Discrete Ricci Curvature on Protein Contact Graphs for Lightweight Fold Classification
Machine Learning
Summary
The authors explore a new way to classify protein folds using a simple, math-based feature called discrete Ricci curvature, which looks at protein structure as a graph. They compare this lightweight method to more complex protein language models and find that their approach performs better despite using far fewer data dimensions. Combining this curvature feature with another topological method improves results further. Their work suggests that simple, interpretable graph measures can effectively identify protein folds, offering a practical alternative to large pretrained models.
Authors
Jianru Shen
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.