The multiplet structure of the genetic code, in one and small number

TL;DR

This paper demonstrates that the multiplet structure of the standard genetic code can be derived from the total number of nucleotides in 64 codons, revealing a mathematical basis for degeneracy classes.

Contribution

It introduces a novel derivation of genetic code multiplet structures based on number theory and nucleotide counts, providing new insights into genetic code organization.

Findings

Degeneracy classes linked to coprimality with Family-Box numbers

Triplet and sextet structures derived from quartets and doublets

Mathematical relationships explain genetic code degeneracy

Abstract

In this short paper, it is shown that the multiplet structure of the standard genetic code is derivable from the total number of nucleotides contained in 64 codons, 192, a small number. The degeneracy class-number is derived as the number of numbers coprime to the number of Family-Boxes involved for the quartets, the doublets and the singlets. Those for the triplet and the sextets are computed as simple linear combinations of the preceeding ones. Some interesting consequences are also presented.