Construction of Dinucleotide Circular Codes Based on Nucleotide Probabilities.

Circular code identified by the codon usage

Circular cut codes in genetic information

The maximal C3 self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses

Mixed circular codes

Genes on the circular code alphabet

Spontaneous evolution of circular codes in theoretical minimal RNA rings

The production of methacrylic acid in Escherichia coli

In 1994, with a statistical study of trinucleotide occurences per frame, D. Arquès and C. Michel identified the fol lowing set of 20 trin- ucleotides in the gene population of both eucaryotes E U K and procaryotes P RO: {AAC , AAT , AC C , ATC,ATT,CAG,CTC,CTG,GAA,GAC,GAG,GAT, GCC,GGC,GGT,GTA,GTC,GTT,TAC,TTC}.Thisset of words of length three on the genetic alphabet A4 = {A, C, G, T } has remarkable properties: it is a self-complementary set, it is a circular code, it is maximal and it has the C3- property. This and other identifications of trinucleotide circular codes in different genomes in the last twenty years raised interest in the concept of trinucleotide circular code for genetics. In 2003 we found an efficient algorithm for testing the circularity of a trinucleotide code and in 2005 we found the list of al l 528 maximal self-complementary circular codes. In 2008 we presented a hierarchy of the self-complementary circular codes and in 2012 we presented a hierarchy of al l circular codes. These circular codes could permit the identification, either in paral lel with or substituting existing methods used by biologist, of as yet unknown coding regions of DNA. A hierarchy of tetranucleotide circular codes is one of our aims in the future. In this paper we begin the study of the unbordered tetranucleotides and of the “forbidden configurations” for tetranucleotides and we give a first result.

Circular code in introns

A genetic scale of reading frame coding

Diletter circular codes over finite alphabets

Potential role of the X circular code in the regulation of gene expression

In 1996, a set 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 has an interesting mathematical property as is a maximal self-complementary trinucleotide circular code. In 2015, by quantifying the inspection approach used in 1996, the circular code 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 . 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 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 . Finally, by studying viral genes, the circular code was found in DNA genomes, RNA genomes, double-stranded genomes, and single-stranded genomes.

Circular codes revisited: A statistical approach

Maximal dinucleotide and trinucleotide circular codes