Background: The Covid19 infection is caused by the SARS-CoV-2 virus, a novel member of the coronavirus (CoV) family. CoV genomes code for a ORF1a / ORF1ab polyprotein and four structural proteins widely studied as major drug targets. The genomes also contain a variable number of open reading frames (ORFs) coding for accessory proteins that are not essential for virus replication, but appear to have a role in pathogenesis. The accessory proteins have been less well characterized and are difficult to predict by classical bioinformatics methods. Methods: We propose a computational tool GOFIX to characterize potential ORFs in virus genomes. In particular, ORF coding potential is estimated by searching for enrichment in motifs of the X circular code, that is known to be over-represented in the reading frames of viral genes. Results: We applied GOFIX to study the SARS-CoV-2 and related genomes including SARS-CoV and SARS-like viruses from bat, civet and pangolin hosts, focusing on the accessory proteins. Our analysis provides evidence supporting the presence of overlapping ORFs 7b, 9b and 9c in all the genomes and thus helps to resolve some differences in current genome annotations. In contrast, we predict that ORF3b is not functional in all genomes. Novel putative ORFs were also predicted, including a truncated form of the ORF10 previously identified in SARS-CoV-2 and a little known ORF overlapping the Spike protein in Civet-CoV and SARS-CoV. Conclusions: Our findings contribute to characterizing sequence properties of accessory genes of SARS coronaviruses, and especially the newly acquired genes making use of overlapping reading frames.

The circular code theory proposes that genes are constituted of two trinucleotide codes: the classical genetic code with 61 trinucleotides for coding the 20 amino acids (except the three stop codons { TAA , TAG , TGA }) and a circular code based on 20 trinucleotides for retrieving, maintaining and synchronizing the reading frame. It relies on two main results: the identification of a maximal C ³ self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses (Michel 2015 J. Theor. Biol. 380, 156–177. ( doi:10.1016/j.jtbi.2015.04.009 ); Arquès & Michel 1996 J. Theor. Biol. 182, 45–58. ( doi:10.1006/jtbi.1996.0142 )) and the finding of X circular code motifs in tRNAs and rRNAs, in particular in the ribosome decoding centre (Michel 2012 Comput. Biol. Chem. 37, 24–37. ( doi:10.1016/j.compbiolchem.2011.10.002 ); El Soufi & Michel 2014 Comput. Biol. Chem. 52, 9–17. ( doi:10.1016/j.compbiolchem.2014.08.001 )). The univerally conserved nucleotides A1492 and A1493 and the conserved nucleotide G530 are included in X circular code motifs. Recently, dinucleotide circular codes were also investigated (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. ( doi:10.1155/2013/538631 ); Fimmel et al. 2015 J. Theor. Biol. 386, 159–165. ( doi:10.1016/j.jtbi.2015.08.034 )). As the genetic motifs of different lengths are ubiquitous in genes and genomes, we introduce a new approach based on graph theory to study in full generality n -nucleotide circular codes X , i.e. of length 2 (dinucleotide), 3 (trinucleotide), 4 (tetranucleotide), etc. Indeed, we prove that an n -nucleotide code X is circular if and only if the corresponding graph is acyclic. Moreover, the maximal length of a path in corresponds to the window of nucleotides in a sequence for detecting the correct reading frame. Finally, the graph theory of tournaments is applied to the study of dinucleotide circular codes. It has full equivalence between the combinatorics theory (Michel & Pirillo 2013 ISRN Biomath. 2013, 538631. ( doi:10.1155/2013/538631 )) and the group theory (Fimmel et al. 2015 J. Theor. Biol. 386, 159–165. ( doi:10.1016/j.jtbi.2015.08.034 )) of dinucleotide circular codes while its mathematical approach is simpler.