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Experimental determination of pHopt is, however, labor-intensive and time-consuming, motivating the development of accurate computational prediction methods. Here, we introduce pHoptNN, an E(n)-equivariant graph neural network designed to predict enzyme pHopt directly from three-dimensional protein structures. pHoptNN was trained on a curated data set comprising nearly 12,000 enzymes with experimentally determined pHopt values and high-confidence structural models obtained from the Protein Data Bank and AlphaFold. The model represents enzymes as atomic-level molecular graphs, integrating structural, chemical, and electrostatic features. Model development was assisted by hyperparameter optimization using genetic and Bayesian search strategies. On a held-out test set, pHoptNN achieved a root-mean-square error (RMSE) of 0.588 pH units, substantially outperforming the sequence-based method EpHod (RMSE = 0.879). The model also showed strong out-of-distribution generalization, achieving RMSE values of 0.594 and 0.611 on test sets comprising held-out EC class 4 enzymes and enzymes sharing &amp;lt;20% sequence identity with the training set, respectively, compared with RMSE values of 0.878 and 0.883 for EpHod. Moreover, pHoptNN maintains robust predictive performance across different enzyme classes and pH ranges. These results demonstrate the utility of structure-based equivariant deep learning for enzyme pHopt prediction and highlight the potential of pHoptNN to accelerate enzyme discovery and engineering workflows.<\/jats:p>","DOI":"10.1021\/acs.jcim.6c01482","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T14:05:39Z","timestamp":1785852339000},"page":"9858-9873","source":"Crossref","is-referenced-by-count":1,"title":["Predicting Enzyme\npH Optima from Structure Using Equivariant\nGraph Neural Networks"],"prefix":"10.1021","volume":"66","author":[{"given":"Rajarshi","family":"SinhaRoy","sequence":"first","affiliation":[{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04103"]},{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04105"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Clau\u00df","sequence":"additional","affiliation":[{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04103"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivan","family":"Ivanikov","sequence":"additional","affiliation":[{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04103"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1799-346X","authenticated-orcid":true,"given":"Georg","family":"Ku\u0308nze","sequence":"additional","affiliation":[{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04103"]},{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04105"]},{"name":"University of Leipzig , , ,","place":["Leipzig, Germany, 04107"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,1]]},"reference":[{"key":"2026083104310985600_cit1","volume-title":"Enzyme: Struktur,\nKinetik und Anwendungen","author":"Bisswanger","year":"2015"},{"key":"2026083104310985600_cit2","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.enzmictec.2016.10.011","article-title":"Deciphering the factors defining the pH-dependence\nof a commercial glycoside hydrolase family 8 enzyme","volume":"96","author":"Barroca","year":"2017","journal-title":"Enzyme Microb. Technol."},{"key":"2026083104310985600_cit3","doi-asserted-by":"publisher","first-page":"D158","DOI":"10.1093\/nar\/gkw1099","article-title":"The UniProt Consortium, UniProt: the universal\nprotein knowledgebase","volume":"45","year":"2017","journal-title":"Nucleic Acids Res."},{"key":"2026083104310985600_cit4","doi-asserted-by":"publisher","first-page":"D498","DOI":"10.1093\/nar\/gkaa1025","article-title":"BRENDA, the\nELIXIR core data resource in 2021: new developments and updates","volume":"49","author":"Chang","year":"2021","journal-title":"Nucleic Acids Res."},{"key":"2026083104310985600_cit5","doi-asserted-by":"publisher","first-page":"D464","DOI":"10.1093\/nar\/gky1004","article-title":"RCSB Protein Data Bank: biological macromolecular structures enabling\nresearch and education in fundamental biology, biomedicine, biotechnology\nand energy","volume":"47","author":"Burley","year":"2019","journal-title":"Nucleic Acids Res."},{"key":"2026083104310985600_cit6","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1038\/msb.2012.61","article-title":"High-throughput\nsequencing for biology\nand medicine","volume":"9","author":"Soon","year":"2013","journal-title":"Mol. Syst. Biol."},{"key":"2026083104310985600_cit7","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1016\/j.ajpath.2015.10.033","article-title":"Biological Processes Discovered by High-Throughput Sequencing","volume":"186","author":"Reon","year":"2016","journal-title":"Am. J. Pathol."},{"key":"2026083104310985600_cit8","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1038\/s42256-025-01026-6","article-title":"Machine learning\nprediction of enzyme optimum pH","volume":"7","author":"Gado","year":"2025","journal-title":"Nat. Mach.\nIntell."},{"key":"2026083104310985600_cit9","first-page":"29287","article-title":"Language models\nenable zero-shot prediction of the effects of mutations on protein\nfunction","author":"Meier","year":"2021","journal-title":"Adv. Neural Inf. Process. 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Biol."},{"key":"2026083104310985600_cit13","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":"2026083104310985600_cit14","doi-asserted-by":"publisher","first-page":"3761","DOI":"10.1021\/acs.jcim.4c02291","article-title":"Deep Retrieval-Enhanced Meta-Learning Framework for\nEnzyme Optimum pH Prediction","volume":"65","author":"Zhang","year":"2025","journal-title":"J. Chem. Inf.\nModel."},{"key":"2026083104310985600_cit15","doi-asserted-by":"publisher","first-page":"5411","DOI":"10.1021\/acs.jcim.5c00526","article-title":"Advancing Enzyme Optimal pH Prediction via Retrieved\nEmbedding Data Augmentation","volume":"65","author":"Zhang","year":"2025","journal-title":"J. Chem. Inf. 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N.; Welling, M.\n          Semi-Supervised\nClassification with Graph Convolutional Networks.  arXiv2017, arXiv.1609.02907.10.48550\/arXiv.1609.02907https:\/\/arxiv.org\/abs\/1609.02907."},{"key":"2026083104310985600_cit39","doi-asserted-by":"publisher","first-page":"arXiv.1412.6980","DOI":"10.48550\/arXiv.1412.6980","article-title":"Adam: A Method for\nStochastic Optimization","author":"Kingma","year":"2015","journal-title":"arXiv"},{"key":"2026083104310985600_cit40","doi-asserted-by":"publisher","first-page":"arXiv.2102.09554","DOI":"10.48550\/arXiv.2102.09554","article-title":"Delving into Deep Imbalanced\nRegression","author":"Yang","year":"2021","journal-title":"arXiv"},{"key":"2026083104310985600_cit41","doi-asserted-by":"publisher","first-page":"189","DOI":"10.12688\/f1000research.7931.1","article-title":"FreeSASA:\nAn open source C library for solvent accessible surface area calculations\n[version 1; peer review: 2 approved]","volume":"5","author":"Mitternacht","year":"2016","journal-title":"F1000Research"},{"key":"2026083104310985600_cit42","doi-asserted-by":"publisher","first-page":"arXiv.1511.06391","DOI":"10.48550\/arXiv.1511.06391","article-title":"Order Matters: Sequence\nto Sequence\nfor Sets","author":"Vinyals","year":"2016","journal-title":"arXiv"},{"key":"2026083104310985600_cit43","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1126\/science.add2187","article-title":"Robust deep learning\u2013based\nprotein sequence design using ProteinMPNN","volume":"378","author":"Dauparas","year":"2022","journal-title":"Science"},{"key":"2026083104310985600_cit44","doi-asserted-by":"publisher","first-page":"D593","DOI":"10.1093\/nar\/gkac860","article-title":"MeDBA: the metalloenzyme data bank\nand analysis platform","volume":"51","author":"Yu","year":"2022","journal-title":"Nucleic Acids Res."},{"key":"2026083104310985600_cit45","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1093\/bioinformatics\/btz648","article-title":"MeLAD: an integrated\nresource for metalloenzyme-ligand associations","volume":"36","author":"Li","year":"2020","journal-title":"Bioinformatics"},{"key":"2026083104310985600_cit46","first-page":"2579","article-title":"Visualizing Data using t-SNE","volume":"9","author":"van der Maaten","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"2026083104310985600_cit47","doi-asserted-by":"publisher","first-page":"1454","DOI":"10.1007\/s12010-013-0437-2","article-title":"Tailoring\nthe pH Dependence of Human Non-pancreatic Secretory Phospholipase\nA2 by Engineering Surface Charges","volume":"171","author":"Qiu","year":"2013","journal-title":"Appl. Biochem.\nBiotechnol."},{"key":"2026083104310985600_cit48","doi-asserted-by":"publisher","first-page":"4165","DOI":"10.1016\/j.ijbiomac.2020.08.229","article-title":"Surface charge-based\nrational design of aspartase modifies the optimal pH for efficient\n\u03b2-aminobutyric acid production","volume":"164","author":"Wang","year":"2020","journal-title":"Int. J.\nBiol. Macromol."},{"key":"2026083104310985600_cit49","doi-asserted-by":"publisher","first-page":"522","DOI":"10.3390\/biology12040522","article-title":"N20D\/N116E Combined\nMutant Downward Shifted the pH Optimum of Bacillus\nsubtilis NADH Oxidase","volume":"12","author":"Yang","year":"2023","journal-title":"Biology"},{"key":"2026083104310985600_cit50","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1186\/s12896-016-0310-9","article-title":"Improvement of alkalophilicity\nof an alkaline xylanase Xyn11A-LC from Bacillus sp. SN5 by random\nmutation and Glu135 saturation mutagenesis","volume":"16","author":"Bai","year":"2016","journal-title":"BMC Biotechnol."},{"key":"2026083104310985600_cit51","doi-asserted-by":"publisher","first-page":"6793","DOI":"10.1007\/s00253-012-4560-8","article-title":"Surface charge\nengineering of a Bacillus\ngibsonii subtilisin protease","volume":"97","author":"Jakob","year":"2013","journal-title":"Appl. Microbiol.\nBiotechnol."},{"key":"2026083104310985600_cit52","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/protein\/15.2.141","article-title":"Engineering of multiple\narginines into the Ser\/Thr surface of Trichoderma reesei endo-1,4-\u03b2-xylanase\nII increases the thermotolerance and shifts the pH optimum towards\nalkaline pH","volume":"15","author":"Turunen","year":"2002","journal-title":"Protein Eng."},{"key":"2026083104310985600_cit53","doi-asserted-by":"publisher","first-page":"4813","DOI":"10.1007\/s00253-019-09790-3","article-title":"Tuning the\npH profile of \u03b2-glucuronidase by rational site-directed mutagenesis\nfor efficient transformation of glycyrrhizin","volume":"103","author":"Li","year":"2019","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"2026083104310985600_cit54","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1016\/j.jbiosc.2012.12.006","article-title":"Alkalophilic adaptation of XynB endoxylanase\nfrom Aspergillus niger via rational design of pKa of catalytic residues","volume":"115","author":"Xu","year":"2013","journal-title":"J. Biosci. Bioeng."},{"key":"2026083104310985600_cit55","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s12257-012-0455-x","article-title":"Shifting\nthe optimum pH of Bacillus\ncirculans xylanase towards acidic side by introducing arginine","volume":"18","author":"Pokhrel","year":"2013","journal-title":"Biotechnol. Bioprocess Eng."},{"key":"2026083104310985600_cit56","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.btre.2014.06.001","article-title":"Mechanism-based\nsite-directed mutagenesis to shift the optimum pH of the phenylalanine\nammonia-lyase from Rhodotorula glutinis JN-1","volume":"3","author":"Zhu","year":"2014","journal-title":"Biotechnol. Rep."},{"key":"2026083104310985600_cit57","doi-asserted-by":"publisher","first-page":"2487","DOI":"10.1016\/j.procbio.2012.10.011","article-title":"Rational design\nof a Bacillus circulans xylanase by introducing charged residue to\nshift the pH optimum","volume":"47","author":"Pokhrel","year":"2012","journal-title":"Process Biochem."},{"key":"2026083104310985600_cit58","doi-asserted-by":"publisher","first-page":"15347","DOI":"10.3390\/ijms232315347","article-title":"Shifting\nthe pH Optima of (R)-Selective Transaminases by Protein Engineering","volume":"23","author":"Xiang","year":"2022","journal-title":"Int. J. Mol. Sci."},{"key":"2026083104310985600_cit59","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.synbio.2016.09.001","article-title":"Sequence homolog-based molecular\nengineering for shifting the enzymatic pH optimum","volume":"1","author":"Ma","year":"2016","journal-title":"Synth. Syst. 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