Gan, Z.; Xu, Y.; Xu, J.; Wu, Z.; Huang, J.; Yin, J.; Chen, G.; Zhang, J. Z. H.

Enzymes drive biological chemistry and offer greener routes to chemicals, materials and medicines, yet their broader use as biocatalysts is often limited by insufficient catalytic turnover. Improving turnover is hard: measured rate constants are scarce and protein sequence space is vast. Deep-learning models now predict the turnover number, Kcat, with growing accuracy, but they are typically applied after sequence generation to score or filter candidates, which separates the kinetic objective from the design itself. To bridge the gap between sequence generation and kinetic evaluation, we introduce CatESO, a differentiable sequence optimizer that enables direct, gradient-guided design of substrate-specific catalytic turnover. By backpropagating through a cross-modal Kcat predictor under continuous sequence relaxation, CatESO co-optimizes predicted catalytic activity, evolutionary plausibility and structural integrity in one end-to-end framework, using ESM-2 and ESMFold to keep designs evolutionarily plausible and foldable. Across seven stringent out-of-distribution enzymes spanning EC classes 1-7, CatESO raised model-predicted Kcat for the vast majority of designs, with a median predicted fold change of 1.52 while every variant retained a pLDDT above 70. Against RFdiffusion3-LigandMPNN pipeline and ZymCtrl, CatESO struck a better balance between predicted activity and structural confidence. By making substrate-conditioned kinetic objectives differentiable, CatESO carries differentiable protein design beyond structure- and binding-centred goals to enzyme catalytic function, giving a general route to function-oriented enzyme engineering.