A rationale for the symmetries by base substitutions of degeneracy in the genetic code

The first symmetry by base substitutions of degeneracy in the genetic code was described by Rumer (1966) and the other symmetries were identified later by Jestin (2006) and Jestin and Soulé (2007). Here, a rationale accounting for these symmetries is reported. The number of non-synonymous substitutions over the replicated coding sequence is written as a function of the substitution matrix, whose elements are the number of substitutions from any codon to any other codon. The p-adic distance used as a similarity measure and applied to this matrix is shown to be biologically relevant. The rationale indicates that symmetries by base substitutions of degeneracy in the genetic code are symmetries of the measures of the number of non-synonymous substitutions for sets of synonymous codons.