PRIME: Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies

TL;DR

PRIME introduces a multiscale, physics-informed hierarchical framework for protein representation, integrating structural information across five levels to improve predictive performance on various benchmarks.

Contribution

It is the first to explicitly model hierarchical relationships across multiple physical structural levels in proteins for representation learning.

Findings

PRIME outperforms baseline methods on Fold Classification benchmarks.

Achieves 84.10% accuracy on Reaction Class prediction, surpassing existing models.

Each structural level provides unique, non-redundant information for protein tasks.

Abstract

Proteins are inherently multiscale physical systems whose functional properties emerge from coordinated structural organization across multiple spatial resolutions, ranging from atomic interactions to global fold topology. However, existing protein representation learning methods typically operate at a single structural level or treat different sources of structural information as parallel modalities, without explicitly modeling their hierarchical relationships. We introduce PRIME (Protein Representation via Physics-Informed Multiscale Equivariant Hierarchies), a unified framework that models proteins as a nested family of five physically grounded structural graphs spanning surface, atomic, residue, secondary-structure, and protein levels. Adjacent levels are connected through deterministic, physics-informed assignment operators, enabling bidirectional information exchange via bottom-up aggregation and top-down contextual refinement. Experiments on standard protein representation learning benchmarks demonstrate strong and competitive performance across diverse tasks, with particularly notable gains on the Fold Classification benchmark, where PRIME outperforms the strongest geometric GNN baseline by margins of 13.80 and 18.30 points on the harder Superfamily and Fold splits, and achieves a state-of-the-art accuracy of 84.10\% on Reaction Class prediction, surpassing all baseline methods, including ESM. Ablation studies confirm that each structural level contributes complementary and non-redundant information, and adaptive cross-attention analysis reveals that PRIME autonomously identifies the most task-relevant structural resolutions at prediction time. Our source code is publicly available at https://github.com/HySonLab/PRIME