Towards Multiscale Graph-based Protein Learning with Geometric Secondary Structural Motifs

TL;DR

This paper tackles multiscale protein representation learning by introducing a secondary-structure–driven hierarchical graph (SSHG) that couples fine-grained intra-motif graphs with a coarse inter-motif graph. A two-stage GNN learns local motif embeddings first and then models long-range dependencies across motifs, aided by orientation features derived from local frames. The authors establish maximal expressiveness guarantees and a sparsity bound, enabling scalable learning while preserving geometric fidelity. Empirically, SSHG improves prediction accuracy and reduces runtime/memory across enzyme reaction classification and protein–ligand binding tasks, with ablations highlighting the value of integrating secondary-structure information and geometric relationships.

Abstract

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale representations and modeling long-range dependencies efficiently. In this work, we propose an efficient multiscale graph-based learning framework tailored to proteins. Our proposed framework contains two crucial components: (1) It constructs a hierarchical graph representation comprising a collection of fine-grained subgraphs, each corresponding to a secondary structure motif (e.g., $α$-helices, $β$-strands, loops), and a single coarse-grained graph that connects these motifs based on their spatial arrangement and relative orientation. (2) It employs two GNNs for feature learning: the first operates within individual secondary motifs to capture local interactions, and the second models higher-level structural relationships across motifs. Our modular framework allows a flexible choice of GNN in each stage. Theoretically, we show that our hierarchical framework preserves the desired maximal expressiveness, ensuring no loss of critical structural information. Empirically, we demonstrate that integrating baseline GNNs into our multiscale framework remarkably improves prediction accuracy and reduces computational cost across various benchmarks.

Figures (5)

• Figure 1: An example of two prion proteins with identical primary structures but distinct secondary structures. The normal form, hamster PrP$^{\rm C}$ (left), contains $\alpha$-helical structures (marked in red). In contrast, its misfolded counterpart, PrP$^{\rm Sc}$, on the right, lacks these helices and adopts a $\beta$-sheet-rich structure (marked in yellow). This structural change leads to abnormal aggregation, ultimately resulting in fatal consequences.
• Figure 2: Overview of the proposed multiscale graph-based framework. We first construct a hierarchical graph representation that includes: (1) fine-grained motif subgraphs, where residues within each secondary structure motif (e.g., $\alpha$-helices, $\beta$-strands, loops) are treated as nodes, and (2) a coarse-grained structural graph, where each motif is abstracted as a single node. The first GNN operates independently on each motif subgraph to learn local embeddings. These learned motif-level features are then used to construct the coarse-grained graph, on which a second GNN performs message passing to model higher-level structure and generate the final prediction.
• Figure 3: A visual illustration of the identification and segmentation process for protein secondary structures. Each residue $v_k$ is assigned a secondary structure (SS) token $s_k$ by DSSP, and consecutive residues with the same token are grouped into subsequences $S_i$.
• Figure 4: Hierarchical geometric graph construction. Left: A synthetic protein-like structure composed of 14 residues $\{v_k\}_{k=1}^{14}$, grouped into four secondary structure subsequences $\{S_i\}_{i= 1}^4$. Middle: Intra-structural graphs ${\mathcal{G}}_i$ capture local information within each subsequence $S_i$ using SCHull. Right: The inter-structural graph ${\mathcal{G}}$ is formed by connecting the geometric centers of each $S_i$, modeling higher-level structural relationships between secondary structural motifs.
• Figure 5: Illustration of the architectures of our SSHG model, with and without the integration of Mamba. The red arrows and red dashed arrows indicate the input-output dependencies in the SSHG and SSHG+Mamba models, respectively.

Theorems & Definitions (14)

• Theorem 2.1
• Remark 2.2
• Remark 3.1
• Proposition 3.1
• Theorem 4.2
• Remark 4.3
• Proposition A.0
• proof : Proof of Proposition \ref{['prop:sparsity']}
• Theorem A.1
• Theorem A.1