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Symmetry: Culture and Science
Volume 35, Number 4, pages 469-491 (2024)
https://doi.org/10.26830/symmetry_2024_4_469

BINARY-GENOMIC NUMBERS AND SYMMETRICAL REGULARITIES IN THE STATISTICAL ORGANIZATION OF GENOMIC DNAS

S. V. Petoukhov^1*, V. I. Svirin²

¹ Department of Biomechanical Systems, Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, M. Kharitonievsky pereulok, 4, 101990, Russia.
Email: spetoukhov@gmail.com
Web: http://petoukhov.com
ORCID: 0000-0001-7355-1813

² Department of Biomechanical Systems, Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, M. Kharitonievsky pereulok, 4, 101990, Russia.
Email: vitaly.i.svirin@gmail.com
ORCID: 0000-0001-9878-5640

^* corresponding author

Abstract: The article presents new phenomenological regularities of symmetric types in statistical organization of information sequences of single-stranded DNAs in genomes of higher and lower organisms. Binary representations of these DNAs, based on binary-opposition structures in molecular DNA alphabets, are studied. These binary representations of genomic DNAs, which are called binary-genomic numbers (BG-numbers), define huge binary numbers with millions of bits. It is revealed that statistical (probability) organization of BG-numbers possesses internal mirror and fractal-like dichotomous symmetries. In this article, special attention is paid to statistical analysis and symmetries in probability structures of genomic DNAs epichains, which are a regular convolution of the whole DNAs. The received results about general probability regularities in genomic DNAs are discussed in connection with thoughts of P. Jordan and E. Schrodinger on existence of special laws in living nature. The importance of probability regularities in biology is also discussed from different points of view.

Keywords: genomic DNA, DNA alphabets, binary oppositions, probability, mirror symmetry, fractal dichotomous trees, biological laws.

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