Development of Models of Quantum Biology Based on the Tensor Product of Matrices

2020

Preprint

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.

mentioning

confidence: 99%

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

2020

Preprint

“…The question on a possible deep connection of physiology and brain functioning with principles of quantum informatics is considered in publications on many authors [Abbott, Davies, Pati, 2008;Altaisky, Filatov, 2001;Fimmel, Petoukhov, 2020;Igamberdiev, 1993Igamberdiev, , 2004Matsuno, Paton, 2000;Patel, 2001a-c;Penrose, 1996;Petoukhov, 2018aPetoukhov, , 2019b. The results presented in this article give new essential materials to this perspective direction of thoughts.…”

mentioning

confidence: 75%

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

2020

Preprint

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 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 rhythmically repeating deviations from model hyperbolic sequences; these deviations are associated with DNA triplets and should be systematically analyzed for a deeper understanding the genetic coding system. The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

“…The materials of this article supplement the author's previously published works on the topic of quantum biology and formalisms of quantum informatics in biology [Petoukhov, 2008[Petoukhov, , 2016[Petoukhov, , 2018[Petoukhov, , 2020a[Petoukhov, ,c, 2021aPetoukhov, He, 2010;Petoukhov, Petukhova, Svirin, 2019;Fimmel, Petoukhov, 2020]. The revealed connection of genetics with quantum informatics opens up the possibility of introducing rich formalisms of quantum mechanics and quantum informatics into algebraic biology for the mutual enrichment of these sciences and the inclusion of biology in the field of developed mathematical natural science.…”

Section: Regarding the Connection Of The Stochastic Phenomenon Of Tetra-colonies Of N-plets Inmentioning

confidence: 90%

“…The work [Dubkov, 2014] notes the following: -in the early 90s in science it was realized that stochastic resonance can play a key role in the functioning of neural networks and in the transfer of information from one group of neurons to another; -Numerical calculations performed in [Longtin, 1993] on the FitzHugh-Nagumo neuron model confirmed the presence of stochastic resonance in the histogram of interspike intervals; -The mechanism of noise-induced order was found even in the human thought process [Usher, Feingold, 2000]; -Noise-induced phenomena are found directly in the part of the brain responsible for image processing. It has been found [Mori, Kai, 2002] that the illumination noise directed to the left eye improves the processing of the periodic signal sent to the human right eye.…”

Section: Genetic Stochastic Resonance In Algebraic Biologymentioning

confidence: 99%

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

2021

Preprint

Self Cite

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.