p-Adic Degeneracy of the Genetic Code

Abstract: Degeneracy of the genetic code is a biological way to minimize effects of the undesirable mutation changes. Degeneration has a natural description on the 5-adic space of 64 codons $\mathcal{C}_5 (64) = {n_0 + n_1 5 + n_2 5^2 : n_i = 1, 2, 3, 4 } ,$ where $n_i$ are digits related to nucleotides as follows: C = 1, A = 2, T = U = 3, G = 4. The smallest 5-adic distance between codons joins them into 16 quadruplets, which under 2-adic distance decay into 32 doublets. p-Adically close codons are assigned to one of 20 amino acids, which are building blocks of proteins, or code termination of protein synthesis. We shown that genetic code multiplets are made of the p-adic nearest codons.