The AstraZeneca vaccine is viral-vector. They are not interchangeable.
So, the point of both the mRNA and the viral-vector is to get the immune system to recognize Covid-19 proteins and kick the crap out of Covid-19.
mRNA works by using your own cells as a bioreactor. The mRNA slides into your cells (it is wrapped in a fragile lipid package do allow that to happen). Your cell starts producing the (utterly useless) spike protein. Your body reacts to the foreign protein and bam, immune response.
The AZ vaccine has a modified chimpanzee virus with RNA that includes "make a spike protein". This virus is very bad at infecting humans, but it can do a bit. So it is injected, it infects some of your cells, and tries to make more chimpanzee virus... and while it is as it, it also makes some of the spike protein.
But because it is so so bad at infecting humans, our body wipes it out really quickly. But it also (hopefully) picks up on that spike protein and learns "spike protein bad!"
The downsides of the AZ live vaccine include that (a) if the person is already immune to that chimpanzee virus, it won't work (this can happen if some other unrelated virus has similar antigens), (b) the person is immune to the chimpanzee virus afterwards, so it cannot be used for this technique ever again.
But in
both cases the end goal is exposing the immune system to that spike protein and generating an immune response to it.
The double-exposure idea is that if you are exposed to a virus once, your body cleans it up and might not
remember it as important. When primed by one exposure, the second exposure goes into overdrive ("that wasn't just a one off thing, we are under attack! All hands, prepare to repel future boarders!")
As
both are trying to do the same thing, it is plausible they can work together.
One possible reason the AZ Chimp virus trick might not work is that that Chimp virus is really, really crappy at infecting humans. So the second dose might get wiped out before it can make any spike proteins, as the immune system is primed from the
first dose to repel it.
(This could explain why a half dose followed by a full dose could be more effective; don't prime the immune system as hard against the Chimp virus, and the 2nd invasion gets as far as making spike proteins).
But we could flip this. Give the AZ vaccine. Then the mRNA virus, which doesn't illicit an immune response from the Chimp virus component of the AZ vaccine, ensuring a robust immune response to the spike protein.
I am not a biologist. This is not meant to be a convincing argument. It is mainly meant to say why it is plausible that two different vaccine technologies could work together.
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The AZ vaccine's big advantage is that it is far, far more stable than the mRNA ones.
You could imagine giving someone the AZ vaccine in the field, and get them to come back in 4 weeks to get the mRNA one at a lab; half as much travel as otherwise.
But if the half-dose full-dose of the AZ vaccine is almost as effective as the mRNA one (we can't be certain due to possibility of p-hacking), then doing two passes in the field might still be better.
Also, we are getting so many different vaccine technologies coming down the pipe. Worrying about the quirks of the first 3 might be obsolete in a few weeks. Still, it is fun.