Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

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 the 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 results concerns additionally the problem of the origin of life. 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 is shown to the analysis of amino acid sequences in long proteins like the protein Titin. The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

“…Successively applying this recurrence relation ( 3) to the f irst te rms x 1 = 1 an d x 2 = 1 /2 of t he ha rmonic progression (1), we obtain the entire series of its terms. It seems i nteresting a nd u seful to i nvestigate in the f uture the harmonic mean ratios in inherited b iological structures and processes.…”

“…F ig. 4 s hows a n i mproved a pproximation of the c ontinuous f unction l n ( x) b y C -harmonic nu mbers H n [m] at m = 3: the area under the hyperbola, representing the natural logarithm, is better approximated by the total area o f t he r ectangles equal t o t he C -harmonic nu mber H n [3] . T he l arger t he va lue m, t he b etter t he approximation o f t he continuous function l n (x) b y discrete C-harmonic numbers H n [m] is provided.…”

“…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):…”

Non-Euclidean Biosymmetries and Algebraic Harmony in Genomes of Higher and Lower Organisms

“…The alphabet of 4 nucleotides of DNA is endowed with binary opposition traits "purine-or-pyrimidine" and "strong-or-weak hydrogen bonds". Taking this binaryoppositional indicators into account, one of the coauthors of this article created a quantum-information model of long DNA-texts, where notions of quantum qubits and their tensor products are used [4,5].…”

“…Therefore, it is important to look for traces of symmetries and invariants of non-Euclidean transformations in the genetic informatics of living bodies, including in the information texts of DNA heredity molecules carrying genetic information in the form of long nucleotide sequences. As a result of the work of the laboratory for research of biomechanical systems of the Mechanical Engineering Research Institute of the Russian Academy of Sciences in 2020, universal hyperbolic rules for the cooperative organization of genomes of higher and lower organisms were discovered [4,5]. These rules are associated with harmonic progression (1), which has long been known in various fields of science and has now received the status of an important participant in genetic informatics, capable of influencing the characteristics of inherited biosymmetries:…”