Ricci Curvature Boosts Lightweight Protein Fold Classification.

This research explores the effectiveness of discrete Ricci curvature, applied to C-alpha contact graphs, as a lightweight structural descriptor for protein fold classification. The study directly compares these handcrafted descriptors against embeddings from large pretrained protein language models, a comparison that has been limited in prior work. Each protein domain is distilled into a compact 22-dimensional feature vector derived from summary statistics and quantiles of Ollivier-Ricci and Forman-Ricci edge curvature distributions. Evaluations on the CATH top-10 Topology and ASTRAL 40%-identity SCOPe top-10 Fold benchmarks revealed compelling results. The lightweight structural descriptors, particularly Ricci curvature alone, substantially outperformed mean-pooled ESM-2 embeddings, despite using significantly fewer dimensions (3.4% of ESM-2's dimensionality). The strongest performance was achieved by combining Ricci curvature with persistent homology, resulting in a 112-dimensional feature vector that yielded macro-F1 scores of 0.71 on CATH and 0.68 on SCOPe. These findings highlight a practical scenario where interpretable graph descriptors offer a highly effective and computationally efficient alternative to complex, large-scale pretrained models for protein fold classification.