p-Adic Modelling of the Genome and the Genetic Code

Драгович, Бранко; Dragovich, A. Yu.

doi:10.1093/comjnl/bxm083

Cited by 48 publications

(41 citation statements)

References 27 publications

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“…Nonlocal structures also appear in noncommutative geometry and string field theory (SFT) [12], p-adic strings [13], zeta strings [14], and strings quantized on a random lattice [15,16]; for a review, see [17]. LQG and causal set approaches are primarily based on nonlocal Wilsonian operators, while nonlocality in the form of an infinite set of derivatives has been discussed in the context of renormalization group arguments within the context of asymptotic safety [18].…”

Section: Introductionmentioning

confidence: 99%

Consistent higher derivative gravitational theories with stable de Sitter and anti–de Sitter backgrounds

2017

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In this paper we provide the criteria for any generally covariant, parity preserving, and torsion free theory of gravity to possess a stable de Sitter (dS) or anti-de Sitter (AdS) background. By stability we mean the absence of tachyonic or ghost-like states in the perturbative spectrum that can lead to classical instabilities and violation of quantum unitarity. While we find that the usual suspects, the F (R) and F (G) theories, can indeed possess consistent (A)dS backgrounds, G being the Gauss-Bonnet term, another interesting class of theories, string-inspired infinite derivative gravity, can also be consistent around such curved vacuum solutions. Our study should not only be relevant for quantum gravity and early universe cosmology involving ultraviolet physics, but also for modifications of gravity in the infra-red sector vying to replace dark energy.

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Section: Introductionmentioning

confidence: 99%

Consistent higher derivative gravitational theories with stable de Sitter and anti–de Sitter backgrounds

2017

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“…As one of the main results that we have obtained is explanation of the structure of the genetic code degeneracy using p -adic distance between codons. Paper (Dragovich and Dragovich, 2010) contains consideration of possible evolution of the genetic code and some generalizations of p -adic modelling of the genetic code. Article ) is related to the role of number theory in modelling the genetic code.…”

Section: Introductionmentioning

confidence: 99%

p-Adic Structure of the Genetic Code

Драгович

2011

Neuroquantology

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The genetic code is connection between 64 codons, which are building blocks of the genes, and 20 amino acids, which are building blocks of the proteins. In addition to coding amino acids, a few codons code stop signal, which is at the end of genes, i.e. it terminates process of protein synthesis. This article is a review of simple modelling of the genetic code and related subjects by concept of p-adic distance. It also contains some new results. In particular, the article presents appropriate structure of the codon space, degeneration and possible evolution of the genetic code. p-Adic modelling of the genetic code is viewed as the first step in further application of padic tools in the information sector of life science.

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“…Other metrics define different spaces; for example, Dragovich and Dragovich [40] use a p-adic, ultrametric norm; the four nucleotides are at one 5-adic and four codons differing only in the 3rd position are at 1/25 5-adic distance from each other. shCherbak [41] assigns codons integer nucleon numbers of their encoded amino acids and develops a digital arithmetic code.…”

Section: Discussionmentioning

confidence: 99%

The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric

Lenstra¹

2015

Symmetry

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Abstract:The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for the 64 codons of the codon set. (Hamming distances equal the number of different codon positions: AAA and AAC are at 1-distance; codons are maximally at 3-distance.) The CodonPolytope, a 9-dimensional geometric object, is spanned by 64 vertices that represent the codons and the Euclidian distances between these vertices correspond one-to-one with intercodon Hamming distances. The CodonGraph represents the vertices and edges of the polytope; each edge equals a Hamming 1-distance. The mirror reflection symmetry group of the polytope is isomorphic to the largest permutation symmetry group of the codon set that preserves Hamming distances. These groups contain 82,944 symmetries. Many polytope symmetries coincide with the degeneracy and similarity patterns of the genetic code. These code symmetries are strongly related with the face structure of the polytope with smaller faces displaying stronger code symmetries. Splitting the polytope stepwise into smaller faces models an early evolution of the code that generates this hierarchy of code symmetries. The canonical code represents a class of 41,472 codes with equivalent symmetries; a single class among an astronomical number of symmetry classes comprising all possible codes.

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p-Adic Modelling of the Genome and the Genetic Code

Cited by 48 publications

References 27 publications

Consistent higher derivative gravitational theories with stable de Sitter and anti–de Sitter backgrounds

Consistent higher derivative gravitational theories with stable de Sitter and anti–de Sitter backgrounds

p-Adic Structure of the Genetic Code

The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric

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