Symmetries of DNA alphabets and quantum informational formalisms

Hyperbolic Numbers in Modeling Genetic Phenomena

“…By this reason they can be used in development of applications of ideas and methods of quantum mechanics and quantum informatics in the field of bioinformatics and algebraic biology. In this connection some of author's works [Petoukhov, 2018a[Petoukhov, ,b, 2019aPetoukhov, Petukhova, Svirin, 2019] are devoted to using formalisms of quantum mechanics and quantum informatics in bioinformatics and algebraic biology including analysis of long genetic and and literary texts. For example, in long DNA sequences of nucleobases, where complementary nucleobases C and G (A and T) are linked by 3 (2) hydrogen bonds, 2 n -dimensional hyperbolic numbers [%3, %2; %2, %3] (n) (where %3 and %2 denote percentages of numbers 3 and 2 of hydrogen bonds in the analyzed DNA sequence; n = 2, 3, 4, 5) effectively models percentages of monoplets, doublets, triplets, tetraplets and pentaplets of these numbers 3 and 2 of hydrogen bonds .…”

“…For example, the well-known second Chargaff rule concerns percentages of separate kinds of nucleotides A, T, C and G in long single-stranded DNA. In contrast to such studies, the author suggested analyzing -in DNA and RNA sequencescharacterizations of their cooperative forms of organization such as the total amounts of those oligomers of the same length, which belong to the same equivalence class, defined by some their general trait [Petoukhov, 2018c;Petoukhov, Petukhova, Svirin, 2019]. Below this approach is explained.…”

“…2.1). Appropriate 2n-qubit systems in so-called separable pure states were constructed, where nucleotides A, T, C, and G (and also DNA doublets and other n-plets) were represented by appropriate computational basis states [Petoukhov, 2018c;Petoukhov, Petukhova, Svirin, 2019]. For example, cytosine C was represented as the computational basis state |00> of the 2-qubit system, thymine T -as the computational basis state |01>, guanine Gas the computational basis state |10>, and adenine A -as the computational basis state |11> of the same 2-qubit system.…”

“…Returning to author's information-algorithmic model, which was published early [Petoukhov, 2018c;Petoukhov, Petukhova, Svirin, 2019], the author emphasizes that that model allows deducing or prognosis the existence of the phenomenological hyperbolic rule, whose discovery is repre-sented above. It can be considered as an example of usefulness of algebraic modeling in biology.…”

Hyperbolic Numbers in Modeling Genetic Phenomena

“…By this reason they can be used in development of applications of ideas and methods of quantum mechanics and quantum informatics in the field of bioinformatics and algebraic biology. In this connection some of author's works [Petoukhov, 2018a[Petoukhov, ,b, 2019aPetoukhov, Petukhova, Svirin, 2019] are devoted to using formalisms of quantum mechanics and quantum informatics in bioinformatics and algebraic biology including analysis of long genetic and and literary texts. For example, in long DNA sequences of nucleobases, where complementary nucleobases C and G (A and T) are linked by 3 (2) hydrogen bonds, 2 n -dimensional hyperbolic numbers [%3, %2; %2, %3] (n) (where %3 and %2 denote percentages of numbers 3 and 2 of hydrogen bonds in the analyzed DNA sequence; n = 2, 3, 4, 5) effectively models percentages of monoplets, doublets, triplets, tetraplets and pentaplets of these numbers 3 and 2 of hydrogen bonds [Petoukhov, 2018].…”