Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 28 May 2020 / Approved: 31 May 2020 / Online: 31 May 2020 (15:19:29 CEST)
Version 2 : Received: 20 June 2020 / Approved: 21 June 2020 / Online: 21 June 2020 (15:26:04 CEST)

How to cite: Petoukhov, S. Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes. Preprints 2020, 2020050471 (doi: 10.20944/preprints202005.0471.v2). Petoukhov, S. Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes. Preprints 2020, 2020050471 (doi: 10.20944/preprints202005.0471.v2).

Abstract

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.

Subject Areas

DNA oligomers; harmonic progression; hyperbolic rules; matrices; tensor product; quantum informatics; oligomer sums method; genomes; genes; viruses; proteins; long Russian texts; phonetic sequences

Comments (1)

Comment 1
Received: 21 June 2020
Commenter: Sergey Petoukhov
Commenter's Conflict of Interests: Author
Comment: Many new materials, figures and references were added in this second version.
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