Abstract
The article is devoted to a new class of biological symmetries related to the oligomer organization of eukaryotic and prokaryotic genomes and genetically inherited physiological systems. The discovery of these symmetries is based on a new analytic method of oligomer sums connected with quantum information modeling of long DNA nucleotide sequences. The focus is on the previously formulated hyperbolic rules for the oligomer cooperative organization of a wide set of eukaryotic and prokaryotic genomes. These rules show the connection of genomic structures with the historically famous harmonic progression 1, 1/2, …, 1/n. The universality of these hyperbolic rules is evidenced by the presented results of a special study of the genomes of species living in extreme conditions of high radiation, high and low temperatures, and so on. Mathematical features of the harmonic progression are described, which are related to the harmonic mean, harmonic numbers, and the basic invariant of projective geometry. These features allow developing not only new model approaches to inherited biological structures related to the genetic code system but also some new methods in biotechnologies and problems of artificial intelligence connected with understanding living bodies as quantum-information entities.
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The authors are grateful to their colleagues M. He, Z. Hu, Yu.I. Manin, I. Stepanyan, and G. Tolokonnikov for research assistance.
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Petoukhov, S.V., Petukhova, E.S., Svirin, V.I., Verevkin, V.V. (2021). Inherited Bio-symmetries and Algebraic Harmony in Genomes of Higher and Lower Organisms. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education IV. AIMEE 2020. Advances in Intelligent Systems and Computing, vol 1315. Springer, Cham. https://doi.org/10.1007/978-3-030-67133-4_19
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