Enrichment of Circular Code Motifs in the Genes of the Yeast Saccharomyces cerevisiae

A set [Formula: see text] of 20 trinucleotides has been found to have the highest average occurrence in the reading frame, compared to the two shifted frames, of genes of bacteria, archaea, eukaryotes, plasmids and viruses. This set [Formula: see text] has an interesting mathematical property, since [Formula: see text] is a maximal [Formula: see text] self-complementary trinucleotide circular code. Furthermore, any motif obtained from this circular code [Formula: see text] has the capacity to retrieve, maintain and synchronize the original (reading) frame. Since 1996, the theory of circular codes in genes has mainly been developed by analysing the properties of the 20 trinucleotides of [Formula: see text] , using combinatorics and statistical approaches. For the first time, we test this theory by analysing the [Formula: see text] motifs, i.e., motifs from the circular code [Formula: see text] , in the complete genome of the yeast Saccharomyces cerevisiae. Several properties of [Formula: see text] motifs are identified by basic statistics (at the frequency level), and evaluated by comparison to [Formula: see text] motifs, i.e., random motifs generated from 30 different random codes [Formula: see text]. We first show that the frequency of [Formula: see text] motifs is significantly greater than that of [Formula: see text] motifs in the genome of S. cerevisiae. We then verify that no significant difference is observed between the frequencies of [Formula: see text] and [Formula: see text] motifs in the non-coding regions of S. cerevisiae, but that the occurrence number of [Formula: see text] motifs is significantly higher than [Formula: see text] motifs in the genes (protein-coding regions). This property is true for all cardinalities of [Formula: see text] motifs (from 4 to 20) and for all 16 chromosomes. We further investigate the distribution of [Formula: see text] motifs in the three frames of S. cerevisiae genes and show that they occur more frequently in the reading frame, regardless of their cardinality or their length. Finally, the ratio of [Formula: see text] genes, i.e., genes with at least one [Formula: see text] motif, to non- [Formula: see text] genes, in the set of verified genes is significantly different to that observed in the set of putative or dubious genes with no experimental evidence. These results, taken together, represent the first evidence for a significant enrichment of [Formula: see text] motifs in the genes of an extant organism. They raise two hypotheses: the [Formula: see text] motifs may be evolutionary relics of the primitive codes used for translation, or they may continue to play a functional role in the complex processes of genome decoding and protein synthesis.