Motif lengths of circular codes in coding sequences

Protein synthesis is a crucial process in any cell. Translation, in which mRNA is translated into proteins, can lead to several errors, notably frame shifts where the ribosome accidentally skips or re-reads one or more nucleotides. So-called circular codes are capable of discovering frame shifts and their codons can be found disproportionately often in coding sequences. Here, we analyzed motifs of circular codes, i.e. sequences only containing codons of circular codes, in biological and artificial sequences. The lengths of these motifs were compared to a statistical model in order to elucidate if coding sequences contain significantly longer motifs than non-coding sequences. Our findings show that coding sequences indeed show on average greater motif lengths than expected by chance. On the other hand, the motifs are too short for a possible frame shift recognition to take place within an entire coding sequence. This suggests that as much as circular codes might have been used in ancient life forms in order to prevent frame shift errors, it remains to be seen whether they are still functional in current organisms.