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Unlike the SARS-CoV-2 virus, the BioNTech/Pfizer SARS-CoV-2 vaccine has two stop UGA codons at the end of the Spike protein:

          V   L   K   G   V   K   L   H   Y   T   s             
Virus:   GUG CUC AAA GGA GUC AAA UUA CAU UAC ACA UAA
Vaccine: GUG CUG AAG GGC GUG AAA CUG CAC UAC ACA UGA UGA 
          V   L   K   G   V   K   L   H   Y   T   s   s          
               !   !   !   !     ! !   !          ! 

What is the motivation behind using two stop UGA codons instead of one in the BioNTech/Pfizer SARS-CoV-2 vaccine?

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The two stop codons are obviously to prevent read-through of the termination codon. Why this should be necessary is not clear to me, but the following may be relevant:

  1. The synthetic mRNA differs from the natural mRNA in a particular respect that is easier to explain with reference to the transcript map of the virus, below. Transcript map of coronavirus The two ORFs 1a and 1b are translated directly from the virus RNA as polyproteins, which are subsequently cleaved, but the proteins at the 3′ side of the viral RNA are transcribed into a series of nested mRNAs, each starting from a different 5′ position immediately preceeding the gene that will be translated. These mRNAs also retain RNA corresponding to the remaining genes (coloured grey, and not translated because of the monocistronic translation of eukaryotic mRNA) and the common 3′ polyA tail. The synthetic mRNA for the spike protein (S) lacks the RNA for the non-translated genes, and has the polyA tail near to the stop codon. Hence the secondary structure near the stop codon in the synthetic mRNA may well differ from that in the natural mRNA and possibly influence the likelihood of readthrough.

  2. The stop codons used in this artificial mRNA are not UGA but 1-Me-ΨGA, as U is replaced by 1-Me-Ψ (1-methyl-pseudouridine*) in they synthetic mRNA to prevent degradation. As the anticodon is recognized by a termination factor — not a tRNA anticodon — the interaction with 1-Me-ΨGA may possibly be poorer than for UGA.

Footnote
*The structural relationship between uridine, pseudouridine and 1-methyl-pseudouridine is shown below. The NH and CO involved in base-pairing are similar in each case.
The sequence is generally written with Ψ, rather than 1-Me-Ψ, for compactness. Uridine, pseudoUridine and Me-pseudoUridine

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As was observed (by others) under related q's here on material from that site, it seems Pfzier/BioNTech has done a global optimization to increase CG contents in the sequence, generally thought to be beneficial to mRNA expression (in addition to all the other things they've done, like U -> m1Ψ global substitution, specific to mRNA therapeutics).

That (global CG target) may also explain why they replaced UAA with UGA, even though the latter is actually a "worse" stop codon, in terms of allowing more read-through. As one paper (preprint) notes:

despite having the lowest efficiency of translation termination among the three, UGA is the most common stop codon in many multicellular eukaryotes. The relative frequencies of the three stop codons are dependent on multiple factors and strongly associated with regional variation in GC content. The frequency of UAA is strongly negatively correlated with GC content, while the use of UAG and particularly of UGA increases with increasing GC content.

Using two UGAs may be a way to compensate for this choice (of using the lowest efficiency stop codon).

Actually, one more complex theory is that the stop thing is actually a tetranucleotide:

In both bacteria and eukaryotes, the base immediately following the STOP codon (position +4, with the first nucleotide of the termination codon marked as +1) exerts the strongest influence on RT (readthrough) efficiency. This has led to the hypothesis that an actual translation termination signal consists of a tetranucleotide sequence, not only the STOP codon itself. Which tetranucleotide is the most efficient in eliciting the RT in eukaryotes remains controversial. [...] For example, the level of basal UGA-C readthrough in mammalian cells (3–4%) was shown to be 3–6 times higher than for the remaining UGA-N tetranucleotides.

If we go by this, then UGAU is the stop tetranucleotide here, which is perhaps better than just UGA, especially if see that a C follows the 2nd UGA in the actual WHO doc, so that might have tripled (or more) the read-through chance if the UGA were not doubled before it:

ΨGA ΨGA CΨC ...

Aside: The CΨC begins... a "double UTR" (dUTR) as they call it (even though this one is composed of two different UTRs) for which there is a published paper that it is more efficient (in terms of stability etc.) than a single UTR. So, generally speaking, the doubled stop seems part of a strategy to "double everything" in that terminal region if it helps with translation efficiency.

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