Numeral series hidden in the distribution of atomic mass of amino acids to codon domains in the genetic code

Abstract

The distribution of codons in the nearly universal genetic code is a long discussed issue. At the atomic level, the numeral series 2x(2) (x=5-0) lies behind electron shells and orbitals. Numeral series appear in formulas for spectral lines of hydrogen. The question here was if some similar scheme could be found in the genetic code. A table of 24 codons was constructed (synonyms counted as one) for 20 amino acids, four of which have two different codons. An atomic mass analysis was performed, built on common isotopes. It was found that a numeral series 5 to 0 with exponent 2/3 times 10(2) revealed detailed congruency with codon-grouped amino acid side-chains, simultaneously with the division on atom kinds, further with main 3rd base groups, backbone chains and with codon-grouped amino acids in relation to their origin from glycolysis or the citrate cycle. Hence, it is proposed that this series in a dynamic way may have guided the selection of amino acids into codon domains. Series with simpler exponents also showed noteworthy correlations with the atomic mass distribution on main codon domains; especially the 2x(2)-series times a factor 16 appeared as a conceivable underlying level, both for the atomic mass and charge distribution. Furthermore, it was found that atomic mass transformations between numeral systems, possibly interpretable as dimension degree steps, connected the atomic mass of codon bases with codon-grouped amino acids and with the exponent 2/3-series in several astonishing ways. Thus, it is suggested that they may be part of a deeper reference system.

Numerical analysis of 3/2-relations in the genetic code and correlations with the basic series of integers 5-0

“…The codon domains G1 + C1 of aas became equal to G2 + C2 = 544, as the sums U1 + A1 equals U2 + A2 = 960. (It should be noted that the basic two Arg and Lys here were counted as charged in agreement with Wohlin and Karlson [8,9].…”

“…In the preceding paper (Section 6) [8] it was suggested on the basis of several examples that transformations between number-base systems (nb-x) as between nb-10, nb-8 and nb-6 could be a hidden reference system in the genetic code. Rewritings of lower nb-numbers with digits from nb-10 were freely used.…”

“…In fact, a related numeral series has been shown to highly correlate to the structure of the genetic code in several different aspects [8]. It was argued that such a structure, dimensionally, geometrically or numerically interpreted, should perhaps not be recognizable at the very first steps of syntheses in the evolution of the code, just gradually revealed by spontaneous self-organization.…”

Analogies of genetic and chemical code

“…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.…”

System-directed pairing of protein amino acids. Part I

“…1A, p. 34); and also 24 of AAs (Damjanović, 1998;Rakočević, 2007a, Tab. 7 [Figure 3.3 and Table E1 in this paper]; Wohlin, 2015). As shown above, it makes sense to read 20 AAs, as many there are in reality, in the standard GC (MMR, 2004a, Tabs 7 and 8, p. 228;Figure 3.1 and 3.2…”