The genomic ssRNA of coronaviruses is packaged within a helical nucleocapsid. Due to transitional symmetry of a helix, weakly specific cooperative interaction between ssRNA and nucleocapsid proteins leads to the natural selection of specific quasi-periodic assembly/packaging signals in the related genomic sequence. Such signals coordinated with the nucleocapsid helical structure were detected and reconstructed in the genomes of the coronaviruses SARS-CoV and SARS-CoV-2. The main period of the signals for both viruses was about 54 nt, that implies 6.75 nt per N protein. The complete coverage of ssRNA genome of length about 30,000 nt by the nucleocapsid would need 4,400 N proteins, that makes them the most abundant among the structural proteins. The repertoires of motifs for SARS-CoV and SARS-CoV-2 were divergent but nearly coincided for different isolates of SARS-CoV-2. We obtained the distributions of assembly/packaging signals over the genomes with non-overlapping windows of width 432 nt. Finally, using the spectral entropy, we compared the load from point mutations and indels during virus age for SARS-CoV and SARS-CoV-2. We found the higher mutational load on SARS-CoV. In this sense, SARS-CoV-2 can be treated as a newborn virus. These observations may be helpful in practical medical applications and are of basic interest.
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