The coronavirus causing the COVID-19 pandemic, SARS-CoV-2, uses −1 programmed ribosomal frameshifting (−1 PRF) to control the relative expression of viral proteins. As modulating −1 PRF can inhibit viral replication, the RNA pseudoknot stimulating −1 PRF may be a fruitful target for therapeutics treating COVID-19. We modeled the unusual 3-stem structure of the stimulatory pseudoknot of SARS-CoV-2 computationally, using multiple blind structural prediction tools followed by μs-long molecular dynamics simulations. The results were compared for consistency with nuclease-protection assays and single-molecule force spectroscopy measurements of the SARS-CoV-1 pseudoknot, to determine the most likely conformations. We found several possible conformations for the SARS-CoV-2 pseudoknot, all having an extended stem 3 but with different packing of stems 1 and 2. Several conformations featured rarely-seen threading of a single strand through junctions formed between two helices. These structural models may help interpret future experiments and support efforts to discover ligands inhibiting −1 PRF in SARS-CoV-2.

The coronavirus causing the COVID-19 pandemic, SARS-CoV-2, uses −1 programmed ribosomal frameshifting (−1 PRF) to control the relative expression of viral proteins. As modulating −1 PRF can inhibit viral replication, the RNA pseudoknot stimulating −1 PRF may be a fruitful target for therapeutics treating COVID-19. We modeled the unusual 3stem structure of the stimulatory pseudoknot of SARS-CoV-2 computationally, using multiple blind structural prediction tools followed by μs-long molecular dynamics simulations. The results were compared for consistency with nuclease-protection assays and single-molecule force spectroscopy measurements of the SARS-CoV-1 pseudoknot, to determine the most likely conformations. We found several possible conformations for the SARS-CoV-2 pseudoknot, all having an extended stem 3 but with different packing of stems 1 and 2. Several conformations featured rarely-seen threading of a single strand through the junction formed between two helices. These structural models may help interpret future experiments and support efforts to discover ligands inhibiting −1 PRF in SARS-CoV-2.

In this work, exact solutions of the Dirac equation are studied for the pseudo-harmonic oscillatory ring-shaped potential by using the supersymmetry method. The un-normalized eigenfunctions and the eigenvalue equation of the Dirac equation are presented. Some numerical results are given. We also discuss the special cases of this potential. In addition, valence energy states can be produced from our solution for the whole state by taking the appropriate transformation of parameters.

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