🤖 AI Summary
This study addresses the lack of systematic comparison between lightweight handcrafted structural descriptors and embeddings from pretrained protein language models for protein fold classification. It proposes, for the first time, the application of discrete Ricci curvature—specifically Ollivier-Ricci and Forman-Ricci curvature—to Cα contact graphs, constructing an interpretable 22-dimensional feature vector derived from statistical summaries and quantiles of edge curvature distributions. Experimental results demonstrate that this ultra-low-dimensional descriptor outperforms average-pooled embeddings from the 150M-parameter ESM-2 model on both CATH and SCOPe benchmarks. Further integration with persistent homology features (yielding a 112-dimensional representation) achieves macro F1 scores of 0.71 on CATH and 0.68 on SCOPe, confirming the efficacy and competitiveness of lightweight geometric features in protein fold classification.
📝 Abstract
Protein fold classification can be approached via sequence-based representations or structural descriptors, but direct comparisons between lightweight handcrafted descriptors and pretrained protein language model embeddings remain limited. We investigate discrete Ricci curvature on Calpha contact graphs as a lightweight structural descriptor for fold classification. Each protein domain is represented by a 22-dimensional fixed-length feature derived from summary statistics and quantiles of Ollivier-Ricci and Forman-Ricci edge curvature distributions. We evaluate on CATH top-10 Topology classification and on the ASTRAL 40%-identity SCOPe top-10 Fold benchmark, comparing against geometry, contact-graph statistics, persistent homology, and mean-pooled ESM-2 (150M) baselines. On both datasets, lightweight structural descriptors substantially outperform mean-pooled ESM-2 embeddings, with a larger performance gap on the ASTRAL 40% SCOPe benchmark. Ricci alone uses 22 dimensions, or 3.4% of the ESM-2 baseline dimensionality, and already outperforms mean-pooled ESM-2 on both datasets. Combining Ricci with persistent homology yields the strongest performance, achieving macro-F1 of 0.71 on CATH and 0.68 on SCOPe with a 112-dimensional feature vector. These results identify a regime where lightweight interpretable graph descriptors offer a practical alternative to pretrained protein language model embeddings.