Elena Fimmel1 and Lutz Strüngmann1
1Mannheim University of Applied Sciences, Paul-Wittsack Str. 10, 68163 Mannheim, Germany
l.struengmann [at] hs-mannheim.de
e.fimmel [at] hs-mannheim.de
Abstract
Codes are the sets of words over arbitrary alphabets with the property of unique decipherability.
Circular codes are a special class of codes. They are the sets of words with the property of unique recognition of the reading frame for any sequence composed of them and written on a circle. They were introduced by Golomb and Gordon in the 60s under the name of codes with bounded synchronization delay, because they have a strong property of synchronization. For this reason, they play an important role in problems of error correction.
In the middle 90’s such a circular code X was identified in the genes of bacteria, eukaryotes, plasmids, and viruses by a comprehensive statistical investigation. The code X contained the 20 trinucleotides that appeared to be the codons that had the highest preference for the correct reading frame compared to frames 1 and 2. Since then intensive research on circular codes in the genetic information and their potential role in maintaining the correct reading frame during the translation process in the ribosome has been done by various authors. In particular, X-motifs were identified in (i) genes “universally” (ii) tRNAs of prokaryotes and eukaryotes; (iii) rRNAs of prokaryotes (16S) and eukaryotes (18S), in particular in the ribosome decoding center where the universally conserved nucleotides G530, A1492, and A1493 are included in the X-motif; and (iv) genomes (non-coding regions of eukaryotes). Circular codes have a highly complex structure and the ones found in genes possess additional properties like e.g. self-complementarity that reflect their biological nature.
In our talk we give a short introduction to the theory of circular codes and an overview on the methods from mathematics, statistics and bioinformatics to explore their properties and their biological role. Finally, a possible model of the evolution of the genetic code from the perspective of circular code theory is presented.
Keywords: Circular Codes, Genetic Code, Frame-Shift, Translation
