p-Adic Side of the Genetic Code and the Genome

The genetic code is a mapping from the set of 64 codons onto the set of 20 amino acids and one stop signal. The codons are ordered triplets composed of the nucleotides cytosine (C), adenine (A), uracil (U) (or thymine (T)), guanine (G) and they are contained in the genes. The amino acids are building blocks of the proteins. The vertebrate mitochondrial code is rather simple and the other genetic codes can be considered as its slight modifications. In the vertebrate mitochondrial code, an amino acid is coded by one, two or three codon doublets. When two codons code the same amino acid, one can say that they are close in the informational sense. We show that the p-adic distance is an adequate mathematical instrument for description of the informational codon closeness (nearness, similarity). We show that the set of codons and the set of amino acids are p-adic ultrametric spaces and that the vertebrate mitochondrial code is an ultrametric network. A p-adic approach to possible evolution of the genetic code is presented. We also demonstrate that p-adic closeness between codons, and between nucleotides, is also useful in the investigation of informational closeness between sequences in the genome.