A taylor-made arithmetic model of the genetic code and applications

An important and notable improvement of our recent arithmetic model of the standard genetic code based on Gödel encoding is presented using a “head/tail” metaphor. Etched in the “head” we have the decimal representation of 23!, with 23 digits, from which Rumer’s division of the genetic code table into the two equal moieties M1 and M1 arises quite naturally. By ultimately reducing every digit-value in the model to its prime-factorization form, we compute the exact degeneracy of the two sets as well as the number of amino acids and stop signals in them and deduce also the degeneracies and the number of amino acids of the five degeneracy-classes of the standard genetic code as well as the three stop signals. This is made possible thanks to a subtle encoding of the doublet-parts of the three sextets, in the doublets. In the “tail” side, on the other hand, we have (also etched) the prime-factorization of 23!, using the fundamental theorem of arithmetic, and leading directly to two other important divisions of the genetic code table into two equal moieties the first-base pyrimidine/purine series and the first-base keto/amino series. In both cases, the degeneracy of the two moieties appears (conspicuously) to be encoded in a Gödelian way, in the exponents of the prime factorization of 23!. This new understanding (two sides of the same “coin”) improves and enriches our model and also paves the way for interesting applications inside and outside the genetic code. In the first instance we successfully include in our model the 21 and 22 coded amino acids Selenocysteine and Pyrrolysine as an almost trivial application. In the second, we derive the carbon and hydrogen atom composition as well as the atom number in the “61 amino acids” of the whole genetic code table, according to characteristic patterns, from the digits representing the amino acids themselves and show also that the degeneracy and the chemical composition of the amino acids are connected. In particular * Address: Department of Physics, Faculty of Science, University of Oran, Es-Sénia, 31100, Oran, Algeria.email: [email protected]; [email protected]