I've read this from several sources. I believe it but does anyone know where I can see the proof? An image/formula of the structures, or something in a research paper perhaps?
First, I think the issue is the gliadin looks a lot like transglutaminase which is a super important enzyme in lots of places (like the thyroid and pancreas). However you'd have a hard time looking at the structures and saying they're similar because they're huge molecules and you don't know where to look for the similarities.
For example, lets say you had a key that could unlock a door. It's totally possible to have a similar key that also unlocks the door, but looks different to you. What matters is the part that the lock looks at is the same.
For example, key #1
And key #2
Now, I made that pretty simple, so you could see the difference, but Lock #1 looks at a smaller section than Lock #2, so Key #1 can open Lock #1 but not Lock #2; however Key #2 can open both locks since it contains the same pattern as Key #1 in the right area.
Your immune system works the same way. It has some things that look at the structures and chemistry of molecules and tries to find matches. But it only looks at a certain subset, and it happens that the subset that it looks at means that gliadin and transglutaminase look the same. And your immune system is "fuzzier" than a lock and key. It only has to be similar to be recognized, not exactly the same.
I don't think it's so much that gliadin resembles thyroid but rather it binds to TTG which is found in higher concentration in the Thyroid than anywhere else. The immune system mistakenly builds and anti-body to itself in other words, confused about what the real enemy is. TTG is found all over the body, btw, so those antibodies can affect far more than the Thyroid. 10% of celiac patients also have neurological problems for example.
The idea is that our own antibodies against gliadin cross react with cell-surface motifs on various tissues, or as you've identified, the thyroid. They may or may not be similar structures by your eye, all that matters is that in the antibody's "eye" they're both good targets for binding. There's loads of cross-reacting proteins in our bodies, it wouldn't be surprising that exogenous proteins also cross-react.
Not quite what you asked for, but Art Ayers has discussed this before:
I have come to the conclusion all gluten intolerance problems are associated with the thyroid and it's lesser know parathyroid. The neurological problems stem from the parathryoid which regulate calcium and all other minerals in the body. The kidneys are unable function properly to make vitamin D and this places the entire body in jepardy.