Bijective transformation circular codes and nucleotide exchanging RNA transcription

The C3 self-complementary circular code X identified in genes of prokaryotes and eukaryotes is a set of 20 trinucleotides enabling reading frame retrieval and maintenance, i.e. a framing code (Arquès and Michel, 1996, Michel, 2012, Michel, 2013). Some mitochondrial RNAs correspond to DNA sequences when RNA transcription systematically exchanges between nucleotides (Seligmann, 2013a, Seligmann, 2013b). We study here the 23 bijective transformation codes ΠX of X which may code nucleotide exchanging RNA transcription as suggested by this mitochondrial observation. The 23 bijective transformation codes ΠX are C3 trinucleotide circular codes, seven of them are also self-complementary. Furthermore, several correlations are observed between the Reading Frame Retrieval (RFR) probability of bijective transformation codes ΠX and the different biological properties of ΠX related to their numbers of RNAs in GenBank's EST database, their polymerization rate, their number of amino acids and the chirality of amino acids they code. Results suggest that the circular code X with the functions of reading frame retrieval and maintenance in regular RNA transcription, may also have, through its bijective transformation codes ΠX, the same functions in nucleotide exchanging RNA transcription. Associations with properties such as amino acid chirality suggest that the RFR of X and its bijective transformations molded the origins of the genetic code's machinery.