The Genetic Code via Godel Encoding

2011

Neuroquantology

A "quantum-like" analogy, introduced in 1998 by Rakočević in his study of the biosynthetic amino acid precursors, with the prime "quantum O37" in the background, is also considered in this paper as a guiding line of thought. We use and extend his results to derive (i) the multiplet structure of the standard genetic code, in a completely new and original way and (ii) several physicochemical quantities, as the number of nucleons in the 61 coded amino acids, the number of nucleons in 20, 23 and 61 amino acid biosynthetic precursors, the number of nucleons in 23 amino acids signals (AASs), the number of atoms in the 64 DNA-codons and in the 64 RNAcodons, and several other interesting quantities. In this way, we show that the fundamental set of seven fundamental amino acid precursors grouped into six amino acid families appears more informative than the larger set of twenty canonical amino acids. In a second part, we find once more a conspicuous numeric "manifestation" of serine, its protonated/neutral octamers and several other serine clusters; these clusters, in particular the serine octamer are thought to have been key players in the origin of homochirality. Also, we find, encoded, water (H 2 O) and, interestingly, the exact number of its characteristic water-water Hydrogen-Bond Contact/Non-Contact configurations (or "degeneracies") according to the body-centered cubic (bcc) lattice gas model for water.

mentioning

confidence: 57%

A “Quantum-Like” Approach to the Genetic Code

2011

Neuroquantology

“…These same relations have also another possible interpretation in terms of the total carbon atom number in the 20 amino acids sidechains which is 67. We have shown recently (Négadi, 2007(Négadi, , 2008 how this number appears from our arithmetical model in the form 67=25+42 (there are 25 carbon atoms in classes 1, 3 and 4, and 42 carbon atoms in classes 2 and 6). In the present case, we could write the sum in Eq.…”

Section: Degeneracy and Chemical Compositionmentioning

confidence: 81%

“…and is written below also in the decimal representation (2) and H+Q+C+Y (1+1+1+1), where as above we have indicated the degeneracies. This is only what we considered in our last paper (Négadi, 2008). Consider now the case (ii).…”

Section: Symmetry and Gödel Encodingmentioning

confidence: 89%

“…In the 61 "amino acids" there are 358 hydrogen atoms (21 in the 5 quartets, 22 in the 3 sextets, 50 in the 9 doublets, 9 in the triplet and 15 in the two singlets, so that 21´4+22´6+50´2+9´3+15´1 =358. Taking the sum of the prime factors of this number (358=2´179), and focusing on the prime indices of these latter and their sum, we have derived what we called shCherbak's proline identity (Négadi, 2008):…”

Section: Degeneracy and Chemical Compositionmentioning

confidence: 99%

See 1 more Smart Citation

The Genetic Code Degeneracy and the Amino Acids Chemical Composition are Connected

2008

Neuroquantology

We show that our recently published Arithmetic Model of the genetic code based on Gödel Encoding is robust against symmetry transformations; specially Rumer's one U«G, A«C and constitutes a link between the degeneracy structure and the chemical composition of the 20 canonical amino acids. As a result, several remarkable atomic patterns involving hydrogen, carbon, nucleon and atom numbers are derived. This study has no obvious practical application(s) but could, we hope, add some new knowledge concerning the physico-mathematical structure of the genetic code.

“…This is really a hard problem. In spite of this difficult problem, we have nonetheless tried, through the recent past years, to make some modest contributions to find mathematical models which, if not derived from "first principles", at least could faithfully reproduce the experimental data for the standard genetic code [3][4][5] and, to some extent, its important variant the Vertebrate Mitochondrial genetic code [4] (one could also find in [3][4][5] reference to other older works by ourselves). Recently, we have used the formalism of q-deformations (see Section 3) to study the case of the various today known genetic code variants [6,7].…”

Section: Introductionmentioning

confidence: 99%

The Genetic Codes: Mathematical Formulae and an Inverse Symmetry-Information Relationship

2016

Information

First, mathematical formulae faithfully describing the distributions of amino acids and codons and reproducing the degeneracies in the various known genetic codes, including the standard genetic code, are constructed, by hand. Second, we summarize another mathematical approach relying on the use of q-deformations to describe these same genetic codes, and add a new application not considered before. Third, by considering these same genetic codes, we find, qualitatively, that an inverse symmetry-information relationship exists.