The genetic code invariance: when Euler and Fibonacci meet

Abstract

The number of atoms in the four ribonucleotides uridine monophosphate, cytidine monophosphate, adenine monophosphate and guanine monophosphate is taken as a key parameter. A mathematical relation describing the condensation of the three basic subunits a nucleobase, a ribose and a phosphate group, to form a ribonucleotide, is first obtained from this parameter. Next, the use of the latter and Euler totient function is shown to lead to the atom number content of the 64 codons and also to Rakocevic pattern. Finally, selected finite sums of Fibonacci numbers are shown to lead to the nucleon number content of the amino acids in various degeneracy patterns, and also to the multiplet structure of the 20 amino acids as well as to the degeneracy.