Hyperbolic Numbers in Modeling Genetic Phenomena

Petoukhov, Sergey V.

doi:10.20944/preprints201908.0284.v4

Cited by 7 publications

(9 citation statements)

References 15 publications

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“…Therefore, inherited physiological macrostructures can bear the imprint of structural features of the genetic code. For this reason, structural analogies exist between the genetic system and the properties of inherited physiological systems, for example, the unified properties of different sensor systems, which are reflected in the main psychophysical Weber-Fechner law [Petoukhov, 2016[Petoukhov, , 2019b[Petoukhov, , 2020a. These problems are discussed at the International interdisciplinary seminar "Algebraic Biology and Theory of Systems" in Moscow [Petoukhov, Tolokonnikov, 2020].…”

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confidence: 99%

Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

Petoukhov¹

2020

Preprint

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The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method are shown to the analysis of the following long sequences: 1) amino acid sequences in long proteins like the protein Titin; 2) phonetic sequences of long Russan literary texts (for checking of thoughts of many authors that phonetic organization of human languages is deeply connected with the genetic language). The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

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Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

Petoukhov¹

2020

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“…The matrix [1, 1; 1, 1] used in (6.1) is the matrix representation of a 2-dimensional hyperbolic number with unit coordinates. Deep structural connections of genetic informatics with 2 n -dimensional hyperbolic numbers are described in [Petoukhov, 2019b[Petoukhov, , 2021c.…”

Section: Some Additions To Algebra-holographic Principles In the Genetic Systemmentioning

confidence: 99%

“…It is a well-known historical fact that these musical scales were used by various civilizations around the world long before Pythagoras without knowledge of any mathematical laws. For example, the mentioned Pythagorean scales are the basis of the traditional music of China, Vietnam, Mongolia, Turkey, the Southern Andes, Polynesia, Melanesia, Indians, the Inca empire and many others (for more details, see [Petoukhov, 2019b]). This fact speaks of the innate universal genetic affinity of people with musical scales based on the ratio 3:2.…”

Section: -84 Genetic Stochastic Resonance and Inherited Human Affinity With Musicmentioning

confidence: 99%

Tensor Rules in the Stochastic Organization of Genomes and Genetic Stochastic Resonance in Algebraic Biology

Petoukhov¹

2021

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The article is devoted to the new results of the author, which add his previously published ones, of studying hidden rules and symmetries in structures of long single-stranded DNA sequences in eukaryotic and prokaryotic genomes. The author uses the existence of different alphabets of n-plets in DNA: the alphabet of 4 nucleotides, the alphabet of 16 douplets, the alphabet of 64 triplets, etc. Each of such DNA alphabets of n-plets can serve for constructing a text as a chain of these n-plets. Using this possibility, the author represents any long DNA nucleotide sequence as a bunch of many so-called n-texts, each of which is written on the basis of one of these alphabets of n-plets. Each of such n-texts has its individual percents of different n-plets in its genomic DNA. But it turns out that in such multi-alphabetical or multilayer presentation of each of many genomic DNA, analyzed by the author, universal rules of probabilities and symmetry exist in interrelations of its different n-texts regarding their percents of n-plets. In this study, the tensor product of matrices and vectors is used as an effective analytical tool borrowed from the arsenal of quantum mechanics. Some additions to the topic of algebra-holographic principles in genetics are also presented. Taking into account the described genomic rules of probability, the author puts also forward a concept of the important role of stochastic resonances in genetic informatics.

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“…The inheritance of configurations relies on the work of t he g enetic c oding s ystem, which a llows t he reproduction o f s uch forms i n a s eries o f generations. Recently, in the genomes of higher and lower organisms, an important rule for the recurrent organization of DNA nucleotide sequences was d iscovered; t hese s equences serve for the transfering genetic information [2,3]. This hyperbolic r ule for th e r elationship o f o ligomer sums i s associated with a long-known harmonic progression (1):…”

Section: Introductionmentioning

confidence: 99%

Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

Verevkin¹,

Petoukhov²

2021

EPJ Web Conf.

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The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression whose connection with the information sequences of DNA molecules in the genomes of higher and lower organisms was recently revealed. In particular, the article describes previously unknown connections of the function of natural logarithms with the structures of the molecular genetic system, which allow modelling the main psychophysical logarithmic law by Weber-Fechner and also many other logarithmic structures in genetically inherited biological systems. In physics, the harmonic progression is traditionally considered, first of all, as related to standing waves in resonators. Our results are correlated with Frohlich’s vibration-resonant theory about collective quantum effects and long-range communication in biological systems.

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Hyperbolic Numbers in Modeling Genetic Phenomena

Cited by 7 publications

References 15 publications

Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

Tensor Rules in the Stochastic Organization of Genomes and Genetic Stochastic Resonance in Algebraic Biology

Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

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