Multi-Scale Protein Structure Modelling with Geometric Graph U-Nets

2025-12-07

AI Summary

Existing geometric graph neural networks (GNNs) and Transformers rely on message passing, limiting their ability to model multi-scale hierarchical interactions in proteins—such as domain assembly and long-range allosteric regulation—that govern biological function. To address this, we propose Geometric Graph U-Nets (GGU-Net), the first geometric graph learning architecture to adopt the U-Net paradigm of multi-scale encoding and decoding. GGU-Net recursively coarsens and refines graphs to enable cross-scale feature fusion, while jointly leveraging both invariant and equivariant geometric features. We theoretically establish that GGU-Net possesses strictly greater expressive power than conventional invariant or equivariant baselines. Empirically, on protein fold classification—a task demanding holistic structural understanding and hierarchical functional reasoning—GGU-Net achieves significant performance gains over state-of-the-art invariant and equivariant models, demonstrating its capacity to capture global structural patterns and hierarchical functional mechanisms.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Models multi-scale protein structure for hierarchical interactions
• Introduces Geometric Graph U-Nets to coarsen and refine protein graphs
• Improves protein fold classification by capturing global structural patterns

Innovation

• Geometric Graph U-Nets for multi-scale protein modeling
• Recursive coarsening and refining of protein graphs
• Hierarchical design capturing global structural patterns