Overlapping 3D ring each with repeated pattern in perspective view

[Coenwolf]

I need to create 3 overlapping 3D rings to look like a traditional simple atomic diagram. However each loop has a different pattern for example one has a dna chain and another is a ring with gear teeth on the surfaces of the rings. They will need to look elliptical since they are in perspective. 

Can I please have guidance or suggestions on positioning the 3 rings in perspective having the patterns mentioned above on the surface. 

I can work things out in 2D and I can use a tutorial to make the 3D gear ring but need help putting them into perspective like in the image I've attached. 

Thanks for any help you can offer.

[Monika Gause]

Not quite sure if I get this right, but it sounds like opacity masks might help you.

https://helpx.adobe.com/in/illustrator/how-to/illustrator-opacity-masks-transparency.html