p-Adic Structure of the Genetic Code

Драгович, Бранко

doi:10.14704/nq.2011.9.4.498

Cited by 16 publications

(20 citation statements)

References 32 publications

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“…It is expected that all these uniqueness correspond to the same, or similar uniqueness, found by other authors ( [16], [17], [18], [19]), what in future researches should be checked.…”

Section: Concluding Remarksupporting

confidence: 80%

Golden and Harmonic Mean in the Genetic Code

Rakočević¹

2017

Preprint

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In previous two works [1], [2] we have shown the determination of genetic code by golden and harmonic mean within standard Genetic Code Table (GCT), i.e. nucleotide triplet table, whereas in this paper we show the same determination through a specific connection between two tables -of nucleotide doublets Table (DT) and triplets Table (TT), over polarity of amino acids, measured by Cloister energy.

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“…It is expected that all these uniqueness correspond to the same, or similar uniqueness, found by other authors ( [16], [17], [18], [19]), what in future researches should be checked.…”

Section: Concluding Remarksupporting

confidence: 80%

Golden and Harmonic Mean in the Genetic Code

Rakočević¹

2017

Preprint

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“…One can note that our study belongs to the field of applications of algebraic methods and notions of quantum mechanics for modeling moleculargenetic structures where works of many authors exist, for example, the following [Dragovich, Dragovich, 2007;Dragovich, Khrennikov, Misic, 2017;Fimmel, Danielli, Strüngmann, 2013;Fimmel, Strüngmann, 2016;Igamberdiev, 1993;Ji, 2015Ji, , 2017Hu, Petoukhov, Petukhova, 2017;Matsuno, 1999Matsuno, , 2003Matsuno, , 2015Matsuno, Paton, 2000;Moon Ho Lee et al, 2017;Pellionis, 2008;Pellionisz et al, 2012;Penrose, 1996;Perez, 2010Perez, , 2013Perez, , 2017Petoukhov, 2008Petoukhov, , 2010aPetoukhov, ,b, 2011Petoukhov, , 2012Petoukhov, , 2015aPetoukhov, ,b,c,d,c, 2016Petoukhov, , 2017aPetoukhov, He, 2009;Petoukhov, Petukhova, 2017a,b;Petoukhov, Svirin, 2012;Rapoport, 2016a,b,c;Rumer, 1968;Simeonov, 2013;Stambuk, 1999].…”

Section: Connections Among Amino Acids and Triplets From The Standpoimentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

Petoukhov¹

2018

Preprint

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Abstract. 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 quantuminformation approaches for modeling genetic systems.

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“…On all the said and some other similar investigations of mathematical regularities of the GC one can see the following works: (Sukhodolets, 1985;Leunissen and De Jong, 1986;Koruga, 1992;Madox, 1992Madox, , 1994Shcherbak, 1993Shcherbak, -2008Damjanović, 1998Damjanović, -2006Qiu and Zhu, 2000;Yang, 2004;Dragovich, 2006Dragovich, -2012Negadi, 2009Negadi, -2014Castro-Chavez, 2010Mišić, 2011;Petoukhov, 2014;2016;Wohlin, 2015;Rakočević, 1988Rakočević, -2014.…”

Section: Some Other Mathematical Formalismsmentioning

confidence: 85%

Analogies of Genetic and Chemical Code

Rakočević¹

2017

Preprint

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Abstract. Starting from the previously established hypothesis on the existence of "the coherence of the chemical and genetic code" (Rakočević, 1991), new facts and new insights on the existence of essential analogies between the genetic and chemical code are presented, whereby the chemical code is derived from the original Mendeleev's work on the periodic system of chemical elements. When, namely, the 14 lanthanides are scheduled into 14 groups of Periodic system of chemical elements (PSE) (Rakočević, 1991), in accordance to Mendeleev's original manuscript tables, then are revealed some very specific mathematical and chemical regularities within the PSE; among others, PSE appears to be a code -the chemical code -in an entity analogy with the terrestrial genetic code. These regularities correspond to the mathematical regularities within the genetic code. Between others relations, it appears also a correspondance between the distribution of codons in the Genetic Code Table and the distribution of chemical elements in the PSE with respect to their even/odd parity and stability/instability of the isotopes. Based on the significant mathematical expressions it is showed a new essence of coding formalism in natural code as such: it cannot be reduced only to two alphabets (which are consequences, and not the cause); a natural code is such an essence that can be represented by an appropriate mathematical expression, which contains a sequence from the series of natural numbers within itself. From this follows that both are natural codes, the Genetic code as well as the Periodic system of chemical elements (PSE).

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p-Adic Structure of the Genetic Code

Cited by 16 publications

References 32 publications

Golden and Harmonic Mean in the Genetic Code

Golden and Harmonic Mean in the Genetic Code

The Genetic Coding System and Unitary Matrices

Analogies of Genetic and Chemical Code

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