Unitary circular code motifs in genomes of eukaryotes.

A set X of 20 trinucleotides was identified in genes of bacteria, eukaryotes, plasmids and viruses, which has in average the highest occurrence in reading frame compared to its two shifted frames (Michel, 2015; Arquès and Michel, 1996). This set X has an interesting mathematical property as X is a circular code (Arquès and Michel, 1996). Thus, the motifs from this circular code X, called X motifs, have the property to always retrieve, synchronize and maintain the reading frame in genes. The origin of this circular code X in genes is an open problem since its discovery in 1996. Here, we first show that the unitary circular codes (UCC), i.e. sets of one word, allow to generate unitary circular code motifs (UCC motifs), i.e. a concatenation of the same motif (simple repeats) leading to low complexity DNA. Three classes of UCC motifs are studied here: repeated dinucleotides (D+ motifs), repeated trinucleotides (T+ motifs) and repeated tetranucleotides (T+ motifs). Thus, the D+ , T+ and T+ motifs allow to retrieve, synchronize and maintain a frame modulo 2, modulo 3 and modulo 4, respectively, and their shifted frames (1 modulo 2; 1 and 2 modulo 3; 1, 2 and 3 modulo 4 according to the C2 , C3 and C4 properties, respectively) in the DNA sequences. The statistical distribution of the D+ , T+ and T+ motifs is analyzed in the genomes of eukaryotes. A UCC motif and its comp lementary UCC motif have the same distribution in the eukaryotic genomes. Furthermore, a UCC motif and its complementary UCC motif have increasing occurrences contrary to their number of hydrogen bonds, very significant with the T+ motifs. The longest D+ , T+ and T+ motifs in the studied eukaryotic genomes are also given. Surprisingly, a scarcity of repeated trinucleotides (T+ motifs) in the large eukaryotic genomes is observed compared to the D+ and T+ motifs. This result has been investigated and may be explained by two outcomes. Repeated trinucleotides (T+ motifs) are identified in the X motifs of low composition (cardinality less than 10) in the genomes of eukaryotes. Furthermore, identical trinucleotide pairs of the circular code X are preferentially used in the gene sequences of eukaryotes. These two results suggest that the unitary circular codes of trinucleotides may have been involved in the formation of the trinucleotide circular code X. Indeed, repeated trinucleotides in the X motifs in the genomes of eukaryotes may represent an intermediary evolution from repeated trinucleotides of cardinality 1 (T+ motifs) in the genomes of eukaryotes up to the X motifs of cardinality 20 in the gene sequences of eukaryotes.