Optimality of circular codes versus the genetic code after frameshift errors.

The standard genetic code (SGC) describes how 64 trinucleotides (codons) encode 20 amino acids and the stop translation signal. Biochemical and statistical studies have shown that the standard genetic code is optimized to reduce the impact of errors caused by incorporation of wrong amino acids during translation. This is achieved by mapping codons that differ by only one nucleotide to the same amino acid or one with similar biochemical properties, so that if misincorporation occurs, the structure and function of the translated protein remain relatively unaltered.

Circular code motifs in the ribosome: a missing link in the evolution of translation?

The origin of the genetic code remains enigmatic five decades after it was elucidated, although there is growing evidence that the code coevolved progressively with the ribosome. A number of primordial codes were proposed as ancestors of the modern genetic code, including comma-free codes such as the , , or codes ( = G or A, = C or T, = any nucleotide), and the circular code, an error-correcting code that also allows identification and maintenance of the reading frame. It was demonstrated previously that motifs of the circular code are significantly enriched in the protein-coding genes of most organisms, from bacteria to eukaryotes.

Evolutionary conservation and functional implications of circular code motifs in eukaryotic genomes.

A set X 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 (Michel, 2015, 2017; Arquès and Michel, 1996). This set X has an interesting mathematical property, since X is a maximal C self-complementary trinucleotide circular code (Arquès and Michel, 1996). Furthermore, any motif obtained from this circular code X has the capacity to retrieve, maintain and synchronize the reading frame in genes.