Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Petoukhov, Sergey V.; Petukhova, Elena S.

doi:10.3390/info8010002

Cited by 15 publications

(7 citation statements)

References 39 publications

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“…This will promote the inclusion of genetics and all biology in the field of profound mathematical natural science. Consideration of biological phenomena, including the phenomena of inheritance of the intellectual abilities of biological bodies, from the standpoint of the theory of quantum computers, gives many valuable opportunities for their comprehension and also for development of artificial intelligence systems [Petoukhov, 2016a,b;Petoukhov, Petukhova, 2017a; (the work [Biamonte et al, 2017] contains a review about quantum computing and the problems of artificial intelligence). For example, an adult human organism has around 10 trillion (10 14 ) human cells and each of cells containts an identical complect of DNA, whose genetic information is used for physiological functioning organism as the holistic system of cells.…”

Section: Some Concluding Remarksmentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

Petoukhov¹

2018

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Information molecules of DNA and RNA should obey principles of quantum mechanics where unitary operators in form of unitary matrices have key meanings. Unitary matrices are the basis of calculations in quantum computers. This article presents some author's results, which show that matrix forms of the representation of structured systems of molecular-genetic alphabets can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation each other.  Decompositions of numeric genetic matrices into sets of sparse unitary matrices are connected with the logical operation of modulo-2 addition used in quantum computers as well. Tensor (or Kronecker)  families of unitary genetic matrices with their fractal-like properties are also considered. The described results are discussed in the frame of development of quantum-information approaches for modeling genetic systems.

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Section: Some Concluding Remarksmentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

Petoukhov¹

2018

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“…The discovery of new binary fractal-like patterns, which are revealed from long genetic sequences by means of this method, provokes many questions about relationship between the genetic system and those fields of science and technology where digital binary fractals are used, for example the fields of fractals in radiophysics, technology of fractal antenna, and fractal codes. In our opinion, the described results are useful for the bio-mathematical concept of geno-logical coding [20][21][22][23].…”

Section: Discussionmentioning

confidence: 99%

“…Its appropriate decimal meanings are 22 and 14. In such way, this 5-mer ATGGC can be represented not only as the appropriate cell with coordinates (22,14) inside the genomatrix [A G; C T] (5) but also as the point with decimal coordinates (22,14) in the orthogonal Cartesian system of coordinates (x, y). Taking into account the chosen connection ( Figure 2) between each sub-alphabet and one of the X, Y, Z axes of the Cartesian system of coordinates, the following correspondence exists between Kronecker families of genomatrices and 2-dimensional planes (x, y), (x, z) and (y, z) of the Cartesian system: …”

Section: Matrix Representations Of Whole Sets Of N-plets (Or N-mers)mentioning

confidence: 99%

“…Our article is devoted to searching for new approaches for visualization of structural peculiarities of long nucleotide sequences in connection with the bio-mathematical conception of geno-logical coding [20][21][22][23]. This concept or biological hypothesis supposes that-besides the known genetic code of amino acid sequences of proteins-an additional coding system exists in biological organisms addressing the inheritance of processes and bio-informational algorithms along the chains of generations.…”

Section: Introductionmentioning

confidence: 99%

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The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences

Stepanyan

Petoukhov

2017

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Abstract:The article is devoted to a matrix method of comparative analysis of long nucleotide sequences by means of presenting each sequence in the form of three digital binary sequences. This method uses a set of symmetries of biochemical attributes of nucleotides. It also uses the possibility of presentation of every whole set of N-mers as one of the members of a Kronecker family of genetic matrices. With this method, a long nucleotide sequence can be visually represented as an individual fractal-like mosaic or another regular mosaic of binary type. In contrast to natural nucleotide sequences, artificial random sequences give non-regular patterns. Examples of binary mosaics of long nucleotide sequences are shown, including cases of human chromosomes and penicillins. The obtained results are then discussed.

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“…But the notion of recurrence sequences of numbers can be generalized to a notion of recurrence sequences of matrices including tensor recurrence sequences of matrices. The author's studies of the systems of the alphabets of the molecular genetic system showed that their structural features are associated with tensor recurrence sequences of matrices, for example, [C, A; T, G] n , or [G, T; C, A] (n) where n = 1, 2, 3,… The systematic analysis of these tensor recurrence sequences, proposed and carried out by the author since 2008, has led to many meaningful results about the hidden relationship of genetic and physiological subsystems, as described in many publications, for example, [Petoukhov, 2008[Petoukhov, , 2011[Petoukhov, , 2012[Petoukhov, , 2016[Petoukhov, , 2017[Petoukhov, -2019[Petoukhov, , 2020aPetoukhov, He, 2010;Petoukhov, Petukhova, 2017;Petoukhov, Petukhova, Sirin, 2019;Petoukhov, Tolokonnikov, 2020].…”

Section: Recurrence Sequences Of Genetic Matricesmentioning

confidence: 99%

Hyperbolic Rules in Genomes, the Harmonic Progression and Recurrence Sequences in Algebraic Biology

Petoukhov¹

2020

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The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

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Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Cited by 15 publications

References 39 publications

The Genetic Coding System and Unitary Matrices

The Genetic Coding System and Unitary Matrices

The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences

Hyperbolic Rules in Genomes, the Harmonic Progression and Recurrence Sequences in Algebraic Biology

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