A role for circular code properties in translation

Circular codes represent a form of coding allowing detection/correction of frame-shift errors. Building on recent theoretical advances on circular codes, we provide evidence that protein coding sequences exhibit in-frame circular code marks, that are absent in introns and are intimately linked to the keto-amino transformation of codon bases. These properties strongly correlate with translation speed, codon influence and protein synthesis levels. Strikingly, circular code marks are absent at the beginning of coding sequences, but stably occur 40 codons after the initiator codon, hinting at the translation elongation process. Finally, we use the lens of circular codes to show that codon influence on translation correlates with the strong-weak dichotomy of the first two bases of the codon. The results can lead to defining new universal tools for sequence indicators and sequence optimization for bioinformatics and biotechnological applications, and can shed light on the molecular mechanisms behind the decoding process.

Equivalence classes of circular codes induced by permutation groups

In the 1950s, Crick proposed the concept of so-called comma-free codes as an answer to the frame-shift problem that biologists have encountered when studying the process of translating a sequence of nucleotide bases into a protein. A little later it turned out that this proposal unfortunately does not correspond to biological reality. However, in the mid-90s, a weaker version of comma-free codes, so-called circular codes, was discovered in nature in J Theor Biol 182:45–58, 1996. Circular codes allow to retrieve the reading frame during the translational process in the ribosome and surprisingly the circular code discovered in nature is even circular in all three possible reading-frames ($$C^3$$ C 3 -property). Moreover, it is maximal in the sense that it contains 20 codons and is self-complementary which means that it consists of pairs of codons and corresponding anticodons. In further investigations, it was found that there are exactly 216 codes that have the same strong properties as the originally found code from J Theor Biol 182:45–58. Using an algebraic approach, it was shown in J Math Biol, 2004 that the class of 216 maximal self-complementary $$C^3$$ C 3 -codes can be partitioned into 27 equally sized equivalence classes by the action of a transformation group $$L \subseteq S_4$$ L ⊆ S 4 which is isomorphic to the dihedral group. Here, we extend the above findings to circular codes over a finite alphabet of even cardinality $$|\Sigma |=2n$$ | Σ | = 2 n for $$n \in {\mathbb {N}}$$ n ∈ N . We describe the corresponding group $$L_n$$ L n using matrices and we investigate what classes of circular codes are split into equally sized equivalence classes under the natural equivalence relation induced by $$L_n$$ L n . Surprisingly, this is not always the case. All results and constructions are illustrated by examples.

A role for circular code properties in translation

Circular codes represent a form of coding allowing detection/correction of frameshift errors. Building on recent theoretical advances on circular codes, we provide evidence that protein coding sequences exhibit in-frame circular code marks, that are absent in introns and are intimately linked to the keto-amino transformation of codon bases. These properties strongly correlate with translation speed, codon influence and protein expression levels. Strikingly, circular code marks are absent at the beginning of coding sequences, but stably occur 40 codons after the initiator codon, hinting at the translation elongation process. Finally, we use the lens of circular codes to show that codon influence on translation correlates with the strong-weak dichotomy of the first two bases of the codon. The results provide promising universal tools for sequence indicators and sequence optimization for bioinformatics and biotechnological applications, and can shed light on the molecular mechanisms behind the decoding process.

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

The X circular code is a set of 20 trinucleotides (codons) that has been identified in the protein-coding genes of most organisms (bacteria, archaea, eukaryotes, plasmids, viruses). It has been shown previously that the X circular code has the important mathematical property of being an error-correcting code. Thus, motifs of the X circular code, i.e. a series of codons belonging to X, which are significantly enriched in the genes, allow identification and maintenance of the reading frame in genes. X motifs have also been identified in many transfer RNA (tRNA) genes and in important functional regions of the ribosomal RNA (rRNA), notably in the peptidyl transferase center and the decoding center. Here, we investigate the potential role of X motifs as functional elements in the regulation of gene expression. Surprisingly, the definition of a simple parameter identifies several relations between the X circular code and gene expression. First, we identify a correlation between the 20 codons of the X circular code and the optimal codons/dicodons that have been shown to influence translation efficiency. Using previously published experimental data, we then demonstrate that the presence of X motifs in genes can be used to predict the level of gene expression. Based on these observations, we propose the hypothesis that the X motifs represent a new genetic signal, contributing to the maintenance of the correct reading frame and the optimization and regulation of gene expression.Author SummaryThe standard genetic code is used by (quasi-) all organisms to translate information in genes into proteins. Recently, other codes have been identified in genomes that increase the versatility of gene decoding. Here, we focus on the circular codes, an important class of genome codes, that have the ability to detect and maintain the reading frame during translation. Motifs of the X circular code are enriched in protein-coding genes from most organisms from bacteria to eukaryotes, as well as in important molecules in the gene translation machinery, including transfer RNA (tRNA) and ribosomal RNA (rRNA). Based on these observations, it has been proposed that the X circular code represents an ancestor of the standard genetic code, that was used in primordial systems to simultaneously decode a smaller set of amino acids and synchronize the reading frame. Using previously published experimental data, we highlight several links between the presence of X motifs in genes and more efficient gene expression, supporting the hypothesis that the X circular code still contributes to the complex dynamics of gene regulation in extant genomes.

Single-Frame, Multiple-Frame and Framing Motifs in Genes

We study the distribution of new classes of motifs in genes, a research field that has not been investigated to date. A single-frame motif SF has no trinucleotide in reading frame (frame 0) that occurs in a shifted frame (frame 1 or 2), e.g., the dicodon AAACAA is SF as the trinucleotides AAA and CAA do not occur in a shifted frame. A motif which is not single-frame SF is multiple-frame MF. Several classes of MF motifs are defined and analysed. The distributions of single-frame SF motifs (associated with an unambiguous trinucleotide decoding in the two 5'–3' and 3'–5' directions) and 5′ unambiguous motifs 5'U (associated with an unambiguous trinucleotide decoding in the 5'–3' direction only) are analysed without and with constraints. The constraints studied are: initiation and stop codons, periodic codons AAA,CCC,GGG,TTT, antiparallel complementarity and parallel complementarity. Taken together, these results suggest that the complementarity property involved in the antiparallel (DNA double helix, RNA stem) and parallel sequences could also be fundamental for coding genes with an unambiguous trinucleotide decoding in the two 5'–3' and 3'–5' directions or the 5'–3' direction only. Furthermore, the single-frame motifs SF with a property of trinucleotide decoding and the framing motifs F (also called circular code motifs; first introduced by Michel (2012)) with a property of reading frame decoding may have been involved in the early life genes to build the modern genetic code and the extant genes. They could have been involved in the stage without anticodon-amino acid interactions or in the Implicated Site Nucleotides (ISN) of RNA interacting with the amino acids. Finally, the SF and MF dipeptides associated with the SF and MF dicodons, respectively, are studied and their importance for biology and the origin of life discussed.