Abstract
The standard genetic code is found to exhibit an exact symmetry under a finite group of order 4 known in mathematics as the Klein group. The same symmetry is also present in almost all non-standard codes, mitochondrial as well as nuclear. Analysis of the phylogenetic tree for the evolution of the mitochondrial codes reveals that all changes along the main line of evolution preserve this symmetry, with a tendency towards symmetry enhancement. In the side branches of the evolutionary tree, the majority of changes also respect the symmetry. The few exceptional cases where it is broken correspond to reassignments that appear to be unstable or incomplete. Since the Klein group emerges naturally from the symplectic model for the prebiotic evolution that has led to the standard code, we interpret these results as lending support to the hypothesis that this symmetry has been selected during the evolution of the genetic code, not only before but also after establishment of the standard code.
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