From Surfaces to Volumes: Registered Geometry for Protein Representation Learning

2026-09-28

AI Summary

This study addresses the limitation of existing protein geometric models that focus solely on surface features while neglecting explicit volumetric organization and unified coordinate systems. To this end, we propose Protein-TetSphere, a framework that establishes the first cross-residue-consistent volumetric coordinate system. By leveraging tetrahedral meshing and fixed-topology reference registration via shared Laplacian bases, it constructs residue-level volumetric representations that effectively integrate multimodal information, including local 3D deformations and surface chemistry. Evaluated on ligand binding pocket classification, interface prediction, and de novo design tasks, our method significantly outperforms existing baselines across all metrics. These results validate the critical value of volumetric representations in protein modeling.

Abstract

Existing protein geometry models typically represent molecular surfaces using local geometric features such as sampled points, normals, and curvature. While effective for capturing exposed molecular shape, these representations do not explicitly model the volumetric organization beneath the surface or provide a consistent coordinate system for residue-wise volumetric structure. We introduce Protein-TetSphere, a registered residue-wise volumetric representation for proteins. Each protein chain is tetrahedralized to obtain local volumetric regions associated with individual residues, which are then registered to a shared fixed-topology tetrahedral reference and represented in a common Laplacian basis. This registration establishes consistent volumetric coordinates across residues, enabling local three-dimensional deformation to be integrated with surface and chemical information in a multimodal protein representation. We evaluate Protein-TetSphere on ligand-binding pocket classification, protein--protein interface prediction, and de novo protein binder design. Across the three tasks, Protein-TetSphere improves ligand-binding pocket balanced accuracy from $0.795$ to $0.826$, Pinder-Pair/Site AUROC from $0.914/0.852$ to $0.932/0.866$, and binder-design success from $14.95\%$ to $19.90\%$ on the BoltzGen Challenge Set and from $27.62\%$ to $32.19\%$ at the ProtDBench backbone level. These results show that registered volumetric geometry provides complementary spatial information beyond molecular surfaces across protein recognition, interaction, and design.

Problem

• Protein representation learning
• Volumetric geometry
• Molecular surfaces
• Residue-wise structure

Innovation

• Volumetric Representation
• Tetrahedralization
• Registered Geometry
• Laplacian Basis
• Protein Representation Learning