Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural features to distinguish accurate structural models from less accurate ones. This raises the question of whether it is possible to learn characteristics of accurate models directly from atomic coordinates of protein complexes, with no prior assumptions. Here we introduce a machine learning method that learns directly from the 3D positions of all atoms to identify accurate models of protein complexes, without using any pre-computed physics-inspired or statistical terms. Our neural network architecture combines multiple ingredients that together enable end-to-end learning from molecular structures containing tens of thousands of atoms: a point-based representation of atoms, equivariance with respect to rotation and translation, local convolutions, and hierarchical subsampling operations. When used in combination with previously developed scoring functions, our network substantially improves the identification of accurate structural models among a large set of possible models. Our network can also be used to predict the accuracy of a given structural model in absolute terms. The architecture we present is readily applicable to other tasks involving learning on 3D structures of large atomic systems.

We introduce tensor field networks, which are locally equivariant to 3D rotations and translations (and invariant to permutations of points) at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate how tensor field networks learn to model simple physics (Newtonian gravitation and moment of inertia), classify simple 3D shapes (trained on one orientation and tested on shapes in arbitrary orientations), and, given a small organic molecule with an atom removed, replace the correct element at the correct location in space.