  Protein complex formation is a central problem in biology, being involved in
most of the cell's processes, and essential for applications, e.g. drug design
or protein engineering. We tackle rigid body protein-protein docking, i.e.,
computationally predicting the 3D structure of a protein-protein complex from
the individual unbound structures, assuming no conformational change within the
proteins happens during binding. We design a novel pairwise-independent
SE(3)-equivariant graph matching network to predict the rotation and
translation to place one of the proteins at the right docked position relative
to the second protein. We mathematically guarantee a basic principle: the
predicted complex is always identical regardless of the initial locations and
orientations of the two structures. Our model, named EquiDock, approximates the
binding pockets and predicts the docking poses using keypoint matching and
alignment, achieved through optimal transport and a differentiable Kabsch
algorithm. Empirically, we achieve significant running time improvements and
often outperform existing docking software despite not relying on heavy
candidate sampling, structure refinement, or templates.
