Algebraic Rules for the Percentage Composition of Oligomers in Genomes

Abstract

The article presents the author's results of studying hidden rules of structural organizations of long DNA sequences in eukaryotic and prokaryotic genomes. The results concern some rules of percentages (or probabilities) of n-plets in genomes. To reveal such rules, the author considers genomic DNA nucleotide sequences as multilayers sequences of n-plets and studies the percentage contents of n-plets in different layers. Unexpected rules of invariance of total sums of percentages in certain tetra-groupings of n-plets in different layers of genomic DNA sequences are revealed. These discovered rules are candidates for the role of universal genomic rules. A tensor family of matrix representations of interrelated DNA-alphabets of 4 nucleotides, 16 doublets, 64 triplets, and 256 tetraplets is used in the study. This matrix approach allows revealing algebraic properties of the mentioned genetic rules of probabilities, which are useful for developing algebraic and quantum biology. Some analogies of the discovered genetic phenomena with phenomena of Gestalt psychology are noted and discussed. The author connects the received results about the genomic percentages rules with a supposition of P. Jordan, who is one of the creators of quantum mechanics and quantum biology, that life's missing laws are the rules of chance and probability of the quantum world. Additional attention is paid to the algebraic features of the system of structured DNA alphabets and their relationship with the methods of algebraic holography, known in the technique of processing discrete signals. The concept of algebraic-holographic genetics is being developed for the understanding of inherited holographic properties of organisms.

The Stochastic Organization of Genomes and the Doctrine of Energy-Information Evolution Based on Bio-Antenna Arrays

“…2.3). This rule adds to the list of genetic gestalt rules, in which the value of the sum practically does not change with a wide variability of the summand values [Petoukhov, 2021a].…”

“…In connection with the author's previous publications on the relationship of DNA alphabets with the formalisms of quantum informatics [Petoukhov, 2021a;Petoukhov, Petukhova, Svirin, 2019], we especially note the following. The four entries of each tetra-breeding matrix B C , B A , B T , B G , giving the unit sum, can be considered as probabilities in a two-qubit quantum system, which is traditionally expressed as follows in Dirac notations [Nielsen, Chuang, 2010, p.16 which is associated with the indicated unit sum rule of genomes (Fig.…”

“…206149 0.207045 0.200019 0.267209 0.189482 0.221009 0.231754 0.295197 1.817864 0.389283 0.196943 0.272874 0.260144 0.286418 0.303943 0.218745 0.255051 2.183400 2.356791 1.642028 1.905139 2.093480 2.143507 1.857555 1.661505 2 It should be additionally noted that the same matrix representation based on the Hadamard product of matrices (like in Figs. 2.1, 2.5) is appropriate for the stochastic organization of n-texts in so-called epi-chains of genomic DNAs; the study of epichains gave pieces of evidence regarding the fractal-like stochastic organization of genomic DNAs [Petoukhov, 2019[Petoukhov, , 2021a. By definition, in a nucleotide sequence N 1 of any DNA strand N 1 (Fig.…”

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

“…6.1-6.3, 6.9, in which the length of a row fragment of one color is equal to the length of a fragment of the next fragment of the row. The article [Petoukhov, 2021b] gives many other examples of meander-like patterns in all the rows of genetic mosaic matrices, which illustrate the universal tetra-grouping rules of probabilities of n-plets in n-texts of DNA of eukaryotic and prokaryotic genomes. Some of the mentioned patterns are reproduced below in Fig.…”

“…1.1-1.4 where all rows and columns are enumerated by 2 n -bit binary numbers. These matrices are initially constructed as corresponding square tables on the bases of binary-oppositional molecular indicators in the alphabet of 4 nucleotides C, A, T, and G [Petoukhov, 2008a[Petoukhov, , 2021bPetoukhov, He, 2010]:…”