Integrating Arrhenius Constraints with Lineage-Aware Meta-Learning for Few-Shot Prediction of Temperature-Dependent Enzyme Kinetics

The engineering of biocatalysts requires a precise understanding of the temperature-dependent catalytic turnover number ( k cat ), which governs the tradeoff between activity and thermal stability. However, kinetic landscape prediction is challenged by the scarcity of multitemperature experimental data and the tendency of purely data-driven models to violate thermodynamic principles. To address this, we present PIMetaKcat, a hybrid computational framework that synergizes phylogenetic information with first-principles thermodynamic constraints. A key advantage of PIMetaKcat is the integration of lineage-aware meta-learning to capture family specific kinetic patterns, enabling accurate predictions for distant homologues even when trained on minimal variants. Simultaneously, the model enforces consistency with the Arrhenius equation to reconstruct the full activity profile, explicitly resolving critical parameters such as optimal temperature ( T opt ) and apparent activation energy ( E a ). On a rigorous low-redundancy benchmark, PIMetaKcat achieves high fidelity (0.957 ± 0.021, 0.565 ± 0.032), demonstrating superior generalization to low-similarity sequences compared to existing baselines. Furthermore, PIMetaKcat autonomously distinguishes distinct thermal niches and enables high-precision ranking of mutant libraries. As a physics-anchored engine, it accelerates the Design-Build-Test (DBT) cycle for rational enzyme design. The code and data are openly available at https://github.com/QiTiaotiao2/PIMetaKcat .