Multi-Scale Protein Structure Modelling with Geometric Graph U-Nets
This work addresses the challenge of modeling hierarchical biological interactions in proteins for computational biology, representing an incremental advancement by adapting U-Net architectures to geometric graphs.
The paper tackled the problem of capturing hierarchical interactions in 3D protein structures by introducing Geometric Graph U-Nets, which recursively coarsen and refine protein graphs to learn multi-scale representations, and empirically showed substantial outperformance over baselines in protein fold classification.
Geometric Graph Neural Networks (GNNs) and Transformers have become state-of-the-art for learning from 3D protein structures. However, their reliance on message passing prevents them from capturing the hierarchical interactions that govern protein function, such as global domains and long-range allosteric regulation. In this work, we argue that the network architecture itself should mirror this biological hierarchy. We introduce Geometric Graph U-Nets, a new class of models that learn multi-scale representations by recursively coarsening and refining the protein graph. We prove that this hierarchical design can theoretically more expressive than standard Geometric GNNs. Empirically, on the task of protein fold classification, Geometric U-Nets substantially outperform invariant and equivariant baselines, demonstrating their ability to learn the global structural patterns that define protein folds. Our work provides a principled foundation for designing geometric deep learning architectures that can learn the multi-scale structure of biomolecules.