear stability along the human genome sequence. It has some implications in explaining several genetic diseases given by some chromosome abnormalities, among other genetic particularities. The multifractal analysis of a genome is carried out by dividing the complete DNA sequence in smaller fragments and calculating the generalized dimension spectrum of each fragment using the chaos game representation and the box-counting method. This is a time consuming process because it involves the processing of large data sets using floating-point representation. In order to reduce the computation time, we designed an application-specific processor, here called multifractal processor, which is based on our proposed hardware-oriented algorithm for calculating efficiently the generalized dimension spectrum of DNA sequences. The multifractal processor was implemented on a low-cost SoC-FPGA and was verified by processing a complete human genome. The execution time and numeric results of the Multifractal processor were compared with the results obtained from the software implementation executed in a 20-core workstation, achieving a speed up of 2.6x and an average error of 0.0003 percent.

Multifractal analysis of HIV-1 genomes

Pathogens like HIV-1, which evolve into many closely related variants displaying differential infectivity and evolutionary dynamics in a short time scale, require fast and accurate classification. Conventional whole genome sequence alignment-based methods are computationally expensive and involve complex analysis. Alignment-free methodologies are increasingly being used to effectively differentiate genomic variations between viral species. Multifractal analysis, which explores the self-similar nature of genomes, is an alignment-free methodology that has been applied to study such variations. However, whether multifractal analysis can quantify variations between closely related genomes, such as the HIV-1 subtypes, is an open question. Here we address the above by implementing the multifractal analysis on four retroviral genomes (HIV-1, HIV-2, SIVcpz, and HTLV-1), and demonstrate that individual multifractal properties can differentiate between different retrovirus types easily. However, the individual multifractal measures do not resolve within-group variations for different known subtypes of HIV-1 M group. We show here that these known subtypes can instead be classified correctly using a combination of the crucial multifractal measures. This method is simple and computationally fast in comparison to the conventional alignment-based methods for whole genome phylogenetic analysis.

The Caenorhabditis elegans genome: a multifractal analysis

The Caenorhabditis elegans genome has several regular and irregular characteristics in its nucleotide composition; these are observed within and between chromosomes. To study these particularities, we carried out a multifractal analysis, which requires a large number of exponents to characterize scaling properties. We looked for a relationship between the genetic information content of the chromosomes and multifractal parameters and found less multifractality compared to the human genome. Differences in multifractality among chromosomes and in regions of chromosomes, and two group averages of chromosome regions were observed. All these differences were mainly dependent on differences in the contents of repetitive DNA. Based on these properties, we propose a nonlinear model for the structure of the C. elegans genome, with some biological implications. These results suggest that examining differences in multifractality is a viable approach for measuring local variations of genomic information contents along chromosomes. This approach could be extended to other genomes in order to characterize structural and functional regions of chromosomes.

Multifractal analysis of DNA walks and trails

The characterization of the long-range order and fractal properties of DNA sequences has proved a difficult though rewarding task mainly due to the mosaic character of DNA consisting of many interwoven patches of various lengths with different nucleotide constitutions. We apply here a recently proposed generalization of the detrended fluctuation analysis method to show that the DNA walk construction, in which the DNA sequence is viewed as a time series, exhibits a monofractal structure regardless of the existence of local trends in the series. In addition, we point out that the monofractal structure of the DNA walks carries over to an apparently alternative graphical construction given by the projection of the DNA walk into the d spatial coordinates, termed DNA trails. In particular, we calculate the fractal dimension D(t) of the DNA trails using a well-known result of fractal theory linking D(t) to the Hurst exponent H of the corresponding DNA walk. Comparison with estimates obtained by the standard box-counting method allows the evaluation of both finite-length and local trends effects.

Statistical analysis of the DNA sequence of human chromosome 22

We study statistical patterns in the DNA sequence of human chromosome 22, the first completely sequenced human chromosome. We find that (i). the 33.4 x 10(6) nucleotide long human chromosome exhibits long-range power-law correlations over more than four orders of magnitude, (ii). the entropies H(n) of the frequency distribution of oligonucleotides of length n (n-mers) grow sublinearly with increasing n, indicating the presence of higher-order correlations for all of the studied lengths 1<or=n<or=10, and (iii). the generalized entropies H(n)(q) of n-mers decrease monotonically with increasing q and the decay of H(n)(q) with q becomes steeper with increasing n<or=10, indicating that the frequency distribution of oligonucleotides becomes increasingly nonuniform as the length n increases. We investigate to what degree known biological features may explain the observed statistical patterns. We find that (iv). the presence of interspersed repeats may cause the sublinear increase of H(n) with n, and that (v). the presence of monomeric tandem repeats as well as the suppression of CG dinucleotides may cause the observed decay of H(n)(q) with q.