  Accurately modeling protein 3D structure is essential for the design of
functional proteins. An important sub-task of structure modeling is protein
side-chain packing: predicting the conformation of side-chains (rotamers) given
the protein's backbone structure and amino-acid sequence. Conventional
approaches for this task rely on expensive sampling procedures over
hand-crafted energy functions and rotamer libraries. Recently, several deep
learning methods have been developed to tackle the problem in a data-driven
way, albeit with vastly different formulations (from image-to-image translation
to directly predicting atomic coordinates). Here, we frame the problem as a
joint regression over the side-chains' true degrees of freedom: the dihedral
$\chi$ angles. We carefully study possible objective functions for this task,
while accounting for the underlying symmetries of the task. We propose
Holographic Packer (H-Packer), a novel two-stage algorithm for side-chain
packing built on top of two light-weight rotationally equivariant neural
networks. We evaluate our method on CASP13 and CASP14 targets. H-Packer is
computationally efficient and shows favorable performance against conventional
physics-based algorithms and is competitive against alternative deep learning
solutions.
