  Structural information about protein-protein interactions, often missing at
the interactome scale, is important for mechanistic understanding of cells and
rational discovery of therapeutics. Protein docking provides a computational
alternative to predict such information. However, ranking near-native docked
models high among a large number of candidates, often known as the scoring
problem, remains a critical challenge. Moreover, estimating model quality, also
known as the quality assessment problem, is rarely addressed in protein
docking.
  In this study the two challenging problems in protein docking are regarded as
relative and absolute scoring, respectively, and addressed in one
physics-inspired deep learning framework. We represent proteins' and encounter
complexes' 3D structures as intra- and inter-molecular residue contact graphs
with atom-resolution node and edge features. And we propose a novel graph
convolutional kernel that pool interacting nodes' features through edge
features so that generalized interaction energies can be learned directly from
graph data. The resulting energy-based graph convolutional networks (EGCN) with
multi-head attention are trained to predict intra- and inter-molecular
energies, binding affinities, and quality measures (interface RMSD) for
encounter complexes. Compared to a state-of-the-art scoring function for model
ranking, EGCN has significantly improved ranking for a CAPRI test set involving
homology docking; and is comparable for Score_set, a CAPRI benchmark set
generated by diverse community-wide docking protocols not known to training
data. For Score_set quality assessment, EGCN shows about 27% improvement to our
previous efforts. Directly learning from 3D structure data in graph
representation, EGCN represents the first successful development of graph
convolutional networks for protein docking.
