Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

Inoculation with Metal-Mobilizing Plant-GrowthPromoting Rhizobacterium Bacillus sp. SC2b and Its Role in Rhizoremediation

A plant growth-promoting bacterial (PGPB) strain SC2b was isolated from the rhizosphere of Sedum plumbizincicola grown in lead (Pb)/zinc (Zn) mine soils and characterized as Bacillus sp. based on (1) morphological and biochemical characteristics and (2) partial 16S ribosomal DNA sequencing analysis. Strain SC2b exhibited high levels of resistance to cadmium (Cd) (300 mg/L), Zn (730 mg/L), and Pb (1400 mg/L). This strain also showed various plant growth-promoting (PGP) features such as utilization of 1-aminocyclopropane-1-carboxylate, solubilization of phosphate, and production of indole-3-acetic acid and siderophore. The strain mobilized high concentration of heavy metals from soils and exhibited different biosorption capacity toward the tested metal ions. Strain SC2b was further assessed for PGP activity by phytagar assay with a model plant Brassica napus. Inoculation of SC2b increased the biomass and vigor index of B. napus. Considering such potential, a pot experiment was conducted to assess the effects of inoculating the metal-resistant PGPB SC2b on growth and uptake of Cd, Zn and Pb by S. plumbizincicola in metal-contaminated agricultural soils. Inoculation with SC2b elevated the shoot and root biomass and leaf chlorophyll content of S. plumbizincicola. Similarly, plants inoculated with SC2b demonstrated markedly higher Cd and Zn accumulation in the root and shoot system, indicating that SC2b enhanced Cd and Zn uptake by S. plumbizincicola through metal mobilization or plant-microbial mediated changes in chemical or biological soil properties. Data demonstrated that the PGPB Bacillus sp. SC2b might serve as a future biofertilizer and an effective metal mobilizing bioinoculant for rhizoremediation of metal polluted soils.

Entropy analysis of DNA code dynamics in human chromosomes

Deoxyribonucleic acid, or DNA, is the most fundamental aspect of life but present day scientific knowledge has merely scratched the surface of the problem posed by its decoding. While experimental methods provide insightful clues, the adoption of analysis tools supported by the formalism of mathematics will lead to a systematic and solid build-up of knowledge. This paper studies human DNA from the perspective of system dynamics. By associating entropy and the Fourier transform, several global properties of the code are revealed. The fractional order characteristics emerge as a natural consequence of the information content. These properties constitute a small piece of scientific knowledge that will support further efforts towards the final aim of establishing a comprehensive theory of the phenomena involved in life.

Shannon, rényie and tsallis entropy analysis of DNA using phase plane

This paper analyzes DNA information using entropy and phase plane concepts. First, the DNA code is converted into a numerical format by means of histograms that capture DNA sequence length ranging from one up to ten bases. This strategy measures dynamical evolutions from 4 up to 410 signal states. The resulting histograms are analyzed using three distinct entropy formulations namely the Shannon, Rényie and Tsallis definitions. Charts of entropy versus sequence length are applied to a set of twenty four species, characterizing 486 chromosomes. The information is synthesized and visualized by adapting phase plane concepts leading to a categorical representation of chromosomes and species.

Wavelet analysis of human DNA

This paper studies the human DNA in the perspective of signal processing. Six wavelets are tested for analyzing the information content of the human DNA. By adopting real Shannon wavelet several fundamental properties of the code are revealed. A quantitative comparison of the chromosomes and visualization through multidimensional and dendograms is developed.

Histogram-based DNA analysis for the visualization of chromosome, genome and species information

We describe a novel approach to explore DNA nucleotide sequence data, aiming to produce high-level categorical and structural information about the underlying chromosomes, genomes and species. The article starts by analyzing chromosomal data through histograms using fixed length DNA sequences. After creating the DNA-related histograms, a correlation between pairs of histograms is computed, producing a global correlation matrix. These data are then used as input to several data processing methods for information extraction and tabular/graphical output generation. A set of 18 species is processed and the extensive results reveal that the proposed method is able to generate significant and diversified outputs, in good accordance with current scientific knowledge in domains such as genomics and phylogenetics.

Multi-dimensional scaling applied to histogram-based DNA analysis

This paper aims to study the relationships between chromosomal DNA sequences of twenty species. We propose a methodology combining DNA-based word frequency histograms, correlation methods, and an MDS technique to visualize structural information underlying chromosomes (CRs) and species. Four statistical measures are tested (Minkowski, Cosine, Pearson product-moment, and Kendall τ rank correlations) to analyze the information content of 421 nuclear CRs from twenty species. The proposed methodology is built on mathematical tools and allows the analysis and visualization of very large amounts of stream data, like DNA sequences, with almost no assumptions other than the predefined DNA “word length.” This methodology is able to produce comprehensible three-dimensional visualizations of CR clustering and related spatial and structural patterns. The results of the four test correlation scenarios show that the high-level information clusterings produced by the MDS tool are qualitatively similar, with small variations due to each correlation method characteristics, and that the clusterings are a consequence of the input data and not method’s artifacts.

Fractional Analysis of the DNA Information

Proceedings of the 12th Conference on 'Dynamical Systems -Theory and Applications'

On the DNA of eleven mammals

This paper studies the DNA code of eleven mammals from the perspective of fractional dynamics. The application of Fourier transform and power law trendlines leads to a categorical representation of species and chromosomes. The DNA information reveals long range memory characteristics.

Analysis and visualization of chromosome information

This paper analyzes the DNA code of several species in the perspective of information content. For that purpose several concepts and mathematical tools are selected towards establishing a quantitative method without a priori distorting the alphabet represented by the sequence of DNA bases. The synergies of associating Gray code, histogram characterization and multidimensional scaling visualization lead to a collection of plots with a categorical representation of species and chromosomes.

Shannon information and power law analysis of the chromosome code

This paper studies the information content of the chromosomes of twenty-three species. Several statistics considering different number of bases for alphabet character encoding are derived. Based on the resulting histograms, word delimiters and character relative frequencies are identified. The knowledge of this data allows moving along each chromosome while evaluating the flow of characters and words. The resulting flux of information is captured by means of Shannon entropy. The results are explored in the perspective of power law relationships allowing a quantitative evaluation of the DNA of the species.

Fractional Order Description of DNA

This study addresses the deoxyribonucleic acid (DNA) and proposes a procedure based on the association of statistics, information theory, signal processing, Fourier analysis and fractional calculus for describing fundamental characteristics of the DNA. In a first phase the 24 chromosomes of the Human are evaluated. In a second phase, 10 chromosomes for different species are also processed and the results compared. The results reveal invariance in the description and close resemblances with fractional Brownian motion.