Fractal organization of the primary structure of DNA

Yuriy Karetin

doi:10.21638/spbu03.2016.110

Authors

Yuriy Karetin A. V. Zhirmunsky Institute of Marine Biology of the Far Eastern Branch of the RAS, 17, ul. Palchevskogo, Vladivostok, 690041, Russian Federation; Far Eastern Federal University, School of Natural Sciences, Laboratory building, L703, Ajax St., Russky Island, Vladivostok, 690950, Russian Federation

DOI:

https://doi.org/10.21638/spbu03.2016.110

Abstract

An analysis of the primary sequence of DNA clearly points to the possibility of considering it as a fractal structure, whose fractal properties depend on the species-specific, evolutionary features of the molecule as a whole and the morphological and functional characteristics of its individual elements. Main features of nucleotide distribution of various sizes are described by scenario of evolution, including insertions, deletions, replacements and duplications of DNA segments. The features of the size distribution and spacing of GA, poly-A, CA-, GC-, TA-, TC-, TG-sequences and of Alu elements were investigated. It was found that the repetitive DNA sequence, taking its origin from transposons, is distributed not chaotically in genome, but co-clustered with other types of repetitive elements, genes and genomic components. Refs 32.

Keywords:

fractal analysis, primary structure of DNA, fractal structure

Downloads

Download data is not yet available.

References

Goldberger A. L., Amaral L. A., Glass L. et al. PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation, 2000, vol. 101, no. 23, pp. 215–220.

Thistle M. E., Schneider D. C., Gregory R. S. et al. Fractal measures of habitat fragmentation: maximum densities of juvenile cod occur at intermediate eelgrass complexity. Mar. Ecol. Prog. Ser., 2010, vol. 405, pp. 39–56.

Jelinek H. F., Fernandez E. Neurons and fractals: how reliable and useful are calculations of fractal dimensions? J. of Neurosci. Methods, 1998, vol. 81, pp. 9–18.

Schierwagen A. Neuronal morphology: Shape characteristics and models. Neirofiziologiya/Neurophysiology, 2008, vol. 40, pp. 366–372.

Banerji A., Ghosh I. Fractal symmetry of protein interior: what have we learned? Cell. Mol. Life Sci., 2011, vol. 68, pp. 2711–2737. https://doi.org/10.1007/s00018-011-0722-6" target="_blank">https://doi.org/10.1007/s00018-011-0722-6

Cattani C. Wavelet Algorithms for DNA Analysis. Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications, 2010, vol. 12, pp. 799–841.

Cattani C., Pierro G., Altieri G. Entropy and Multifractality for the Myeloma Multiple TET 2 Gene. Mathematical Problems in Engineering, 2011, Article ID 193761, pp. 14.

Cattani C. On the existence of wavelet symmetries in archaea DNA. Computational and Mathematical Methods in Medicine, 2012, Article ID 673934, pp. 21.

Pierro G. Sequence Complexity of Chromosome 3 in Caenorhabditis elegans. Advances in Bioinformatics, 2012, Article ID 287486, pp. 12.

Dey P., Banik T. Fractal dimension of chromatin texture of squamous intraepithelial lesions of cervix. Diagnostic Cytopathology, 2012, vol. 40, pp. 152–154.

Ferro D. P., Falconi M. A., Adam R. L. et al. Fractal characteristics of May — Grünwald — Giemsa stained chromatin are independent prognostic factors for survival in multiple myeloma. PLoS ONE, 2011, vol. 6, e20706. https://doi.org/10.1371/journal.pone.0020706" target="_blank">https://doi.org/10.1371/journal.pone.0020706

Fukushima A., Kinouchi M., Kanaya S., Ikemura T. Statistical Analysis of Genomic Information: Long-Range Correlation in DNA Sequences. Genome Informatics, 2001, vol. 12, pp. 435–436.

Codling E. A., Plank M. J., Benhamou S. Random walk models in biology. Journal of The Royal Society Interface, 2008, vol. 5(25), pp. 813–834.

Fudenberg G., Mirny L. A. Higher-order chromatin structure: bridging physics and biology. Current opinion in genetics & development, 2012, vol. 22, pp. 115–124.

Sobottka M., Hart A. G. On the nucleotide distribution in bacterial DNA sequences. Nature Precedings, 2010. https://doi.org/10.1038/npre.2010.5245.1" target="_blank">https://doi.org/10.1038/npre.2010.5245.1

Lopes R., Betrouni N. Fractal and multifractal analysis: a review. Medical image analysis, 2009, vol. 13, pp. 634–649.

Kirillova O. V. Entropy concepts and DNA investigations. Physics Letters A, 2000, vol. 274, pp. 247–253.

Pantic I., Harhaji-Trajkovic L., Pantovic A. et al. Changes in fractal dimension and lacunarity as early markers of UV-induced apoptosis. J. of Theor. Biol., 2012, vol. 303, pp. 87–92.

Albrecht-Buehler G. Fractal genome sequences. Gene, 2012, vol. 498, pp. 20–27. https://doi.org/10.1016/j.gene.2012.01.090" target="_blank">https://doi.org/10.1016/j.gene.2012.01.090

Cattani C., Pierro G. On the fractal geometry of DNA by the binary image analysis. Bull. Math. Biol., 2013, vol. 75, pp. 1544–1570. https://doi.org/10.1007/s11538-013-9859-9" target="_blank">https://doi.org/10.1007/s11538-013-9859-9

Klimopoulos A., Sellis D., Almirantis Y. Widespread occurrence of power-law distributions in inter-repeat distances shaped by genome dynamics. Gene, 2012, vol. 499, pp. 88–98. https://doi.org/10.1016/j.gene.2012.02.005" target="_blank">https://doi.org/10.1016/j.gene.2012.02.005

Hassan S. S., Choudhury P. P., Guha R. et al. DNA sequence evolution through Integral Value Transformations. Interdiscip. Sci., 2012, vol. 4, pp. 128–132. https://doi.org/10.1007/s12539-012-0103-3" target="_blank">https://doi.org/10.1007/s12539-012-0103-3

Stan C., Cristescu M. T., Luiza B. I., Cristescu C. P. Investigation on series of length of coding and non-coding DNA sequences of bacteria using multifractal detrended cross-correlation analysis. J. Theor. Biol., 2013, vol. 321, pp. 54–62. https://doi.org/10.1016/j.jtbi.2012.12.027" target="_blank">https://doi.org/10.1016/j.jtbi.2012.12.027

Moreno P. A., Vélez P. E., Martínez E. et al. The human genome: a multifractal analysis. BMC Genomics, 2011, vol. 12, pp. 506. https://doi.org/10.1186/1471-2164-12-506" target="_blank">https://doi.org/10.1186/1471-2164-12-506

de Sousa Vieira M. Statistics of DNA sequences: a low-frequency analysis. Phys. Rev. E., 1999, vol. 60, pp. 5932–5937.

Vélez P. E., Garreta L. E., Martínez E. et al. The Caenorhabditis elegans genome: a multifractal analysis. Genet. Mol. Res., 2010, vol. 9, pp. 949–965. https://doi.org/10.4238/vol9-2gmr756" target="_blank">https://doi.org/10.4238/vol9-2gmr756

Provata A., Katsaloulis P. Hierarchical multifractal representation of symbolic sequences and application to human chromosomes. Phys. Rev. E. Stat. Nonlin. Soft . Matter. Phys., 2010, vol. 81, no. 2: Art. No. 026102 Part 2.

Nagai N., Kuwata K., Hayashi T. et al. Evolution of the periodicity and the self-similarity in DNA sequence: a Fourier transform analysis. Jpn. J. Physiol., 2001, vol. 51, pp. 159–168.

Abramson G., Cerdeira H. A., Bruschi C. Fractal properties of DNA walks. Biosystems, 1999, vol. 49, pp. 63–70.

Provata A., Oikonomou T. Power law exponents characterizing human DNA. Phys. Rev. E. Stat. Nonlin. Soft Matter. Phys., 2007, vol. 75:056102.

Tiunin A. P., Karetin Iu. A., Kiselev K. V. Analiz izmeneniia avtokorelliatsionnoi funktsii tsitozinovogo metilirovaniia DNK v sostave genov stil'ben sintaz v kul'ture kletok vinograda amurskogo Vitis amurensis Rupr. [Analysis of changes in autocorellation function of DNA methylation of cytosine in the composition of stilbene synthase genes in cell culture of the Amur grape Vitis amurensis Rupr.]. Vestnik KrasGAU [Bulletin of KrasGAU], 2013, no. 12, pp. 108–113. (In Russian)

Oiwa N. N., Goldman C. On the analysis of large-scale genomic structures. Cell Biochem. Biophys., 2005, vol. 42, pp. 145–65.