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I found this thread which is worth reviewing as context to my question(s) since there is some overlap in potential discussion, although it's concern is with mRNA ingress rather than spike protein.

Does the mRNA of the covid19 spike protein contain any nuclear localization signals

It focuses on nuclear localization signals, but there are other mechanisms by which proteins or small enough macromolecules may ingress through NPC's (nuclear pore complexes)

First, see:

Which is bigger, mRNA or the protein it codes for? http://book.bionumbers.org/which-is-bigger-mrna-or-the-protein-it-codes-for/

mRNA is, somewhat paradoxically (although not really) larger, mass wise, than the proteins it codes for. And passive diffusion is influenced by molecular weight (a fair model,) so before being concerned about the larger mRNA sequence, we should first be concerned about the manufactured spike protein (either by wild type SARS-CoV2 or vaccine) both produced at the ribosomes of the ER. An additional concern though could be the geometry / spatial extent of the mRNA or spike protein (in both it's conformations); ex: since mRNA may typically be more linear than globular, passive diffusion curves will be substantially modified as most NPC diffusion curves I've perused all consider globular macromolecules.

Second, see for proof of concept where an accessory protein on SARS-CoV is found to ingress via passive diffusion:

SARS-CoV 9b Protein Diffuses into Nucleus, Undergoes Active Crm1 Mediated Nucleocytoplasmic Export and Triggers Apoptosis When Retained in the Nucleus (2011) https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0019436

Background 9b is an accessory protein of the SARS-CoV. It is a small protein of 98 amino acids and its structure has been solved recently. 9b is known to localize in the extra-nuclear region and has been postulated to possess a nuclear export signal (NES), however the role of NES in 9b functioning is not well understood. Principal Findings/Methodology In this report, we demonstrate that 9b in the absence of any nuclear localization signal (NLS) enters the nucleus by passive transport. Using various cell cycle inhibitors, we have shown that the nuclear entry of 9b is independent of the cell cycle. Further, we found that 9b interacts with the cellular protein Crm1 and gets exported out of the… Show more

Simple rules for passive diffusion through the nuclear pore complex (2016) https://rupress.org/jcb/article/215/1/57/38760/Simple-rules-for-passive-diffusion-through-the

Recent in vitro studies over the last two decades also suggested a relatively sharp threshold of 30–60 kD (Keminer and Peters, 1999; Ribbeck and Görlich, 2001; Mohr et al., 2009; Ma et al., 2012), although such in vitro systems have recently been shown to be quite sensitive to the precise experimental conditions (e.g., the concentration of transport receptors and the nuclear factor Ran; Ma et al., 2012; Lowe et al., 2015). Larger molecules up to 230 kD in size have also been observed to permeate the NPCs in vivo on the time scale of many minutes to hours (Wang and Brattain, 2007; Popken et al., 2015).

SARS-CoV-2 spike protein: pathogenesis, vaccines, and potential therapies (2021) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8326314/

SARS-CoV-2 S protein is a class I fusion transmembrane structural glycoprotein that is composed of S1 and S2 subunits [ 71 ]. It is a homotrimer with a size of 180-200 kDa

Back to a quote from Rockefeller University press paper above, I found this very interesting:

Nonetheless, the prevailing functional model of passive transport, which we term the “rigid barrier” model, is that of a barrier with a firm size threshold of 40 kD for passive diffusion (Christie et al., 2016; Knockenhauer and Schwartz, 2016; Musser and Grünwald, 2016; Schmidt and Görlich, 2016). According to this prevailing view, the slow permeation of larger macromolecules across the NPC is regarded as residual leakage beyond such a firm threshold (Kirli et al., 2015; Fig. 1 A, red curve). However, this supposed “leakage” may be also interpreted by an alternative “soft barrier” model of transport. In this model, passive transport rates are expected to decrease much more gradually with increasing molecular mass than previously realized (Fig. 1 A, black curve).

Note that last part, which is somewhat telling (and the curve in the paper)

So invoking:

Larger molecules up to 230 kD in size have also been observed to permeate the NPCs in vivo on the time scale of many minutes to hours

And

It is a homotrimer with a size of 180-200 kDa

Could spike protein manufactured at the endoplasmic reticulum ingress by way of passive diffusion into the nucleus or not? If so, has this been studied?

Is it possible to be unconcerned because such a small 'negligible' quantity would ingress as such (without a NLS)?

Does the geometry / spatial extent of the spike protein (or secondarily, mRNA) itself augment how it would passive diffuse through a normally protected protein complex?

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    $\begingroup$ Welcome to the site. What would be your concern if the protein was capable of entering the nucleus? $\endgroup$
    – bob1
    Commented Jun 21, 2022 at 4:44
  • $\begingroup$ Thanks bob1. I'm not sure. I'm just trying to understand the mechanism and validity of the idea (summarized by the title of the post) before hypothesizing potential outcomes if it were possible. $\endgroup$
    – Ben Shaman
    Commented Jun 21, 2022 at 11:18
  • $\begingroup$ Ok, was just trying to see if there was some motive behind the question. Generally proteins of the spike sort aren't freely floating and are actively transported to the surface of the cell for virion assembly. However, if it were free-floating I don't see that it couldn't occur via passive diffusion, but I'll let a better cell biologist answer. $\endgroup$
    – bob1
    Commented Jun 21, 2022 at 21:10
  • $\begingroup$ Fair enough on diffusion. "Generally proteins of the spike sort aren't freely floating". Have a source for this? What is different about 9b accessory protein as described in the paper cited in my original question? Yes, all of the sub-unit proteins are 'expected' to be shuttled for virion assembly, but it appears this doesnt always happen. Also, according to, ncbi.nlm.nih.gov/pmc/articles/PMC7112327, the earlier studies theorized assembly at intracellular membrane, but later ones suggest the tubes between ER and Golgi Apparatus as the location of coronavirus morphogenesis. $\endgroup$
    – Ben Shaman
    Commented Jun 22, 2022 at 2:03
  • $\begingroup$ On that last bit, its definitely more complicated, as some sub units also appear to be assembled elsewhere, for instance, in the cytoplasm, which would be where passive diffusion through NPC becomes more possible. Depending on the protein, this would naturally vary. That particular paper describes S protein migration oddly, at least in my opinion: "During its transport to the cell surface, either alone or as part of virions, the S protein undergoes further modifications". So it could be either? $\endgroup$
    – Ben Shaman
    Commented Jun 22, 2022 at 2:19

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