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Quantitatively mapping enzyme sequence-catalysis landscapes remains a critical challenge in understanding enzyme function, evolution, and design. In this study, we leveraged emerging microfluidic technology to measure catalytic constants- and -for hundreds of diverse orthologs and mutants of adenylate kinase (ADK). We dissected this sequence-catalysis landscape's topology, navigability, and mechanistic underpinnings, revealing catalytically heterogeneous neighborhoods organized by domain architecture. These results challenge long-standing hypotheses in enzyme adaptation, demonstrating that thermophilic enzymes are not universally slower than their mesophilic counterparts. Semisupervised models that combine our data with the rich sequence representations from large protein language models predict orthologous ADK-sequence catalytic parameters better than existing approaches. Our work demonstrates a promising strategy for dissecting sequence-catalysis landscapes across enzymatic evolution, opening previously unexplored avenues for enzyme engineering and functional prediction.