Learning the shape of the protein universe with 3D-equivariant holographic convolutional neural networks*

Proteins are the machinery of life facilitating the key processes that drive living organisms. The physical arrangement of amino acids dictates how proteins fold and interact with their environment. Recent advances have increased the number of experimentally resolved or computationally predicted tertiary structures, however we still lack a practical understanding of how 3D structure determines the function of a protein. While machine learning has been at the forefront of protein science, the inferred models are often hard to interpret physically. Here, we introduce holographic convolutional neural networks (H-CNNs) that take atomic coordinates of a protein structure as input and, through 3D equivariant transformations that respect the rotational symmetries in data, learn interpretable models of protein micro-environments reflecting the underlying biophysics. With H-CNNs, we infer amino acid preferences given a surrounding atomic neighborhood and predict the impact of evolutionary substitutions in proteins. Our computational approach establishes an interpretable model for how biological function emerges from protein micro-environments. The flexibility and efficiency of H-CNNs also show promise for building generative models to design novel protein structures with desired function.