New Symmetries and Fractal-Like Structures in the Genetic Coding System

  • Sergey Petoukhov
  • Elena Petukhova
  • Vitaliy Svirin
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)

Abstract

The achievements of molecular genetics and bioinformatics lead to significant changes in technological, medical and many other areas of our lives. This article is devoted to new results of study of structural organization of genetic information in living organisms. A new class of symmetries and fractal-like patterns in long DNA-texts is represented in addition to two Chargaff’s parity rules, which played an important role in development of genetics and bioinformatics. Our results provide new approaches for modeling genetic informatics from viewpoints of quantum informatics and theory of dynamic chaos.

Keywords

DNA Symmetry Fractal Probability Quantum informatics Cancer 

References

  1. 1.
    Petoukhov, S.V.: Matrix Genetics, Algebras of the Genetic Code, Noise Immunity. RCD, Moscow, Russia (2008). (in Russian)Google Scholar
  2. 2.
    Petoukhov, S.V., He, M.: Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics: Advanced Patterns and Applications. IGI Global, Hershey (2010)CrossRefGoogle Scholar
  3. 3.
    Petoukhov, S., Petukhova, E., Hazina, L., Stepanyan, I., Svirin, V., Silova, T.: The genetic coding, united-hypercomplex numbers and artificial intelligence. In: Hu, Z., Petoukhov, S., He, M. (eds.) Advances in Artificial Systems for Medicine and Education. AIMEE 2017. Advances in Intelligent Systems and Computing, vol. 658. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-67349-3_1. Print ISBN 978-3-319-67348-6, Online ISBN 978-3-319-67349-3. https://link.springer.com/search?query=978-3-319-67348-6. Accessed 20 Aug 2017Google Scholar
  4. 4.
    Petoukhov, S.V.: The rules of long DNA-sequences and tetra-groups of oligonucleotides (2017). (https://arxiv.org/abs/1709.04943)
  5. 5.
    Hu, Z.B., Petoukhov, S.V., Petukhova, E.S.: I-Ching, dyadic groups of binary numbers and the geno-logic coding in living bodies. Progress in Biophysics and Molecular Biology (2017, in press). http://authors.elsevier.com/sd/article/S0079610717300949. Accessed 18 Sept 2017CrossRefGoogle Scholar
  6. 6.
    Hu, Z.B., Petoukhov, S.V.: Generalized crystallography, the genetic system and biochemical esthetics. Struct. Chem. 28(1), 239–247 (2017).  https://doi.org/10.1007/s11224-016-0880-0. http://link.springer.com/journal/11224/28/1/page/2
  7. 7.
    Fickett, J., Burks, C.: Development of a database for nucleotide sequences. In: Waterman, M.S. (ed.) Mathematical Methods in DNA Sequences, pp. 1–34. CRC Press, Florida (1989)Google Scholar
  8. 8.
    Chargaff, E.: Preface to a grammar of biology: a hundred years of nucleic acid research. Science 172, 637–642 (1971)CrossRefGoogle Scholar
  9. 9.
    Chargaff, E.: Structure and function of nucleic acids as cell constituents. Fed. Proc. 10, 654–659 (1951)Google Scholar
  10. 10.
    Albrecht-Buehler, G.: Asymptotically increasing compliance of genomes with Chargaff’s second parity rules through inversions and inverted transpositions. Proc. Nat. Acad. Sci. USA 103(47), 17828–17833 (2006)CrossRefGoogle Scholar
  11. 11.
    Baisnee, P.-F., Hampson, S., Baldi, P.: Why are complementary DNA strands symmetric? Bioinformatics 18(8), 1021–1033 (2002)CrossRefGoogle Scholar
  12. 12.
    Bell, S.J., Forsdyke, D.R.: Deviations from Chargaff’s second parity rule correlate with direction of transcription. J. Theor. Biol. 197, 63–76 (1999)CrossRefGoogle Scholar
  13. 13.
    Chargaff, E.: A fever of reason. Ann. Rev. Biochem. 44, 1–20 (1975)CrossRefGoogle Scholar
  14. 14.
    Dong, Q., Cuticchia, A.J.: Compositional symmetries in complete genomes. Bioinformatics 17, 557–559 (2001)CrossRefGoogle Scholar
  15. 15.
    Forsdyke, D.R.: A stem-loop “kissing” model for the initiation of recombination and the origin of introns. Mol. Biol. Evol. 12, 949–958 (1995)Google Scholar
  16. 16.
    Forsdyke, D.R.: Symmetry observations in long nucleotide sequences: a commentary on the discovery of Qi and Cuticchia. Bioinf. Lett. 18(1), 215–217 (2002)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Forsdyke, D.R.: Evolutionary Bioinformatics. Springer, New York (2006)CrossRefGoogle Scholar
  18. 18.
    Forsdyke, D.R., Bell, S.J.: Purine-loading, stem-loops, and Chargaff’s second parity rule. Appl. Bioinf. 3, 3–8 (2004)CrossRefGoogle Scholar
  19. 19.
    Mitchell, D., Bridge, R.: A test of Chargaff’s second rule. BBRC 340, 90–94 (2006)CrossRefGoogle Scholar
  20. 20.
    Okamura, K., Wei, J., Scherer, S.: Evolutionary implications of inversions that have caused intra-strand parity in DNA. BMC Genomics 8, 160–166 (2007). http://www.gutenberg.org/files/39713/39713-h/39713-h.htm#Page_264CrossRefGoogle Scholar
  21. 21.
    Perez, J.-C.: The “3 genomic numbers” discovery: how our genome single-stranded DNA sequence is “self-designed” as a numerical whole. Appl. Math. 4, 37–53 (2013). http://dx.doi.org/10.4236/am.2013.410A2004CrossRefGoogle Scholar
  22. 22.
    Prabhu, V.V.: Symmetry observation in long nucleotide sequences. Nucleic Acids Res. 21, 2797–2800 (1993)CrossRefGoogle Scholar
  23. 23.
    Rapoport, A.E., Trifonov, E.N.: Compensatory nature of Chargaff’s second parity rule. J. Biomol. Struct. Dyn. 1–13 (2012).  https://doi.org/10.1080/07391102.2012.736757
  24. 24.
    Sueoka, N.: Intrastrand parity rules of DNA base composition and usage biases of synonymous codons. J. Mol. Evol. 40, 318–325 (1995)CrossRefGoogle Scholar
  25. 25.
    Yamagishi, M., Herai, R.: Chargaff’s “Grammar of Biology”: New Fractal-like Rules. http://128.84.158.119/abs/1112.1528v1 (2011)
  26. 26.
    Petoukhov, S.V., Svirin, V.I.: Fractal genetic nets and symmetry principles in long nucleotide 
sequences. Symmetry Cult. Sci. 23(3–4), 303–322 (2012). http://petoukhov.com/PETOUKHOV_SVIRIN_FGN.pdf
  27. 27.
    Jeffrey, H.J.: Chaos game representation of gene structure. Nucleic Acids Res. 18(8), 2163–2170 (1990)CrossRefGoogle Scholar
  28. 28.
    Peng, C.K., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Sclortino, F., Simons, M., Stanley, H.E.: Long-range correlations in nucleotide sequences. Nature 356, 168–170 (1992)CrossRefGoogle Scholar
  29. 29.
    Peng, C.K., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Sclortino, F., Simons, M., Stanley, H.E.: Fractal landscape analysis of DNA walks. Phys. A 191(1–4), 25–29 (1992)CrossRefGoogle Scholar
  30. 30.
    Pellionis, A.J.: The principle of recursive genome function. Cerebellum 7, 348–359 (2008).  https://doi.org/10.1007/s12311-008-0035-yCrossRefGoogle Scholar
  31. 31.
    Pellionisz, A.J., Graham, R., Pellionisz, P.A. Perez, J.C.: Recursive genome function of the cerebellum: geometric unification of neuroscience and genomics, In: Manto, M., Gruol, D.L., Schmahmann, J.D., Koibuchi, N., Rossi, F. (eds.) Handbook of the Cerebellum and Cerebellar Disorders, pp. 1381–1423 (2012)CrossRefGoogle Scholar
  32. 32.
    Perez, J.C.: Codon populations in single-stranded whole human genome DNA are fractal and fine-tuned by the Golden Ratio 1.618. Interdiscip. Sci. Comput. Life Sci. 2, 228–240 (2010).  https://doi.org/10.1007/s12539-010-0022-0CrossRefGoogle Scholar
  33. 33.
    Lieberman-Aiden, E., van Berkum, N.L., Williams, L., Imakaev, M., Ragoszy, T., Telling, A., Lajoie, B.R., Sabo, P.J., Dorschner, M.O., Sandstrom, R., Bernstein, B., Bender, M.A., Groudine, M., Gnirke, A., Stamatoyannopoulos, J., Mirny, L.A., Lander, E.S., Dekker, J.: Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science 326(5950), 289–293 (2009).  https://doi.org/10.1126/science.1181369CrossRefGoogle Scholar
  34. 34.
    Baish, J.W., Jain, R.K.: Fractals and cancer. Can. Res. 60, 3683–3688 (2000)Google Scholar
  35. 35.
    Bizzarri, M., Giuliani, A., Cucina, A., Anselmi, F.D., Soto, A.M., Sonnenschein, C.: Fractal analysis in a systems biology approach to cancer. Semin. Cancer Biol. 21(3), 175–182 (2011).  https://doi.org/10.1016/j.semcancer.2011.04.002CrossRefGoogle Scholar
  36. 36.
    Lennon, F.E., Cianci, G.C., Cipriani, N.A., Hensing, T.A., Zhang, H.J., Chen, C.-T., Murgu, S.D., Vokes, E.E., Vannier, M.W., Salgia, R.: Lung cancer - a fractal viewpoint. Nat. Rev. Clin. Oncol. 12(11), 664–675 (2015)  https://doi.org/10.1038/nrclinonc.2015.108
  37. 37.
    Dokukin, M.E., Guz, N.V., Woodworth, C.D., Sokolov, I.: Emergence of fractal geometry on the surface of human cervical epithelial cells during progression towards cancer. New J. Phys. 17(3), 033019 (2015)CrossRefGoogle Scholar
  38. 38.
    Perez, J.C.: Sapiens mitochondrial DNA genome circular long range numerical meta structures are highly correlated with cancers and genetic diseases mtDNA mutations. J. Cancer Sci. Ther. 9, 6 (2017).  https://doi.org/10.4172/1948-5956.1000469
  39. 39.
    Abo-Zahhad, M., Ahmed, S.M., Abd-Elrahman, S.A.: Genomic analysis and classification of exon and intron sequences using DNA numerical mapping techniques. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 4(8), 22–36 (2012)CrossRefGoogle Scholar
  40. 40.
    Abo-Zahhad, M., Ahmed, S.M., Abd-Elrahman, S.A.: A novel circular mapping technique for spectral classification of exons and introns in human DNA sequences. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 6(4), 19–29 (2014).  https://doi.org/10.5815/ijitcs.2014.04.02CrossRefGoogle Scholar
  41. 41.
    Meher, J.K., Panigrahi, M.R., Dash, G.N., Meher, P.K.: Wavelet based lossless DNA sequence compression for faster detection of eukaryotic protein coding regions. Int. J. Image Graph. Sig. Process. (IJIGSP) 4(7), 47–53 (2012).  https://doi.org/10.5815/ijigsp.2012.07.05CrossRefGoogle Scholar
  42. 42.
    Srivastava, P.C., Agrawal, A., Mishra, K.N., Ojha, P.K., Garg, R.: Fingerprints, Iris and DNA features based multimodal systems: a review. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 5(2), 88–111 (2013).  https://doi.org/10.5815/ijitcs.2013.02.10CrossRefGoogle Scholar
  43. 43.
    Mousa, H.M.: DNA-genetic encryption technique. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 8(7), 1–9 (2016).  https://doi.org/10.5815/ijcnis.2016.07.01CrossRefGoogle Scholar
  44. 44.
    Hossein, S.M., Roy, S.: A compression & encryption algorithm on DNA sequences using dynamic look up table and modified Huffman techniques. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 5(10), 39–61 (2013).  https://doi.org/10.5815/ijitcs.2013.10.05CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Sergey Petoukhov
    • 1
  • Elena Petukhova
    • 1
  • Vitaliy Svirin
    • 1
  1. 1.Mechanical Engineering Research InstituteRussian Academy of SciencesMoscowRussia

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