Structure and symmetries of the genetic codes for vertebrate, ascidian and yeast mitochondria

Genetic codes assign sixty-four codons to twenty amino acids. These assignments are known to follow certain rules. One question long considered but still unresolved is if these rules are derived from an underlying structure in genetic codes. Knowledge of such structure could facilitate better understanding of the biochemical, physico-chemical and evolutionary causes of the observed codon assignments. Our first finding reveals a coherent and symmetric structure in the genetic codes of vertebrate, ascidian, and yeast mitochondria. This structure is derived from a "simple" code that assigns all four codons with the same second nucleotide to a single amino acid if the first nucleotide is C or G, and assigns pairs of codons with the same second nucleotide to a single amino acid if the first nucleotide is A or U, and their third nucleotides are both purines (A and G) or both pyrimidines (U and C). The translation mechanism for the three mitochondria reflects this structure, one tRNA decoding each group of two or four codons into an amino acid. Our second finding is that the mycoplasma/spiroplasma and standard genetic codes are obtained by small sequential modifications of the vertebrate mitochondrial code and retain almost all its symmetries. We use group theory to characterize the symmetries of the simple and mitochondrial codes, and speculate on the implications of the structure for detecting translation errors and the evolution of the genetic code.