The Maximal C(3) Self-Complementary Trinucleotide Circular Code X in Genes of Bacteria, Archaea, Eukaryotes, Plasmids and Viruses

In 1996, a set [Formula: see text] of 20 trinucleotides was identified in genes of both prokaryotes and eukaryotes which has on average the highest occurrence in reading frame compared to its two shifted frames. Furthermore, this set [Formula: see text] has an interesting mathematical property as [Formula: see text] is a maximal [Formula: see text] self-complementary trinucleotide circular code. In 2015, by quantifying the inspection approach used in 1996, the circular code [Formula: see text] was confirmed in the genes of bacteria and eukaryotes and was also identified in the genes of plasmids and viruses. The method was based on the preferential occurrence of trinucleotides among the three frames at the gene population level. We extend here this definition at the gene level. This new statistical approach considers all the genes, i.e., of large and small lengths, with the same weight for searching the circular code [Formula: see text]. As a consequence, the concept of circular code, in particular the reading frame retrieval, is directly associated to each gene. At the gene level, the circular code [Formula: see text] is strengthened in the genes of bacteria, eukaryotes, plasmids, and viruses, and is now also identified in the genes of archaea. The genes of mitochondria and chloroplasts contain a subset of the circular code [Formula: see text]. Finally, by studying viral genes, the circular code [Formula: see text] was found in DNA genomes, RNA genomes, double-stranded genomes, and single-stranded genomes.