LEEN: local equivariant energy networks with evolution-guided structural reasoning for protein stability prediction

Accurate prediction of changes in protein thermodynamic stability ( Δ Δ G ) caused by single amino acid substitutions is important for protein engineering, therapeutic design, and interpretation of disease-associated variants. Recent approaches combine protein language models with structural neural networks via feature fusion, often yielding large, computationally expensive models that do not explicitly enforce thermodynamic consistency. We present LEEN (Local Equivariant Energy Network), a lightweight architecture that combines energy-based prediction with evolution-guided structural reasoning for protein stability prediction. LEEN is based on three complementary principles. First, mutation effects are predicted as the difference between mutant and wild-type energies evaluated in a shared local context, which guarantees fixed-context anti-symmetry algebraically; a symmetrized-context variant extends this to exact anti-symmetry when the same symmetrized context is applied to both mutation directions. Second, local protein geometry surrounding the mutation site is encoded using an E(n)-equivariant graph neural network, enabling rotation- and translation-equivariant structural representation learning. Third, evolutionary information extracted from a protein language model is incorporated via message gating, allowing sequence-derived context to modulate the flow of structural information rather than being concatenated with structural features. Despite using only approximately 2–3 million trainable parameters, LEEN achieves competitive performance on multiple low-sequence-similarity protein stability benchmarks. The full model obtains Spearman correlations of 0.657 on S461 and 0.470 on S669, while the best-performing variants reach 0.658 and 0.482, respectively. Ablation studies further show that incorporating evolutionary information contributes substantially more to predictive performance than the choice or complexity of the geometric encoder, while gating provides an additional, benchmark-dependent benefit. LEEN provides a compact framework for protein stability prediction that combines local equivariant structural reasoning with evolutionary information from frozen protein language model representations. The energy-difference formulation guarantees fixed-context anti-symmetry, and a symmetrized-context variant extends this to exact anti-symmetry for independently constructed mutation inputs when a shared symmetrized context is used, at a measurable accuracy cost. Across eleven benchmarks, LEEN achieves competitive predictive performance with a substantially smaller task-specific trainable component than larger multimodal predictors. These results highlight the importance of integrating evolutionary and structural information while making the trade-offs between predictive accuracy and thermodynamic consistency explicit.