Spherical convolutions on molecular graphs for protein model quality assessment

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. We will make the method available at https://team.inria.fr/nano-d/software/s-gcn/.

ScanNet: An interpretable geometric deep learning model for structure-based protein binding site prediction

“…The above parameterization offers several advantages over other choices such as Multilayer perceptrons [25,70,71] or spherical harmonics [35,72]. First, it is straightforward to interpret: a filter m with large entries of the tensor W sc for some g,n is positively activated by points having attribute n and located near the center of the Gaussian g. Similarly, the matrix W s encodes attribute-independent spatial sensitivity and W b is a bias vector.…”

Protein sequence‐to‐structure learning: Is this the end(‐to‐end revolution)?

“…This allowed to effectively encode mutual angular dependence of neighboring graph nodes using spherical harmonics expansions. 108 In its turn, GNNRefine predicted distances between protein atoms using graph neural networks, and then converted these distances into interatomic potentials and employed them for protein structure refinement. 113 A more recent method, GVP-GNN, 114 augments graph networks with the ability to reason about protein features expressed as geometric vectors in an equivariant manner.…”

Graph representation learning for structural proteomics

“…Predicting the 3D structure of a protein given its sequence is one of the most challenging problems in the field of computational biology [ 84 ]. Despite the undoubtedly great advances that Alphafold [ 8 , 9 ] has achieved in the recent critical assessment of protein structure prediction (CASP) challenges, the problem is still far from being solved, as the accuracy of predictions can still vary significantly [ 66 ]. Therefore, estimating the reliability of a modeled structure is very important.…”

“…Using the resulting graph, a GNN predicts local qualities of 3D protein folds. Finally, S-GCN [ 66 ] is a different convolution operator based on spherical harmonics, which is more suited in exploiting geometrical and topological information of the protein graph, achieving superior performance to state-of-the-art QA methods.…”