Spherical convolutions on molecular graphs for protein model quality assessment

TL;DR

This paper introduces Spherical Graph Convolutional Network (S-GCN), a rotation-equivariant method for analyzing 3D protein structures as graphs, improving model quality assessment by leveraging local coordinate systems and spherical filters.

Contribution

The paper presents a novel spherical convolution approach for protein graphs that achieves rotation-equivariance and enhances model quality assessment performance.

Findings

Significantly improves protein model quality assessment accuracy.

Performs comparably to state-of-the-art methods on CASP benchmarks.

Operates solely on geometric features, ensuring broad applicability.

Abstract

Processing information on 3D objects requires methods stable to rigid-body transformations, in particular rotations, of the input data. In image processing tasks, convolutional neural networks achieve this property using rotation-equivariant operations. However, contrary to images, graphs generally have irregular topology. This makes it challenging to define a rotation-equivariant convolution operation on these structures. In this work, we propose Spherical Graph Convolutional Network (S-GCN) that processes 3D models of proteins represented as molecular graphs. In a protein molecule, individual amino acids have common topological elements. This allows us to unambiguously associate each amino acid with a local coordinate system and construct rotation-equivariant spherical filters that operate on angular information between graph nodes. Within the framework of the protein model quality assessment problem, we demonstrate that the proposed spherical convolution method significantly improves the quality of model assessment compared to the standard message-passing approach. It is also comparable to state-of-the-art methods, as we demonstrate on Critical Assessment of Structure Prediction (CASP) benchmarks. The proposed technique operates only on geometric features of protein 3D models. This makes it universal and applicable to any other geometric-learning task where the graph structure allows constructing local coordinate systems.