1. ChainTree: A tale of two hierarchies  Transform hierarchy: approximates kinematics of protein backbone at successive resolutions  Bounding volume hierarchy: approximates geometry of protein at successive resolutions

2. Hierarchy of transforms

3. A B C D E F G H I T AB T BC T AC T HI T CD T DE T EF T FG T GH T CE T EG T GI T AE T EI T AI

4. Hierarchy of bounding volumesB BABA BHBH BGBG BFBF BEBE BDBD BCBC B CD B EF B GH B AB B AD B EH B AH

5. The ChainTree T AB B A T BC B B T CD B C T DE B D T EF B E T FG B F T GH B G T HI B H T AC B AB T CE B CD T EG B EF T GI B GH T AE B AD T EI B EH T AI B AH A B C D E F G H I

6. Updating the ChainTree T AB B A T BC B B T CD B C T DE B D T EF B E T FG B F T GH B G T HI B H T AC B AB T CE B CD T EG B EF T GI B GH T AE B AD T EI B EH T AI B AH A B C D E F G H I