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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 m1ΨGA, as U is replaced by m1Ψ (N1-Methylpseudouridine)* in the synthetic mRNA to prevent degradation. As the anticodon is recognized by a termination factor — not a tRNA anticodon — the interaction with m1ΨGA may possibly be poorer than for UGA.

Footnote
*The structural relationship between uridine, pseudouridine and N1-methylpseudouridine is shown below. The NH and CO involved in base-pairing are similar in each case.
In displaying the base in RNA sequences — where single characters are normally used to represent nucleotides — N1-methypseudouridine is generally represented as Ψ, rather than m1Ψ. However this is not necessary in other circumstances, and, because of the ambiguity it introduces, is highly discouraged.

Uridine, pseudoUridine and N1-Methylpseudouridine

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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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Detailed Dissection and Critical Evaluation of the Pfizer/BioNTech and Moderna mRNA Vaccines hypothesizes that it is a fail-safe against misreading (but maybe not a very good one (and the premise that m1Ψ leads to misreading may itself be incorrect)):

When nucleotide U in stop codons was replaced by Ψ, the rate of misreading of a stop codon by a near-cognate tRNAs increased [17]. Such readthrough events would not only decrease the number of immunogenic proteins, but also produce a longer protein of unknown fate with potentially deleterious effects.

Pfizer/BioNTech’s BNT162b2 mRNA features two consecutive UGA stop codons. Moderna’s mRNA-1273 uses all three different stop codons UGAUAAUAG.

One might think that the consecutive stop codons in the two vaccine mRNAs would offer a fail-safe mechanism

However, in many cases, misreading UGA stop codons in prokaryotes is associated with a +1 frameshift [81–84].

With such a +1 frameshifting, a downstream in-frame stop codon cannot serve as a fail-safe mechanism. UGA is a poor choice of a stop codon, and UGAU in Pfizer/BioNTech and Moderna mRNA vaccines could be even worse.

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    $\begingroup$ Thanks for sharing this interesting quote! $\endgroup$ Feb 6 at 2:24
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    $\begingroup$ From my knowledge of frameshifting, the wider sequence context of the position of the shift seems to be the primary determinant. Hence I am highly dubious regarding this postulate of Xia. One imagines the developers of these vaccines analysed the products of translation of the artificial mRNAs very carefully. To suggest that they achieve the opposite of their presumed purpose seems rather naïve. $\endgroup$
    – David
    Feb 6 at 18:21

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