{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:46:11Z","timestamp":1792784771739,"version":"4.5.0"},"reference-count":117,"publisher":"American Chemical Society (ACS)","issue":"36","license":[{"start":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T00:00:00Z","timestamp":1788480000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T00:00:00Z","timestamp":1788480000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T00:00:00Z","timestamp":1788480000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"name":"The National Key Research and Development Program of China for Young Scientists","award":["2025YFC2708700"],"award-info":[{"award-number":["2025YFC2708700"]}]},{"name":"The Strategic Priority Research Program of the Chinese Academy of Sciences","award":["XDB1900000"],"award-info":[{"award-number":["XDB1900000"]}],"id":[{"id":"https:\/\/ror.org\/034t30j35","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>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\u20137, CatESO raised model-predicted Kcat for many designs, with a median predicted fold change of 1.52, while every variant retained a pLDDT above 70. Against the 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-centered goals to enzyme catalytic function, giving a general route to function-oriented enzyme engineering.<\/jats:p>","DOI":"10.1021\/jacs.6c14365","type":"journal-article","created":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T13:49:39Z","timestamp":1788529779000},"page":"39258-39272","source":"Crossref","is-referenced-by-count":0,"title":["CatESO: Differentiable Enzyme Sequence Optimization\nGuided by Substrate-Aware\n                    <i>K<\/i>\n                    cat Prediction"],"prefix":"10.1021","volume":"148","author":[{"given":"Zhenjia","family":"Gan","sequence":"first","affiliation":[{"name":"East China Normal University , , ,","place":["Shanghai, China, 200062"]},{"name":"NYU-ECNU Center for Computational Chemistry at NYU Shanghai , ,","place":["Shanghai, China, 200062"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuzhi","family":"Xu","sequence":"additional","affiliation":[{"name":"New York University , , , ,","place":["New York, New York, United States, 10003"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junde","family":"Xu","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong , , Shatin, , ,","place":["New Territories, Hong Kong SAR, China, 999077"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhihao","family":"Wu","sequence":"additional","affiliation":[{"name":"Zhejiang University , , ,","place":["Hangzhou, China, 310027"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juping","family":"Huang","sequence":"additional","affiliation":[{"name":"Fudan University , , ,","place":["Shanghai, China, 200237"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiabin","family":"Yin","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University , , ,","place":["Shanghai, China, 200240"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangyong","family":"Chen","sequence":"additional","affiliation":[{"name":"Hangzhou Institute of Medicine, Chinese Academy of Sciences , ,","place":["Hangzhou, China, 310018"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4612-1863","authenticated-orcid":true,"given":"John Z.H.","family":"Zhang","sequence":"additional","affiliation":[{"name":"NYU-ECNU Center for Computational Chemistry at NYU Shanghai , ,","place":["Shanghai, China, 200062"]},{"name":"New York University , , , ,","place":["New York, New York, United States, 10003"]},{"name":"Shenzhen University of Advanced Technology , , ,","place":["Shenzhen, China, 518107"]},{"name":"Shanxi University , , , ,","place":["Taiyuan, Shanxi, China, 030006"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,4]]},"reference":[{"issue":"10","key":"2026091609125023100_cit1","doi-asserted-by":"publisher","first-page":"1516","DOI":"10.1038\/s41592-023-02006-7","article-title":"EzMechanism: An Automated Tool to\nPropose Catalytic\nMechanisms of Enzyme Reactions","volume":"20","author":"Ribeiro","year":"2023","journal-title":"Nat. Methods"},{"issue":"12","key":"2026091609125023100_cit2","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1038\/s41570-019-0143-x","article-title":"The Importance of Catalytic Promiscuity\nfor Enzyme Design and Evolution","volume":"3","author":"Leveson-Gower","year":"2019","journal-title":"Nat. Rev. Chem."},{"issue":"3","key":"2026091609125023100_cit3","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1038\/s41929-019-0385-5","article-title":"Engineering\nNew Catalytic Activities in Enzymes","volume":"3","author":"Chen","year":"2020","journal-title":"Nat. Catal."},{"issue":"8095","key":"2026091609125023100_cit4","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1038\/s41586-025-09747-9","article-title":"Computational\nEnzyme Design by Catalytic Motif Scaffolding","volume":"649","author":"Braun","year":"2026","journal-title":"Nature"},{"issue":"45","key":"2026091609125023100_cit5","doi-asserted-by":"publisher","first-page":"6032","DOI":"10.1002\/anie.200460416","article-title":"Catalytic Promiscuity in Biocatalysis:\nUsing Old Enzymes\nto Form New Bonds and Follow New Pathways","volume":"43","author":"Bornscheuer","year":"2004","journal-title":"Angew.\nChem., Int. Ed."},{"issue":"2","key":"2026091609125023100_cit6","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1080\/87559129.2019.1695835","article-title":"Enzyme Engineering:\nCurrent Trends and Future Perspectives","volume":"37","author":"Sharma","year":"2021","journal-title":"Food\nRev. Int."},{"key":"2026091609125023100_cit7","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/978-1-4939-7366-8_2","article-title":"Rational\nand Semirational Protein Design","volume":"1685","author":"Korendovych","year":"2018","journal-title":"Protein Eng.\nMethods Protoc."},{"issue":"3","key":"2026091609125023100_cit8","doi-asserted-by":"publisher","DOI":"10.5936\/csbj.201209010","article-title":"Recent Advances in Rational Approaches\nfor Enzyme Engineering","volume":"2","author":"Steiner","year":"2012","journal-title":"Comput. Struct. Biotechnol.\nJ."},{"issue":"12","key":"2026091609125023100_cit9","doi-asserted-by":"publisher","first-page":"6454","DOI":"10.1021\/acs.jafc.3c08620","article-title":"Semirational\nDesign Based on Consensus Sequences to Balance the Enzyme Activity-Stability\nTrade-Off","volume":"72","author":"Zhao","year":"2024","journal-title":"J. Agric. Food Chem."},{"issue":"10","key":"2026091609125023100_cit10","doi-asserted-by":"publisher","first-page":"2481","DOI":"10.1016\/j.checat.2022.09.036","article-title":"Modern Computational Methods for\nRational Enzyme Engineering","volume":"2","author":"Ferreira","year":"2022","journal-title":"Chem. Catal."},{"key":"2026091609125023100_cit11","doi-asserted-by":"publisher","first-page":"1129149","DOI":"10.3389\/fbioe.2023.1129149","article-title":"Rational Design\nof Enzyme Activity and Enantioselectivity","volume":"11","author":"Song","year":"2023","journal-title":"Front.\nBioeng. Biotechnol."},{"issue":"1","key":"2026091609125023100_cit12","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.tibtech.2009.10.001","article-title":"Enzyme\nEngineering for Enantioselectivity:\nFrom Trial-and-Error to Rational Design?","volume":"28","author":"Otten","year":"2010","journal-title":"Trends\nBiotechnol."},{"issue":"14","key":"2026091609125023100_cit13","doi-asserted-by":"publisher","first-page":"13062","DOI":"10.1021\/acsnano.3c04378","article-title":"Rational Design\nStrategies for Nanozymes","volume":"17","author":"Chen","year":"2023","journal-title":"ACS Nano"},{"key":"2026091609125023100_cit14","doi-asserted-by":"publisher","first-page":"6018","DOI":"10.1021\/acscatal.7b01766","article-title":"Toward Rational Design of High-Efficiency Enzyme Cascades","volume":"7","author":"Zhang","year":"2017","journal-title":"ACS Catal."},{"issue":"1","key":"2026091609125023100_cit15","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1021\/acssynbio.4c00625","article-title":"LevSeq: Rapid Generation of Sequence-Function\nData\nfor Directed Evolution and Machine Learning","volume":"14","author":"Long","year":"2025","journal-title":"ACS Synth. Biol."},{"issue":"1","key":"2026091609125023100_cit16","doi-asserted-by":"publisher","first-page":"8662","DOI":"10.1038\/s41467-025-63802-7","article-title":"Distal Mutations\nEnhance Catalysis in Designed Enzymes\nby Facilitating Substrate Binding and Product Release","volume":"16","author":"Zarifi","year":"2025","journal-title":"Nat. Commun."},{"issue":"5","key":"2026091609125023100_cit17","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1038\/s41929-024-01117-4","article-title":"Epistasis\nArises from Shifting the Rate-Limiting Step during Enzyme Evolution\nof a \u03b2-Lactamase","volume":"7","author":"Fro\u0308hlich","year":"2024","journal-title":"Nat. Catal."},{"issue":"23","key":"2026091609125023100_cit18","doi-asserted-by":"publisher","first-page":"7256","DOI":"10.1021\/jacs.8b03490","article-title":"Directed Evolution\nMimics Allosteric Activation by\nStepwise Tuning of the Conformational Ensemble","volume":"140","author":"Buller","year":"2018","journal-title":"J. Am. Chem. Soc."},{"issue":"3","key":"2026091609125023100_cit19","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1021\/ar960017f","article-title":"Design\nby Directed Evolution","volume":"31","author":"Arnold","year":"1998","journal-title":"Acc. Chem. Res."},{"issue":"20","key":"2026091609125023100_cit20","doi-asserted-by":"publisher","first-page":"12384","DOI":"10.1021\/acs.chemrev.1c00260","article-title":"Directed Evolution:\nMethodologies and Applications","volume":"121","author":"Wang","year":"2021","journal-title":"Chem. Rev."},{"issue":"7397","key":"2026091609125023100_cit21","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1038\/nature11117","article-title":"Engineering the Third Wave of Biocatalysis","volume":"485","author":"Bornscheuer","year":"2012","journal-title":"Nature"},{"issue":"9","key":"2026091609125023100_cit22","doi-asserted-by":"publisher","first-page":"5571","DOI":"10.1021\/acs.chemrev.2c00910","article-title":"Ultrahigh-Throughput Enzyme Engineering\nand Discovery\nin in Vitro Compartments","volume":"123","author":"Gantz","year":"2023","journal-title":"Chem. Rev."},{"issue":"4","key":"2026091609125023100_cit23","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1016\/j.copbio.2005.06.004","article-title":"Semi-Rational Approaches to Engineering\nEnzyme Activity: Combining the Benefits of Directed Evolution and\nRational Design","volume":"16","author":"Chica","year":"2005","journal-title":"Curr. Opin. Biotechnol."},{"issue":"6","key":"2026091609125023100_cit24","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1016\/j.copbio.2010.08.011","article-title":"Beyond Directed\nEvolution\u2500Semi-Rational Protein Engineering and Design","volume":"21","author":"Lutz","year":"2010","journal-title":"Curr. Opin. Biotechnol."},{"issue":"27","key":"2026091609125023100_cit25","doi-asserted-by":"publisher","first-page":"4192","DOI":"10.1002\/anie.200500767","article-title":"Expanding\nthe Range of Substrate Acceptance of Enzymes: Combinatorial Active-Site\nSaturation Test","volume":"44","author":"Reetz","year":"2005","journal-title":"Angew. Chem., Int. Ed."},{"issue":"20","key":"2026091609125023100_cit26","doi-asserted-by":"publisher","first-page":"6086","DOI":"10.1111\/febs.16124","article-title":"A Guide to\nthe Michaelis\u2013Menten Equation: Steady State and Beyond","volume":"289","author":"Srinivasan","year":"2022","journal-title":"FEBS J."},{"issue":"13","key":"2026091609125023100_cit27","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2023348118","article-title":"The Number of Catalytic\nCycles in an Enzyme\u2019s Lifetime and Why It Matters to Metabolic\nEngineering","volume":"118","author":"Hanson","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026091609125023100_cit28","volume-title":"xPharm:\nthe Comprehensive\nPharmacology Reference","author":"Enna","year":"2008"},{"key":"2026091609125023100_cit29","doi-asserted-by":"crossref","DOI":"10.1002\/9783527806461","volume-title":"Enzyme Kinetics:\nprinciples And Methods","author":"Bisswanger","year":"2017"},{"key":"2026091609125023100_cit30","volume-title":"Enzyme Kinetics: a\nModern Approach","author":"Marangoni","year":"2003"},{"issue":"6","key":"2026091609125023100_cit31","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1016\/j.cels.2017.11.013","article-title":"Metabolic\nModels of Protein Allocation\nCall for the Kinetome","volume":"5","author":"Nilsson","year":"2017","journal-title":"Cell Syst."},{"issue":"22","key":"2026091609125023100_cit32","doi-asserted-by":"publisher","first-page":"5841","DOI":"10.1021\/acs.jcim.2c01139","article-title":"IntEnzyDB:\nAn Integrated Structure\u2013Kinetics\nEnzymology Database","volume":"62","author":"Yan","year":"2022","journal-title":"J. Chem. Inf. Model."},{"issue":"D1","key":"2026091609125023100_cit33","doi-asserted-by":"publisher","first-page":"D790","DOI":"10.1093\/nar\/gkr1046","article-title":"SABIO-RK\u2500Database\nfor Biochemical Reaction Kinetics","volume":"40","author":"Wittig","year":"2012","journal-title":"Nucleic Acids\nRes."},{"issue":"1","key":"2026091609125023100_cit34","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1093\/nar\/30.1.47","article-title":"BRENDA Enzyme Data and Metabolic\nInformation","volume":"30","author":"Schomburg","year":"2002","journal-title":"Nucleic Acids Res."},{"issue":"8","key":"2026091609125023100_cit35","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1038\/s41929-022-00798-z","article-title":"Deep Learning-Based\nk Cat Prediction Enables Improved Enzyme-Constrained Model Reconstruction","volume":"5","author":"Li","year":"2022","journal-title":"Nat. Catal."},{"issue":"1","key":"2026091609125023100_cit36","doi-asserted-by":"publisher","first-page":"6405","DOI":"10.1038\/s41467-024-50712-3","article-title":"Neural Network Extrapolation\nto Distant Regions of the Protein Fitness Landscape","volume":"15","author":"Freschlin","year":"2024","journal-title":"Nat. Commun."},{"issue":"1","key":"2026091609125023100_cit37","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1038\/s41467-025-55987-8","article-title":"H. Active Learning-Assisted Directed Evolution","volume":"16","author":"Yang","year":"2025","journal-title":"Nat. Commun."},{"issue":"1","key":"2026091609125023100_cit38","doi-asserted-by":"publisher","first-page":"1553","DOI":"10.1038\/s41467-025-56751-8","article-title":"others. Integrating\nProtein Language Models and Automatic Biofoundry\nfor Enhanced Protein Evolution","volume":"16","author":"Zhang","year":"2025","journal-title":"Nat. Commun."},{"issue":"12","key":"2026091609125023100_cit39","doi-asserted-by":"publisher","first-page":"866","DOI":"10.1038\/nrm2805","article-title":"Exploring Protein\nFitness Landscapes by Directed Evolution","volume":"10","author":"Romero","year":"2009","journal-title":"Nat.\nRev. Mol. Cell Biol."},{"key":"2026091609125023100_cit40","doi-asserted-by":"publisher","first-page":"102713","DOI":"10.1016\/j.copbio.2022.102713","article-title":"Machine\nLearning to Navigate Fitness\nLandscapes for Protein Engineering","volume":"75","author":"Freschlin","year":"2022","journal-title":"Curr. Opin.\nBiotechnol."},{"issue":"1","key":"2026091609125023100_cit41","doi-asserted-by":"publisher","first-page":"8211","DOI":"10.1038\/s41467-023-44113-1","article-title":"UniKP: A Unified\nFramework for the Prediction of Enzyme Kinetic Parameters","volume":"14","author":"Luo","year":"2023","journal-title":"Nat. Commun."},{"issue":"1","key":"2026091609125023100_cit42","doi-asserted-by":"publisher","first-page":"2072","DOI":"10.1038\/s41467-025-57215-9","article-title":"CatPred: A Comprehensive Framework\nfor Deep Learning\nin Vitro Enzyme Kinetic Parameters","volume":"16","author":"Boorla","year":"2025","journal-title":"Nat. Commun."},{"key":"2026091609125023100_cit43","doi-asserted-by":"publisher","article-title":"OmniESI: A Unified\nFramework for Enzyme-Substrate\nInteraction Prediction with Progressive Conditional Deep Learning","author":"Nie","DOI":"10.48550\/arXiv.2506.17963"},{"issue":"1","key":"2026091609125023100_cit44","doi-asserted-by":"publisher","first-page":"2736","DOI":"10.1038\/s41467-025-58038-4","article-title":"Robust Enzyme Discovery\nand Engineering with Deep Learning Using CataPro","volume":"16","author":"Wang","year":"2025","journal-title":"Nat. Commun."},{"issue":"10","key":"2026091609125023100_cit45","doi-asserted-by":"publisher","first-page":"1828","DOI":"10.1021\/acscentsci.5c00949","article-title":"others. Of Revolutions and Roadblocks: The Emerging\nRole of Machine Learning in Biocatalysis","volume":"11","author":"Vornholt","year":"2025","journal-title":"ACS\nCent. Sci."},{"issue":"2","key":"2026091609125023100_cit46","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1038\/s41587-024-02133-2","article-title":"Sparks of Function by de Novo Protein Design","volume":"42","author":"Chu","year":"2024","journal-title":"Nat. Biotechnol."},{"issue":"2","key":"2026091609125023100_cit47","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1038\/s41587-024-02127-0","article-title":"Machine Learning\nfor Functional Protein Design","volume":"42","author":"Notin","year":"2024","journal-title":"Nat. Biotechnol."},{"issue":"12","key":"2026091609125023100_cit48","doi-asserted-by":"publisher","first-page":"1034","DOI":"10.1038\/s44222-025-00349-8","article-title":"AI-Driven Protein Design","volume":"3","author":"Koh","year":"2025","journal-title":"Nat.\nRev. Bioeng."},{"issue":"12","key":"2026091609125023100_cit49","doi-asserted-by":"publisher","first-page":"7065","DOI":"10.1021\/acs.jafc.4c13201","article-title":"Artificial Intelligence\nTechnology Assists Enzyme Prediction and Rational Design","volume":"73","author":"Wang","year":"2025","journal-title":"J. Agric. Food Chem."},{"issue":"8","key":"2026091609125023100_cit50","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1038\/s41587-022-01618-2","article-title":"Large Language\nModels Generate Functional Protein Sequences across Diverse Families","volume":"41","author":"Madani","year":"2023","journal-title":"Nat. Biotechnol."},{"key":"2026091609125023100_cit51","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2405.08205","article-title":"Generative Enzyme Design Guided by Functionally Important\nSites and\nSmall-Molecule Substrates","author":"Song","year":"2024","journal-title":"arXiv"},{"issue":"6615","key":"2026091609125023100_cit52","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1126\/science.add2187","article-title":"Robust Deep\nLearning\u2013Based Protein Sequence\nDesign Using ProteinMPNN","volume":"378","author":"Dauparas","year":"2022","journal-title":"Science"},{"issue":"7976","key":"2026091609125023100_cit53","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1038\/s41586-023-06415-8","article-title":"De\nNovo Design of Protein Structure and Function\nwith RFdiffusion","volume":"620","author":"Watson","year":"2023","journal-title":"Nature"},{"issue":"3","key":"2026091609125023100_cit54","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1016\/j.cell.2023.12.028","article-title":"De Novo Protein\nDesign\u2500from New Structures to Programmable Functions","volume":"187","author":"Kortemme","year":"2024","journal-title":"Cell"},{"key":"2026091609125023100_cit55","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1038\/s41592-025-02975-x","article-title":"Atom Level Enzyme Active\nSite Scaffolding Using Rfdiffusion 2","volume":"23","author":"Ahern","year":"2025","journal-title":"Nat Methods"},{"issue":"4","key":"2026091609125023100_cit56","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1038\/s41592-025-02626-1","article-title":"Atomic Context-Conditioned\nProtein\nSequence Design Using LigandMPNN","volume":"22","author":"Dauparas","year":"2025","journal-title":"Nat. Methods"},{"key":"2026091609125023100_cit57","volume-title":"ZymCTRL: A Conditional\nLanguage Model for the Controllable Generation of Artificial Enzymes","author":"Munsamy"},{"key":"2026091609125023100_cit58","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2410.00327","article-title":"Enzymeflow: Generating\nReaction-Specific Enzyme Catalytic Pockets through Flow Matching and\nCo-Evolutionary Dynamics","author":"Hua","year":"2024","journal-title":"arXiv"},{"key":"2026091609125023100_cit59","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2411.16694","article-title":"Reaction-Conditioned\nde Novo\nEnzyme Design with Genzyme","author":"Hua","year":"2024","journal-title":"arXiv"},{"issue":"8095","key":"2026091609125023100_cit60","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1038\/s41586-025-09746-w","article-title":"Computational Design\nof Metallohydrolases","volume":"649","author":"Kim","year":"2026","journal-title":"Nature"},{"key":"2026091609125023100_cit61","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2505.04823","article-title":"ProteinGuide:\nOn-the-Fly Property\nGuidance for Protein Sequence Generative Models","author":"Xiong","year":"2025","journal-title":"arXiv"},{"key":"2026091609125023100_cit62","first-page":"9786","volume-title":"Biological Sequence Design with Gflownets","author":"Jain","year":"2022"},{"issue":"3","key":"2026091609125023100_cit63","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1038\/s41587-024-02214-2","article-title":"Computational Scoring and Experimental Evaluation of\nEnzymes Generated by Neural Networks","volume":"43","author":"Johnson","year":"2025","journal-title":"Nat. Biotechnol."},{"key":"2026091609125023100_cit64","doi-asserted-by":"publisher","first-page":"103535","DOI":"10.1016\/j.artint.2021.103535","article-title":"Reward Is Enough","volume":"299","author":"Silver","year":"2021","journal-title":"Artif. Intell."},{"issue":"8","key":"2026091609125023100_cit65","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1038\/s41592-019-0496-6","article-title":"Machine-Learning-Guided Directed Evolution for Protein\nEngineering","volume":"16","author":"Yang","year":"2019","journal-title":"Nat. Methods"},{"issue":"2","key":"2026091609125023100_cit66","doi-asserted-by":"publisher","first-page":"025014","DOI":"10.1088\/2632-2153\/accacd","article-title":"Plug\n& Play Directed Evolution of Proteins with Gradient-Based Discrete\nMCMC","volume":"4","author":"Emami","year":"2023","journal-title":"Mach. Learn.: sci. Technol."},{"issue":"4","key":"2026091609125023100_cit67","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1038\/s41592-021-01100-y","article-title":"Low-N Protein\nEngineering with Data-Efficient Deep Learning","volume":"18","author":"Biswas","year":"2021","journal-title":"Nat. Methods"},{"key":"2026091609125023100_cit68","doi-asserted-by":"publisher","DOI":"10.1186\/s12859-021-04437-5","article-title":"Fast\nDifferentiable\nDNA and Protein Sequence Optimization for Molecular Design","author":"Linder","year":"2020","journal-title":"arXiv"},{"key":"2026091609125023100_cit69","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2307.00494","article-title":"Optimizing Protein Fitness Using Gibbs\nSampling with Graph-Based Smoothing","author":"Kirjner","year":"2023","journal-title":"arXiv"},{"issue":"7873","key":"2026091609125023100_cit70","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1038\/s41586-021-03819-2","article-title":"others.Highly Accurate Protein Structure Prediction\nwith AlphaFold","volume":"596","author":"Jumper","year":"2021","journal-title":"Nature"},{"issue":"7889","key":"2026091609125023100_cit71","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1038\/s41586-021-04184-w","article-title":"De Novo\nProtein Design by Deep Network Hallucination","volume":"600","author":"Anishchenko","year":"2021","journal-title":"Nature"},{"issue":"6615","key":"2026091609125023100_cit72","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1126\/science.add1964","article-title":"Hallucinating\nSymmetric Protein Assemblies","volume":"378","author":"Wicky","year":"2022","journal-title":"Science"},{"issue":"6720","key":"2026091609125023100_cit73","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1126\/science.adq1741","article-title":"others. Scalable\nProtein Design Using\nOptimization in a Relaxed Sequence Space","volume":"386","author":"Frank","year":"2024","journal-title":"Science"},{"key":"2026091609125023100_cit74","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1312.6199","article-title":"Intriguing\nProperties of Neural Networks","author":"Szegedy","year":"2013","journal-title":"arXiv"},{"key":"2026091609125023100_cit75","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1412.6572","article-title":"Explaining\nand Harnessing Adversarial Examples","author":"Goodfellow","year":"2014","journal-title":"arXiv"},{"issue":"8084","key":"2026091609125023100_cit76","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1038\/s41586-025-09429-6","article-title":"One-Shot Design of Functional\nProtein Binders with BindCraft","volume":"646","author":"Pacesa","year":"2025","journal-title":"Nature"},{"key":"2026091609125023100_cit77","volume-title":"The Concrete Distribution:\nA Continuous Relaxation of Discrete Random Variables","author":"Maddison","year":"2016"},{"issue":"1","key":"2026091609125023100_cit78","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1186\/s12859-021-04437-5","article-title":"Fast Activation Maximization for Molecular Sequence\nDesign","volume":"22","author":"Linder","year":"2021","journal-title":"BMC Bioinf"},{"key":"2026091609125023100_cit79","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1611.01144","article-title":"Categorical Reparameterization\nwith\nGumbel-Softmax","author":"Jang","year":"2016","journal-title":"arXiv"},{"key":"2026091609125023100_cit80","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2410.13643","article-title":"Fine-Tuning Discrete Diffusion Models via Reward Optimization\nwith\nApplications to Dna and Protein Design","author":"Wang","year":"2024","journal-title":"arXiv"},{"key":"2026091609125023100_cit81","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2503.17361","article-title":"Gumbel-Softmax\nScore and Flow Matching\nfor Discrete Biological Sequence Generation","author":"Tang","year":"2025","journal-title":"arXiv"},{"issue":"6637","key":"2026091609125023100_cit82","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1126\/science.ade2574","article-title":"Evolutionary-Scale\nPrediction of Atomic-Level Protein Structure with\na Language Model","volume":"379","author":"Lin","year":"2023","journal-title":"Science"},{"key":"2026091609125023100_cit83","doi-asserted-by":"publisher","first-page":"2026","DOI":"10.64898\/2026.02.05.703733","article-title":"Protenix-v1:\nToward High-Accuracy Open-Source Biomolecular Structure Prediction","author":"Team","year":"2026","journal-title":"bioRxiv"},{"issue":"5","key":"2026091609125023100_cit84","doi-asserted-by":"publisher","first-page":"1172","DOI":"10.1039\/C4CS00351A","article-title":"Synthetic Biology\nfor the Directed Evolution of Protein Biocatalysts: Navigating Sequence\nSpace Intelligently","volume":"44","author":"Currin","year":"2015","journal-title":"Chem. Soc. Rev."},{"issue":"5","key":"2026091609125023100_cit85","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1016\/j.sbi.2009.08.003","article-title":"Stability Effects\nof Mutations and Protein Evolvability","volume":"19","author":"Tokuriki","year":"2009","journal-title":"Curr.\nOpin. Struct. Biol."},{"issue":"8","key":"2026091609125023100_cit86","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1038\/nmeth.3027","article-title":"Deep Mutational Scanning: A New Style\nof Protein Science","volume":"11","author":"Fowler","year":"2014","journal-title":"Nat. Methods"},{"issue":"1","key":"2026091609125023100_cit87","doi-asserted-by":"publisher","first-page":"1807","DOI":"10.1038\/s41467-024-45630-3","article-title":"Understanding\nActivity-Stability Tradeoffs in Biocatalysts\nby Enzyme Proximity Sequencing","volume":"15","author":"Vanella","year":"2024","journal-title":"Nat. Commun."},{"issue":"8074","key":"2026091609125023100_cit88","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.1038\/s41586-025-09136-2","article-title":"Complete\nComputational Design of High-Efficiency Kemp Elimination Enzymes","volume":"643","author":"Listov","year":"2025","journal-title":"Nature"},{"issue":"10","key":"2026091609125023100_cit89","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1038\/s41557-021-00763-6","article-title":"Evolution of Dynamical Networks Enhances\nCatalysis in a Designer Enzyme","volume":"13","author":"Bunzel","year":"2021","journal-title":"Nat. Chem."},{"key":"2026091609125023100_cit90","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.06181","article-title":"Extensive\nSite-Directed Mutagenesis Reveals Interconnected Functional Units\nin the Alkaline Phosphatase Active Site","volume":"4","author":"Sunden","year":"2015","journal-title":"Elife"},{"issue":"7476","key":"2026091609125023100_cit91","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1038\/nature12623","article-title":"Precision\nIs Essential\nfor Efficient Catalysis in an Evolved Kemp Eliminase","volume":"503","author":"Blomberg","year":"2013","journal-title":"Nature"},{"issue":"1","key":"2026091609125023100_cit92","doi-asserted-by":"publisher","first-page":"3900","DOI":"10.1038\/s41467-018-06305-y","article-title":"The Evolution of Multiple\nActive Site Configurations in a Designed Enzyme","volume":"9","author":"Hong","year":"2018","journal-title":"Nat. Commun."},{"issue":"1","key":"2026091609125023100_cit93","doi-asserted-by":"publisher","first-page":"4808","DOI":"10.1038\/s41467-020-18619-x","article-title":"Ensemble-Based\nEnzyme Design Can Recapitulate the Effects of Laboratory Directed\nEvolution in Silico","volume":"11","author":"Broom","year":"2020","journal-title":"Nat. Commun."},{"issue":"1","key":"2026091609125023100_cit94","doi-asserted-by":"publisher","first-page":"1621","DOI":"10.1038\/s41467-021-21833-w","article-title":"Pervasive Cooperative\nMutational\nEffects on Multiple Catalytic Enzyme Traits Emerge via Long-Range\nConformational Dynamics","volume":"12","author":"Acevedo-Rocha","year":"2021","journal-title":"Nat. Commun."},{"key":"2026091609125023100_cit95","doi-asserted-by":"publisher","DOI":"10.1101\/2025.09.18.676967","article-title":"De Novo Design\nof All-Atom Biomolecular\nInteractions with Rfdiffusion3","author":"Butcher","year":"2025","journal-title":"bioRxiv"},{"issue":"7","key":"2026091609125023100_cit96","doi-asserted-by":"publisher","first-page":"2302","DOI":"10.1093\/nar\/gki524","article-title":"TM-Align: A Protein\nStructure Alignment Algorithm Based\non the TM-Score","volume":"33","author":"Zhang","year":"2005","journal-title":"Nucleic Acids Res."},{"issue":"2","key":"2026091609125023100_cit97","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1038\/s41587-023-01773-0","article-title":"Fast and Accurate Protein Structure\nSearch with Foldseek","volume":"42","author":"Van Kempen","year":"2024","journal-title":"Nat. Biotechnol."},{"issue":"7","key":"2026091609125023100_cit98","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1093\/bioinformatics\/btq066","article-title":"How Significant\nIs a Protein Structure Similarity with TM-Score=\n0.5?","volume":"26","author":"Xu","year":"2010","journal-title":"Bioinformatics"},{"issue":"15","key":"2026091609125023100_cit99","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2016239118","article-title":"Biological Structure\nand Function Emerge from Scaling\nUnsupervised Learning to 250 Million Protein Sequences","volume":"118","author":"Rives","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026091609125023100_cit100","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1609.02907","article-title":"Semi-Supervised\nClassification with Graph Convolutional Networks","author":"Kipf","year":"2016","journal-title":"arXiv"},{"key":"2026091609125023100_cit101","first-page":"30","article-title":"Attention\nIs All You Need","volume-title":"Proceedings of the 31st International\nConference on Neural\nInformation Processing Systems","author":"Vaswani","year":"2017"},{"key":"2026091609125023100_cit102","article-title":"ViLBERT: Pretraining Task-Agnostic\nVisiolinguistic Representations for Vision-and-Language Tasks","volume-title":"Proceedings of the 33rd International Conference on Neural\nInformation Processing Systems","author":"Lu","year":"2019"},{"key":"2026091609125023100_cit103","first-page":"1352","volume-title":"ReZero Is\nAll You Need: Fast Convergence at Large Depth","author":"Bachlechner","year":"2021"},{"key":"2026091609125023100_cit104","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/ICCV48922.2021.00010","article-title":"Going Deeper with Image Transformers","volume-title":"2021 IEEE\/CVF International Conference on Computer Vision\n(ICCV)","author":"Touvron","year":"2021"},{"key":"2026091609125023100_cit105","volume-title":"Visualizing Higher-Layer\nFeatures Of a Deep Network, 1341","author":"Erhan","year":"2009"},{"key":"2026091609125023100_cit106","volume-title":"Deep inside Convolutional\nNetworks: Visualising Image Classification Models and Saliency Maps","author":"Simonyan","year":"2013"},{"issue":"1","key":"2026091609125023100_cit107","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On Information and Sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"2026091609125023100_cit108","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1007\/978-3-319-46475-6_43","article-title":"Perceptual\nLosses for Real-Time\nStyle Transfer and Super-Resolution","volume-title":"Computer\nVision \u2013 ECCV 2016","author":"Johnson","year":"2016"},{"key":"2026091609125023100_cit109","doi-asserted-by":"publisher","first-page":"2414","DOI":"10.1109\/CVPR.2016.265","article-title":"Image Style Transfer\nUsing Convolutional Neural Networks","volume-title":"2016\nIEEE Conference on Computer Vision and Pattern Recognition (CVPR)","author":"Gatys","year":"2016"},{"key":"2026091609125023100_cit110","first-page":"807","article-title":"Rectified Linear\nUnits Improve Restricted Boltzmann Machines","volume-title":"Proceedings of the 27th International Conference on International\nConference on Machine Learning","author":"Nair","year":"2010"},{"key":"2026091609125023100_cit111","first-page":"472","article-title":"Incorporating\nSecond-Order\nFunctional Knowledge for Better Option Pricing","volume-title":"Proceedings of the 14th International Conference on Neural Information\nProcessing Systems","author":"Dugas","year":"2001"},{"key":"2026091609125023100_cit112","first-page":"1","article-title":"Loss Functions\nfor Preference Levels: Regression with Discrete Ordered Labels","volume-title":"Proceedings of the IJCAI multidisciplinary workshop on advances\nin preference handling","author":"Rennie","year":"2005"},{"key":"2026091609125023100_cit113","doi-asserted-by":"publisher","first-page":"7482","DOI":"10.1109\/CVPR.2018.00781","article-title":"Multi-Task Learning\nUsing Uncertainty\nto Weigh Losses for Scene Geometry and Semantics","volume-title":"2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition","author":"Cipolla","year":"2018"},{"key":"2026091609125023100_cit114","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd","year":"2004"},{"key":"2026091609125023100_cit115","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1909.01315","article-title":"Deep Graph Library: A Graph-Centric,\nHighly-Performant Package for Graph Neural Networks","author":"Wang","year":"2019","journal-title":"arXiv"},{"issue":"41","key":"2026091609125023100_cit116","doi-asserted-by":"publisher","first-page":"27233","DOI":"10.1021\/acsomega.1c04017","article-title":"Dgl-Lifesci:\nAn Open-Source Toolkit for Deep Learning\non Graphs in Life Science","volume":"6","author":"Li","year":"2021","journal-title":"ACS Omega"},{"key":"2026091609125023100_cit117","first-page":"82","article-title":"Pymol: An Open-Source\nMolecular Graphics Tool","volume-title":"CCP4 Newsl. Protein\nCrystallographic","author":"DeLano","year":"2002"}],"container-title":["Journal of the American\nChemical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/jacs.6c14365","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jacsat\/article-pdf\/148\/36\/39258\/68371908\/jacs.6c14365.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jacsat\/article-pdf\/148\/36\/39258\/68371908\/jacs.6c14365.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T13:27:02Z","timestamp":1789565222000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jacsat\/article\/148\/36\/39258\/5420431\/CatESO-Differentiable-Enzyme-Sequence-Optimization"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,4]]},"references-count":117,"journal-issue":{"issue":"36","published-online":{"date-parts":[[2026,9,4]]},"published-print":{"date-parts":[[2026,9,16]]}},"URL":"https:\/\/doi.org\/10.1021\/jacs.6c14365","relation":{},"ISSN":["0002-7863","1520-5126"],"issn-type":[{"value":"0002-7863","type":"print"},{"value":"1520-5126","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,4]]}}}