  A protein performs biological functions by folding to a particular 3D
structure. To accurately model the protein structures, both the overall
geometric topology and local fine-grained relations between amino acids (e.g.
side-chain torsion angles and inter-amino-acid orientations) should be
carefully considered. In this work, we propose the Directed Weight Neural
Network for better capturing geometric relations among different amino acids.
Extending a single weight from a scalar to a 3D directed vector, our new
framework supports a rich set of geometric operations on both classical and
SO(3)--representation features, on top of which we construct a perceptron unit
for processing amino-acid information. In addition, we introduce an equivariant
message passing paradigm on proteins for plugging the directed weight
perceptrons into existing Graph Neural Networks, showing superior versatility
in maintaining SO(3)-equivariance at the global scale. Experiments show that
our network has remarkably better expressiveness in representing geometric
relations in comparison to classical neural networks and the (globally)
equivariant networks. It also achieves state-of-the-art performance on various
computational biology applications related to protein 3D structures.
