Protein Representation Learning with Secondary-Structure and Energy-Filtered Hydrogen-Bond Graphs

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

Recent advances in generative modeling show that pretrained representations can improve generation as conditioning features or alignment targets. Motivated by this, we study protein representations for predicting structures beyond conventional function annotation. We propose TriProRep, a structure-aware pretraining method that jointly models three aligned residue-level views: amino-acid identity, backbone geometry, and local full-atom geometry, discretely encoded via VQ-VAE tokenizers. By pretraining to recover original tokens from generator-corrupted views, TriProRep learns to distinguish plausible but incorrect cross-view augmentations from the original protein. We further introduce RepSP, a benchmark for evaluating protein representations in structure-predictive settings. RepSP tests three uses of representations: homodimer co-folding from apo-chain representations, residue-level prediction of homodimer-derived interaction properties, and representation-aligned monomer structure prediction. Across these tasks, TriProRep improves over sequence-only and prior structure-aware representation models, while maintaining competitive performance on conventional benchmarks.

Protein language models such as ESM-2 learn rich residue representations that achieve strong performance on protein function prediction, but their features remain difficult to interpret as structural $\&$ evolutionary signals are encoded in dense latent spaces. We propose a plug-$\&$-play framework that projects ESM-2 representations onto protein contact graphs $\&$ applies $\textbf{SoftBlobGIN}$, a lightweight Graph Isomorphism Network with differentiable Gumbel-softmax substructure pooling, to perform structure-aware message passing $\&$ learn coarse functional substructures for downstream prediction tasks. Across enzyme classification, SoftBlobGIN achieves 92.8% accuracy $\&$ 0.898 macro-F1. Unlike post hoc analysis of protein language models alone, our method produces directly auditable structural explanations: GNNExplainer recovers biologically meaningful active-site residues, spatially localized functional clusters, $\&$ catalytic contact patterns. On binding-site detection, SoftBlobGIN improves residue AUROC from $0.885$ using an ESM-2 linear probe to $0.983$, indicating that these structural explanations are not recoverable from language-model features alone. Learned blob partitions provide an additional layer of interpretability by automatically grouping residues into functional substructures, with blobs containing annotated active-site residues showing $1.85\times$ higher importance than other blobs ($ρ{=}0.339$, $p{=}0.009$), without any active-site supervision. Our framework requires no retraining of the language model, adds only $\sim$1.1M parameters, $\&$ generalises across ProteinShake tasks, achieving $F_{\max}$ of $0.733$ on Gene Ontology prediction $\&$ AUROC of $0.969$ on binding-site detection. We position this as an interpretable structural companion to protein language models that makes their predictions more transparent $\&$ auditable.