The Arithmetical Origin of the Genetic Code

The Genetic Code via Godel Encoding

“…As for (i), 3, 5 and 8 appear to be the 3rd, 4th and 5th from the Fibonacci series {1, 2, 3, 5, 8, 13, …}, to the extent that the "initial conditions" F(0)=0 and F(1)=1 are discarded. We see therefore here some manifestation of the "Egyptian Triangle", or the first Pythagorean triple {3, 4, 5}, see [6]. Even the coefficients SC and MC introduced for the doublets, in respectively sections 1 and 2, have values that appear as ratios of the first Fibonacci numbers 1/2, 2/3, 3/5, .… Finally, returning a last time to the number 117, we have a 0 (117)=19 which could maybe refer to proline, "it would indeed shine by its absence", as there 19 true amino acids and one unique "imino acid", proline.…”

“…is also very interesting: (i) it has as digits three Fibonacci numbers 3, 5 and 8 and (ii) it has a 0 (358)=2+179=181. These relations seem hidding the mathematical pattern of the exceptional structure of proline and also the related famous "Egyptian Triangle", see [6]. From (ii), 2 is the first prime and 179 and 181 are two twin primes, respectively, 41st and 42nd so that in terms of the prime ranking index, we have 1+41=42 (or 42-1=41).…”

“…Trevors and Abel express however a lack of full satisfaction and leave the door open to other new approaches and ideas. As a matter of fact, among the people cited by the above authors, shCherbak, see [6], has clearly detected the presence of the decimal place-value numerical system as well as an acting zero inside the genetic code and also many beautiful unique summations. We think that our present Arithmetical Model, which relies also on the decimal numerical system, with also a zero playing distinct roles, agrees with shCherbak's work and goes along parallel lines of thought.…”

“…(17)), without being related, or even equal, to the degeneracy of the corresponding amino acid, as it was the case in the standard genetic code. The relevance of zero in the arithmetical approach to the genetic code has been recently emphasized by shCherbak [6]. Our second important remark concerns the specific choice, we made, for the partition of the genetic code table into two equal moieties, to be encoded (see the introduction).…”

“…As several codons could code for one amino acid, one speaks about degeneracy and results a multiplet structure which is shown in Eq. (6). There are 5 quartets, 9 doublets, 3 sextets, 1 triplet and 2 singlets.…”