Hyperbolic Protein Representation Learning with Shared Structural Motifs

Protein structures reuse local geometric patterns across diverse proteins, providing a natural basis for sharing structural knowledge. Exploiting this reuse requires representations that capture both multiscale composition and geometric variation among motif occurrences. We introduce MORPH (MOtif Relations for Protein representations in Hyperbolic space), a framework for learning hyperbolic protein representations through shared structural motifs. MORPH uses RamaBPE to construct a reusable vocabulary of variable-length motifs and their ordered multiscale compositions from backbone geometry. Hyperbolic entailment constraints organize compositional relations among both shared motif types and protein-specific occurrences, while explicit type-to-occurrence instantiation loss connects occurrences to their corresponding types. Complementary supervision derived from three-dimensional structures captures continuous geometric relations among occurrences. These signals train a mixture-of-curvature adapter over frozen ESM3 representations, combining Euclidean and Lorentz experts to produce hyperbolic residue representations for downstream prediction. MORPH demonstrates strong downstream transfer across functional site prediction, structural flexibility prediction, and protein-level fold classification. Analysis of motif occurrence representations further reveals composition-related radial organization in hyperbolic space. These findings support shared motif relations and occurrence-level geometric supervision as an effective basis for adapting pretrained protein representations.