{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:29:49Z","timestamp":1777634989959,"version":"3.51.4"},"reference-count":102,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T00:00:00Z","timestamp":1689811200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T00:00:00Z","timestamp":1689811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Mach Intell"],"DOI":"10.1038\/s42256-023-00691-9","type":"journal-article","created":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T16:02:27Z","timestamp":1689868947000},"page":"845-860","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":64,"title":["Self-play reinforcement learning guides protein engineering"],"prefix":"10.1038","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3722-1176","authenticated-orcid":false,"given":"Yi","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9279-9005","authenticated-orcid":false,"given":"Hui","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9319-821X","authenticated-orcid":false,"given":"Lichao","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lulu","family":"Pan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9645-1636","authenticated-orcid":false,"given":"Lixiang","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huanming","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0496-4996","authenticated-orcid":false,"given":"Feng","family":"Mu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5630-6357","authenticated-orcid":false,"given":"Meng","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"key":"691_CR1","doi-asserted-by":"publisher","first-page":"866","DOI":"10.1038\/nrm2805","volume":"10","author":"PA Romero","year":"2009","unstructured":"Romero, P. A. & Arnold, F. H. Exploring protein fitness landscapes by directed evolution. Nat. Rev. Mol. Cell Biol. 10, 866\u2013876 (2009).","journal-title":"Nat. Rev. Mol. Cell Biol."},{"key":"691_CR2","doi-asserted-by":"publisher","first-page":"8852","DOI":"10.1073\/pnas.1901979116","volume":"116","author":"Z Wu","year":"2019","unstructured":"Wu, Z., Kan, S. J., Lewis, R. D., Wittmann, B. J. & Arnold, F. H. Machine learning-assisted directed protein evolution with combinatorial libraries. Proc. Natl Acad. Sci. USA 116, 8852\u20138858 (2019).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"691_CR3","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1038\/s41592-019-0496-6","volume":"16","author":"KK Yang","year":"2019","unstructured":"Yang, K. K., Wu, Z. & Arnold, F. H. Machine-learning-guided directed evolution for protein engineering. Nat. Methods 16, 687\u2013694 (2019).","journal-title":"Nat. Methods"},{"key":"691_CR4","doi-asserted-by":"publisher","first-page":"5743","DOI":"10.1038\/s41467-021-25976-8","volume":"12","author":"Y Luo","year":"2021","unstructured":"Luo, Y. et al. ECNet is an evolutionary context-integrated deep learning framework for protein engineering. Nat. Commun. 12, 5743\u20135756 (2021).","journal-title":"Nat. Commun."},{"key":"691_CR5","doi-asserted-by":"publisher","first-page":"5825","DOI":"10.1038\/s41467-021-25831-w","volume":"12","author":"JC Greenhalgh","year":"2021","unstructured":"Greenhalgh, J. C., Fahlberg, S. A., Pfleger, B. F. & Romero, P. A. Machine learning-guided acyl-ACP reductase engineering for improved in vivo fatty alcohol production. Nat. Commun. 12, 5825\u20135834 (2021).","journal-title":"Nat. Commun."},{"key":"691_CR6","doi-asserted-by":"publisher","first-page":"1026","DOI":"10.1016\/j.cels.2021.07.008","volume":"12","author":"BJ Wittmann","year":"2021","unstructured":"Wittmann, B. J., Yue, Y. & Arnold, F. H. Informed training set design enables efficient machine learning-assisted directed protein evolution. Cell Syst. 12, 1026\u20131045 (2021).","journal-title":"Cell Syst."},{"key":"691_CR7","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.sbi.2021.11.002","volume":"72","author":"BL Hie","year":"2022","unstructured":"Hie, B. L. & Yang, K. K. Adaptive machine learning for protein engineering. Curr. Opin. Struct. Biol. 72, 145\u2013152 (2022).","journal-title":"Curr. Opin. Struct. Biol."},{"key":"691_CR8","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1038\/s43588-021-00168-y","volume":"1","author":"Y Qiu","year":"2021","unstructured":"Qiu, Y., Hu, J. & Wei, G.-W. Cluster learning-assisted directed evolution. Nat. Comput. Sci. 1, 809\u2013818 (2021).","journal-title":"Nat. Comput. Sci."},{"key":"691_CR9","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1093\/nar\/28.1.374","volume":"28","author":"S Kawashima","year":"2000","unstructured":"Kawashima, S. & Kanehisa, M. AAindex: amino acid index database. Nucleic Acids Res. 28, 374 (2000).","journal-title":"Nucleic Acids Res."},{"key":"691_CR10","doi-asserted-by":"publisher","first-page":"3429","DOI":"10.1093\/bioinformatics\/btv345","volume":"31","author":"D Ofer","year":"2015","unstructured":"Ofer, D. & Linial, M. ProFET: feature engineering captures high-level protein functions. Bioinformatics 31, 3429\u20133436 (2015).","journal-title":"Bioinformatics"},{"key":"691_CR11","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1089\/cmb.2008.0173","volume":"16","author":"AG Georgiev","year":"2009","unstructured":"Georgiev, A. G. Interpretable numerical descriptors of amino acid space. J. Comput. Biol. 16, 703\u2013723 (2009).","journal-title":"J. Comput. Biol."},{"key":"691_CR12","doi-asserted-by":"publisher","first-page":"7112","DOI":"10.1109\/TPAMI.2021.3095381","volume":"44","author":"A Elnaggar","year":"2022","unstructured":"Elnaggar, A. et al. ProtTrans: toward understanding the language of life through self-supervised learning. IEEE Trans. Pattern Anal. Mach. Intell. 44, 7112\u20137127 (2022).","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"691_CR13","doi-asserted-by":"publisher","first-page":"e2016239118","DOI":"10.1073\/pnas.2016239118","volume":"118","author":"A Rives","year":"2021","unstructured":"Rives, A. et al. Biological structure and function emerge from scaling unsupervised learning to 250 million protein sequences. Proc. Natl Acad. Sci. USA 118, e2016239118 (2021).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"691_CR14","doi-asserted-by":"crossref","unstructured":"Rao, R. M. et al. MSA Transformer. Proc. Mach. Learning Res. 139, 8844\u20138856 (2021).","DOI":"10.1101\/2021.02.12.430858"},{"key":"691_CR15","unstructured":"Sinai, S. et al. AdaLead: a simple and robust adaptive greedy search algorithm for sequence design. Preprint at https:\/\/arxiv.org\/abs\/2010.02141 (2020)."},{"key":"691_CR16","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1038\/s41592-021-01100-y","volume":"18","author":"S Biswas","year":"2021","unstructured":"Biswas, S., Khimulya, G., Alley, E. C., Esvelt, K. M. & Church, G. M. Low-N protein engineering with data-efficient deep learning. Nat. Methods 18, 389\u2013396 (2021).","journal-title":"Nat. Methods"},{"key":"691_CR17","doi-asserted-by":"crossref","unstructured":"Ren, Z. et al. Proximal exploration for model-guided protein sequence design. Proc. Mach. Learning Res. 162, 18520\u201318536 (2022).","DOI":"10.1101\/2022.04.12.487986"},{"key":"691_CR18","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1038\/s41586-021-04184-w","volume":"600","author":"I Anishchenko","year":"2021","unstructured":"Anishchenko, I. et al. De novo protein design by deep network hallucination. Nature 600, 547\u2013552 (2021).","journal-title":"Nature"},{"key":"691_CR19","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1126\/science.ade2574","volume":"379","author":"L Zeming","year":"2023","unstructured":"Zeming, L. et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 379, 1123\u20131130 (2023).","journal-title":"Science"},{"key":"691_CR20","doi-asserted-by":"publisher","unstructured":"Verkuil, R. et al. Language models generalize beyond natural proteins. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2022.12.21.521521 (2022).","DOI":"10.1101\/2022.12.21.521521"},{"key":"691_CR21","doi-asserted-by":"publisher","unstructured":"Hie, B. et al. A high-level programming language for generative protein design. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2022.12.21.521526 (2022).","DOI":"10.1101\/2022.12.21.521526"},{"key":"691_CR22","first-page":"648","volume":"51","author":"J Gonz\u00e1lez","year":"2016","unstructured":"Gonz\u00e1lez, J. et al. Batch Bayesian optimization via local penalization. Proc. Mach. Learning Res. 51, 648\u2013657 (2016).","journal-title":"Proc. Mach. Learning Res."},{"key":"691_CR23","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1016\/j.cels.2020.09.007","volume":"11","author":"B Hie","year":"2020","unstructured":"Hie, B., Bryson, B. D. & Berger, B. Leveraging uncertainty in machine learning accelerates biological discovery and design. Cell Syst. 11, 461\u2013477 (2020).","journal-title":"Cell Syst."},{"key":"691_CR24","doi-asserted-by":"crossref","unstructured":"Williams, C. K. & Rasmussen, C. E. Gaussian Processes for Machine Learning (MIT Press, 2006).","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"691_CR25","doi-asserted-by":"publisher","first-page":"E193","DOI":"10.1073\/pnas.1215251110","volume":"110","author":"PA Romero","year":"2013","unstructured":"Romero, P. A., Krause, A. & Arnold, F. H. Navigating the protein fitness landscape with Gaussian processes. Proc. Natl Acad. Sci. USA 110, E193\u2013E201 (2013).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"691_CR26","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1038\/s41587-020-00793-4","volume":"39","author":"DH Bryant","year":"2021","unstructured":"Bryant, D. H. et al. Deep diversification of an AAV capsid protein by machine learning. Nat. Biotechnol. 39, 691\u2013696 (2021).","journal-title":"Nat. Biotechnol."},{"key":"691_CR27","unstructured":"Brookes, D. H. & Listgarten, J. Design by adaptive sampling. Preprint at https:\/\/arxiv.org\/abs\/1810.03714 (2018)."},{"key":"691_CR28","unstructured":"Brookes, D., Park, H. & Listgarten, J. Conditioning by adaptive sampling for robust design. Proc. Mach. Learning Res. 97, 773\u2013782 (2019)."},{"key":"691_CR29","doi-asserted-by":"publisher","first-page":"840","DOI":"10.1038\/s42256-022-00532-1","volume":"4","author":"E Castro","year":"2022","unstructured":"Castro, E. et al. Transformer-based protein generation with regularized latent space optimization. Nat. Mach. Intell. 4, 840\u2013851 (2022).","journal-title":"Nat. Mach. Intell."},{"key":"691_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TCIAIG.2012.2186810","volume":"4","author":"CB Browne","year":"2012","unstructured":"Browne, C. B. et al. A survey of Monte Carlo tree search methods. IEEE Trans. Comput. Intell. AI Games 4, 1\u201343 (2012).","journal-title":"IEEE Trans. Comput. Intell. AI Games"},{"key":"691_CR31","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1038\/nature16961","volume":"529","author":"D Silver","year":"2016","unstructured":"Silver, D. et al. Mastering the game of Go with deep neural networks and tree search. Nature 529, 484\u2013489 (2016).","journal-title":"Nature"},{"key":"691_CR32","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1038\/nature24270","volume":"550","author":"D Silver","year":"2017","unstructured":"Silver, D. et al. Mastering the game of Go without human knowledge. Nature 550, 354\u2013359 (2017).","journal-title":"Nature"},{"key":"691_CR33","doi-asserted-by":"publisher","first-page":"1140","DOI":"10.1126\/science.aar6404","volume":"362","author":"D Silver","year":"2018","unstructured":"Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science 362, 1140\u20131144 (2018).","journal-title":"Science"},{"key":"691_CR34","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1038\/s41586-021-03544-w","volume":"594","author":"A Mirhoseini","year":"2021","unstructured":"Mirhoseini, A. et al. A graph placement methodology for fast chip design. Nature 594, 207\u2013212 (2021).","journal-title":"Nature"},{"key":"691_CR35","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1038\/s41586-021-04301-9","volume":"602","author":"J Degrave","year":"2022","unstructured":"Degrave, J. et al. Magnetic control of tokamak plasmas through deep reinforcement learning. Nature 602, 414\u2013419 (2022).","journal-title":"Nature"},{"key":"691_CR36","doi-asserted-by":"publisher","first-page":"720","DOI":"10.1038\/s42256-022-00506-3","volume":"4","author":"SV Shree Sowndarya","year":"2022","unstructured":"Shree Sowndarya, S. V. et al. Multi-objective goal-directed optimization of de novo stable organic radicals for aqueous redox flow batteries. Nat. Mach. Intell. 4, 720\u2013730 (2022).","journal-title":"Nat. Mach. Intell."},{"key":"691_CR37","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1038\/s41586-022-05172-4","volume":"610","author":"A Fawzi","year":"2022","unstructured":"Fawzi, A. et al. Discovering faster matrix multiplication algorithms with reinforcement learning. Nature 610, 47\u201353 (2022).","journal-title":"Nature"},{"key":"691_CR38","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1038\/s41586-023-05732-2","volume":"615","author":"S Feng","year":"2023","unstructured":"Feng, S. et al. Dense reinforcement learning for safety validation of autonomous vehicles. Nature 615, 620\u2013627 (2023).","journal-title":"Nature"},{"key":"691_CR39","unstructured":"Angermueller, C. et al. Model-based reinforcement learning for biological sequence design. In International Conference on Learning Representations (eds A. Rush), April 1\u201323 (ICLR, 2020)."},{"key":"691_CR40","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1126\/science.adf6591","volume":"380","author":"ID Isaac","year":"2023","unstructured":"Isaac, I. D. et al. Top-down design of protein architectures with reinforcement learning. Science 380, 266\u2013273 (2023).","journal-title":"Science"},{"key":"691_CR41","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1038\/nature04542","volume":"440","author":"T Nakatsu","year":"2006","unstructured":"Nakatsu, T. et al. Structural basis for the spectral difference in luciferase bioluminescence. Nature 440, 372\u2013376 (2006).","journal-title":"Nature"},{"key":"691_CR42","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1038\/nature17995","volume":"533","author":"KS Sarkisyan","year":"2016","unstructured":"Sarkisyan, K. S. et al. Local fitness landscape of the green fluorescent protein. Nature 533, 397\u2013401 (2016).","journal-title":"Nature"},{"key":"691_CR43","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1261\/rna.040709.113","volume":"19","author":"D Melamed","year":"2013","unstructured":"Melamed, D., Young, D. L., Gamble, C. E., Miller, C. R. & Fields, S. Deep mutational scanning of an RRM domain of the Saccharomyces cerevisiae poly(A)-binding protein. RNA 19, 1537\u20131551 (2013).","journal-title":"RNA"},{"key":"691_CR44","first-page":"9786","volume":"162","author":"M Jain","year":"2022","unstructured":"Jain, M. et al. Biological sequence design with GFlowNets. Proc. Mach. Learning Res. 162, 9786\u20139801 (2022).","journal-title":"Proc. Mach. Learning Res."},{"key":"691_CR45","first-page":"9689","volume":"32","author":"R Rao","year":"2019","unstructured":"Rao, R. et al. Evaluating protein transfer learning with TAPE. Adv. Neural Inf. Process Syst. 32, 9689\u20139701 (2019).","journal-title":"Adv. Neural Inf. Process Syst."},{"key":"691_CR46","unstructured":"Haarnoja, T., Zhou, A., Abbeel, P. & Levine, S. Soft Actor-Critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor. Proc. Mach. Learning Res. 80, 1861\u20131870 (2018)."},{"key":"691_CR47","unstructured":"Shanehsazzadeh, A., Belanger, D. & Dohan, D. Is transfer learning necessary for protein landscape prediction? Preprint at https:\/\/arxiv.org\/abs\/2011.03443 (2020)."},{"key":"691_CR48","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1038\/s41592-019-0598-1","volume":"16","author":"EC Alley","year":"2019","unstructured":"Alley, E. C., Khimulya, G., Biswas, S., AlQuraishi, M. & Church, G. M. Unified rational protein engineering with sequence-based deep representation learning. Nat. Methods 16, 1315\u20131322 (2019).","journal-title":"Nat. Methods"},{"key":"691_CR49","doi-asserted-by":"publisher","unstructured":"Illig, A.-M., Siedhoff, N. E., Schwaneberg, U. & Davari, M. D. A hybrid model combining evolutionary probability and machine learning leverages data-driven protein engineering. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2022.06.07.495081 (2022).","DOI":"10.1101\/2022.06.07.495081"},{"key":"691_CR50","doi-asserted-by":"crossref","unstructured":"Meier, J. et al. Language models enable zero-shot prediction of the effects of mutations on protein function. In Advances in Neural Information Processing Systems 34 (eds M. Ranzato), 29287\u201329303 (NeurIPS, 2021).","DOI":"10.1101\/2021.07.09.450648"},{"key":"691_CR51","doi-asserted-by":"publisher","first-page":"1453","DOI":"10.1016\/j.str.2003.10.002","volume":"11","author":"R Linding","year":"2003","unstructured":"Linding, R. et al. Protein disorder prediction: implications for structural proteomics. Structure 11, 1453\u20131459 (2003).","journal-title":"Structure"},{"key":"691_CR52","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1038\/s41586-021-03819-2","volume":"596","author":"J Jumper","year":"2021","unstructured":"Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583\u2013589 (2021).","journal-title":"Nature"},{"key":"691_CR53","doi-asserted-by":"publisher","unstructured":"Evans, R. et al. Protein complex prediction with AlphaFold-Multimer. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2021.10.04.463034 (2022).","DOI":"10.1101\/2021.10.04.463034"},{"key":"691_CR54","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1038\/s41467-021-27838-9","volume":"13","author":"T Tsaban","year":"2022","unstructured":"Tsaban, T. et al. Harnessing protein folding neural networks for peptide\u2013protein docking. Nat. Commun. 13, 176 (2022).","journal-title":"Nat. Commun."},{"key":"691_CR55","doi-asserted-by":"publisher","unstructured":"Jendrusch, M., Korbel, J. O. & Sadiq, S. K. AlphaDesign: a de novo protein design framework based on AlphaFold. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2021.10.11.463937 (2021).","DOI":"10.1101\/2021.10.11.463937"},{"key":"691_CR56","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1126\/science.add1964","volume":"378","author":"B Wicky","year":"2022","unstructured":"Wicky, B. et al. Hallucinating symmetric protein assemblies. Science 378, 56\u201361 (2022).","journal-title":"Science"},{"key":"691_CR57","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1126\/science.add2187","volume":"378","author":"J Dauparas","year":"2022","unstructured":"Dauparas, J. et al. Robust deep learning-based protein sequence design using ProteinMPNN. Science 378, 49\u201356 (2022).","journal-title":"Science"},{"key":"691_CR58","doi-asserted-by":"publisher","first-page":"2625","DOI":"10.1038\/s41467-023-38328-5","volume":"14","author":"NR Bennett","year":"2023","unstructured":"Bennett, N. R. et al. Improving de novo protein binder design with deep learning. Nat. Commun. 14, 2625\u20132633 (2023).","journal-title":"Nat. Commun."},{"key":"691_CR59","doi-asserted-by":"publisher","unstructured":"Bryant, P. & Elofsson, A. EvoBind: in silico directed evolution of peptide binders with AlphaFold. Preprint at bioRxiv https:\/\/doi.org\/10.1101\/2022.07.23.501214 (2022).","DOI":"10.1101\/2022.07.23.501214"},{"key":"691_CR60","doi-asserted-by":"crossref","unstructured":"Mirdita, M. et al. ColabFold: making protein folding accessible to all. Nat. Methods 19, 679\u2013682 (2022).","DOI":"10.1038\/s41592-022-01488-1"},{"key":"691_CR61","doi-asserted-by":"publisher","first-page":"2272","DOI":"10.1093\/bioinformatics\/btz921","volume":"36","author":"A Tareen","year":"2020","unstructured":"Tareen, A. & Kinney, J. B. Logomaker: beautiful sequence logos in Python. Bioinformatics 36, 2272\u20132274 (2020).","journal-title":"Bioinformatics"},{"key":"691_CR62","doi-asserted-by":"crossref","unstructured":"Miller, B. R. III et al. MMPBSA.py: an efficient program for end-state free energy calculations. J. Chem. Theory Comput. 8, 3314\u20133321 (2012).","DOI":"10.1021\/ct300418h"},{"key":"691_CR63","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1093\/bioinformatics\/bty862","volume":"35","author":"TA Hopf","year":"2019","unstructured":"Hopf, T. A. et al. The EVcouplings Python framework for coevolutionary sequence analysis. Bioinformatics 35, 1582\u20131584 (2019).","journal-title":"Bioinformatics"},{"key":"691_CR64","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/j.bbrc.2009.09.006","volume":"389","author":"JP Welsh","year":"2009","unstructured":"Welsh, J. P., Patel, K. G., Manthiram, K. & Swartz, J. R. Multiply mutated Gaussia luciferases provide prolonged and intense bioluminescence. Biochem. Biophys. Res. Commun. 389, 563\u2013568 (2009).","journal-title":"Biochem. Biophys. Res. Commun."},{"key":"691_CR65","doi-asserted-by":"publisher","first-page":"8732","DOI":"10.1021\/ac2021882","volume":"83","author":"SB Kim","year":"2011","unstructured":"Kim, S. B., Suzuki, H., Sato, M. & Tao, H. Superluminescent variants of marine luciferases for bioassays. Anal. Chem. 83, 8732\u20138740 (2011).","journal-title":"Anal. Chem."},{"key":"691_CR66","doi-asserted-by":"publisher","first-page":"2105","DOI":"10.1093\/bioinformatics\/btz863","volume":"36","author":"C Zhang","year":"2020","unstructured":"Zhang, C., Zheng, W., Mortuza, S., Li, Y. & Zhang, Y. DeepMSA: constructing deep multiple sequence alignment to improve contact prediction and fold-recognition for distant-homology proteins. Bioinformatics 36, 2105\u20132112 (2020).","journal-title":"Bioinformatics"},{"key":"691_CR67","doi-asserted-by":"publisher","first-page":"20069","DOI":"10.1038\/s41598-020-76486-4","volume":"10","author":"N Wu","year":"2020","unstructured":"Wu, N. et al. Solution structure of Gaussia luciferase with five disulfide bonds and identification of a putative coelenterazine binding cavity by heteronuclear NMR. Sci. Rep. 10, 20069 (2020).","journal-title":"Sci. Rep."},{"key":"691_CR68","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1038\/s41586-022-04599-z","volume":"604","author":"H Lu","year":"2022","unstructured":"Lu, H. et al. Machine learning-aided engineering of hydrolases for PET depolymerization. Nature 604, 662\u2013667 (2022).","journal-title":"Nature"},{"key":"691_CR69","doi-asserted-by":"publisher","first-page":"e2017228118","DOI":"10.1073\/pnas.2017228118","volume":"118","author":"C Norn","year":"2021","unstructured":"Norn, C. et al. Protein sequence design by conformational landscape optimization. Proc. Natl Acad. Sci. USA 118, e2017228118 (2021).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"691_CR70","first-page":"8946","volume":"162","author":"C Hsu","year":"2022","unstructured":"Hsu, C. et al. Learning inverse folding from millions of predicted structures. Proc. Mach. Learning Res. 162, 8946\u20138970 (2022).","journal-title":"Proc. Mach. Learning Res."},{"key":"691_CR71","doi-asserted-by":"publisher","first-page":"3788","DOI":"10.1038\/s41467-022-31457-3","volume":"13","author":"EK Makowski","year":"2022","unstructured":"Makowski, E. K. et al. Co-optimization of therapeutic antibody affinity and specificity using machine learning models that generalize to novel mutational space. Nat. Commun. 13, 3788 (2022).","journal-title":"Nat. Commun."},{"key":"691_CR72","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1039\/C8CS00981C","volume":"49","author":"U Markel","year":"2020","unstructured":"Markel, U. et al. Advances in ultrahigh-throughput screening for directed enzyme evolution. Chem. Soc. Rev. 49, 233\u2013262 (2020).","journal-title":"Chem. Soc. Rev."},{"key":"691_CR73","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1038\/s41587-020-0466-7","volume":"38","author":"A G\u00e9rard","year":"2020","unstructured":"G\u00e9rard, A. et al. High-throughput single-cell activity-based screening and sequencing of antibodies using droplet microfluidics. Nat. Biotechnol. 38, 715\u2013721 (2020).","journal-title":"Nat. Biotechnol."},{"key":"691_CR74","first-page":"1421","volume":"113","author":"M D\u00f6rr","year":"2016","unstructured":"D\u00f6rr, M. et al. Fully automatized high\u2010throughput enzyme library screening using a robotic platform. Appl. Biochem. Biotechnol. 113, 1421\u20131432 (2016).","journal-title":"Appl. Biochem. Biotechnol."},{"key":"691_CR75","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1021\/acssynbio.1c00592","volume":"11","author":"BJ Wittmann","year":"2022","unstructured":"Wittmann, B. J. et al. evSeq: cost-effective amplicon sequencing of every variant in a protein library. ACS Synth. Biol. 11, 1313\u20131324 (2022).","journal-title":"ACS Synth. Biol."},{"key":"691_CR76","unstructured":"Ingraham, J., Garg, V., Barzilay, R. & Jaakkola, T. Generative models for graph-based protein design. In Advances in Neural Information Processing Systems 32 (eds H. Wallach et al.) 15820\u201315831 (NeurIPS, 2019)."},{"key":"691_CR77","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1126\/science.abn2100","volume":"377","author":"J Wang","year":"2022","unstructured":"Wang, J. et al. Scaffolding protein functional sites using deep learning. Science 377, 387\u2013394 (2022).","journal-title":"Science"},{"key":"691_CR78","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1038\/s43586-021-00044-z","volume":"1","author":"EL Bell","year":"2021","unstructured":"Bell, E. L. et al. Biocatalysis. Nat. Rev. Methods Primers 1, 45 (2021).","journal-title":"Nat. Rev. Methods Primers"},{"key":"691_CR79","doi-asserted-by":"publisher","unstructured":"Hie, B. L. et al. Efficient evolution of human antibodies from general protein language models and sequence information alone. Nat. Biotechnol. https:\/\/doi.org\/10.1038\/s41587-023-01763-2 (2023).","DOI":"10.1038\/s41587-023-01763-2"},{"key":"691_CR80","unstructured":"The PyMOL Molecular Graphics System v.1.2 r3pre (Schr\u00f6dinger, 2011)."},{"key":"691_CR81","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1093\/bioinformatics\/btz740","volume":"36","author":"X Huang","year":"2020","unstructured":"Huang, X., Pearce, R. & Zhang, Y. EvoEF2: accurate and fast energy function for computational protein design. Bioinformatics 36, 1135\u20131142 (2020).","journal-title":"Bioinformatics"},{"key":"691_CR82","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1186\/s12859-019-3019-7","volume":"20","author":"M Steinegger","year":"2019","unstructured":"Steinegger, M. et al. HH-suite3 for fast remote homology detection and deep protein annotation. BMC Bioinform. 20, 473 (2019).","journal-title":"BMC Bioinform."},{"key":"691_CR83","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1126\/science.1257360","volume":"347","author":"AI Podgornaia","year":"2015","unstructured":"Podgornaia, A. I. & Laub, M. T. Pervasive degeneracy and epistasis in a protein\u2013protein interface. Science 347, 673\u2013677 (2015).","journal-title":"Science"},{"key":"691_CR84","unstructured":"Bergstra, J., Yamins, D. & Cox, D. Making a science of model search: hyperparameter optimization in hundreds of dimensions for vision architectures. Proc. Mach. Learning Res. 28, 115\u2013123 (2013)."},{"key":"691_CR85","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1038\/nbt.3769","volume":"35","author":"TA Hopf","year":"2017","unstructured":"Hopf, T. A. et al. Mutation effects predicted from sequence co-variation. Nat. Biotechnol. 35, 128\u2013135 (2017).","journal-title":"Nat. Biotechnol."},{"key":"691_CR86","doi-asserted-by":"publisher","first-page":"1188","DOI":"10.1101\/gr.849004","volume":"14","author":"GE Crooks","year":"2004","unstructured":"Crooks, G. E., Hon, G., Chandonia, J.-M. & Brenner, S. E. WebLogo: a sequence logo generator. Genome Res. 14, 1188\u20131190 (2004).","journal-title":"Genome Res."},{"key":"691_CR87","doi-asserted-by":"publisher","first-page":"6097","DOI":"10.1093\/nar\/18.20.6097","volume":"18","author":"TD Schneider","year":"1990","unstructured":"Schneider, T. D. & Stephens, R. M. Sequence logos: a new way to display consensus sequences. Nucleic Acids Res. 18, 6097\u20136100 (1990).","journal-title":"Nucleic Acids Res."},{"key":"691_CR88","doi-asserted-by":"publisher","first-page":"2785","DOI":"10.1002\/jcc.21256","volume":"30","author":"G Morris","year":"2009","unstructured":"Morris, G. et al. AutoDock4 and AutoDockTools4: automated docking with selective receptor flexibility. J. Comput. Chem. 30, 2785\u20132791 (2009).","journal-title":"J. Comput. Chem."},{"key":"691_CR89","doi-asserted-by":"publisher","first-page":"1701","DOI":"10.1002\/jcc.20291","volume":"26","author":"D Van Der Spoel","year":"2005","unstructured":"Van Der Spoel, D. et al. GROMACS: fast, flexible, and free. J. Comput. Chem. 26, 1701\u20131718 (2005).","journal-title":"J. Comput. Chem."},{"key":"691_CR90","doi-asserted-by":"publisher","first-page":"1950","DOI":"10.1002\/prot.22711","volume":"78","author":"K Lindorff\u2010Larsen","year":"2010","unstructured":"Lindorff\u2010Larsen, K. et al. Improved side\u2010chain torsion potentials for the Amber ff99SB protein force field. Proteins 78, 1950\u20131958 (2010).","journal-title":"Proteins"},{"key":"691_CR91","unstructured":"Lu, T. Sobtop v.1.0 (dev3.1) http:\/\/sobereva.com\/soft\/Sobtop (2022)."},{"key":"691_CR92","doi-asserted-by":"publisher","first-page":"e1606","DOI":"10.1002\/wcms.1606","volume":"12","author":"F Neese","year":"2022","unstructured":"Neese, F. Software update: the ORCA program system\u2014Version 5.0. Wiley Interdiscip. Rev. Comput. Mol. Sci. 12, e1606 (2022).","journal-title":"Wiley Interdiscip. Rev. Comput. Mol. Sci."},{"key":"691_CR93","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1063\/1.445869","volume":"79","author":"WL Jorgensen","year":"1983","unstructured":"Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. & Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, 926\u2013935 (1983).","journal-title":"J. Chem. Phys."},{"key":"691_CR94","doi-asserted-by":"publisher","first-page":"10089","DOI":"10.1063\/1.464397","volume":"98","author":"T Darden","year":"1993","unstructured":"Darden, T., York, D. & Pedersen, L. Particle mesh Ewald: an N\u00b7log(N) method for Ewald sums in large systems. J. Chem. Phys. 98, 10089\u201310092 (1993).","journal-title":"J. Chem. Phys."},{"key":"691_CR95","doi-asserted-by":"publisher","first-page":"014101","DOI":"10.1063\/1.2408420","volume":"126","author":"G Bussi","year":"2007","unstructured":"Bussi, G., Donadio, D. & Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 126, 014101 (2007).","journal-title":"J. Chem. Phys."},{"key":"691_CR96","doi-asserted-by":"publisher","first-page":"7182","DOI":"10.1063\/1.328693","volume":"52","author":"M Parrinello","year":"1981","unstructured":"Parrinello, M. & Rahman, A. Polymorphic transitions in single crystals: a new molecular dynamics method. J. Appl. Phys. 52, 7182\u20137190 (1981).","journal-title":"J. Appl. Phys."},{"key":"691_CR97","doi-asserted-by":"publisher","unstructured":"Huang, L. GFP & PAB1 training data of EvoPlay Figshare https:\/\/doi.org\/10.6084\/m9.figshare.23498195 (2023).","DOI":"10.6084\/m9.figshare.23498195"},{"key":"691_CR98","doi-asserted-by":"publisher","unstructured":"Huang, L GB1 & PhoQ data of EvoPlay Figshare https:\/\/doi.org\/10.6084\/m9.figshare.21767369.v3 (2023).","DOI":"10.6084\/m9.figshare.21767369.v3"},{"key":"691_CR99","doi-asserted-by":"publisher","unstructured":"Huang, L. Peptide and receptor sequences of the wild type for 1ssc, 2cnz, 3r7g and 6seo Figshare https:\/\/doi.org\/10.6084\/m9.figshare.23375666.v1 (2023).","DOI":"10.6084\/m9.figshare.23375666.v1"},{"key":"691_CR100","doi-asserted-by":"publisher","unstructured":"Huang, L. EvoPlay Figs. 2\u20135 Source Data Figshare https:\/\/doi.org\/10.6084\/m9.figshare.23437295.v1 (2023).","DOI":"10.6084\/m9.figshare.23437295.v1"},{"key":"691_CR101","doi-asserted-by":"publisher","unstructured":"melobio. (2023). melobio\/EvoPlay: v1.0.0 (v1.0.0) Zenodo https:\/\/doi.org\/10.5281\/zenodo.8059425 (2023).","DOI":"10.5281\/zenodo.8059425"},{"key":"691_CR102","doi-asserted-by":"publisher","unstructured":"Meng, Y. Self-play reinforcement learning guides protein engineering Code Ocean https:\/\/doi.org\/10.24433\/CO.1846781.v2 (2023).","DOI":"10.24433\/CO.1846781.v2"}],"updated-by":[{"DOI":"10.1038\/s42256-023-00713-6","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T00:00:00Z","timestamp":1691452800000}}],"container-title":["Nature Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00691-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00691-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00691-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T15:10:30Z","timestamp":1692630630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s42256-023-00691-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,20]]},"references-count":102,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["691"],"URL":"https:\/\/doi.org\/10.1038\/s42256-023-00691-9","relation":{"correction":[{"id-type":"doi","id":"10.1038\/s42256-023-00713-6","asserted-by":"object"}]},"ISSN":["2522-5839"],"issn-type":[{"value":"2522-5839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,20]]},"assertion":[{"value":"30 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 August 2023","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1038\/s42256-023-00713-6","URL":"https:\/\/doi.org\/10.1038\/s42256-023-00713-6","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 newly designed and validated GLuc mutants are undergoing patent filing (PCT\/CN2023\/087445). F.M. declares stock holdings in MGI. The remaining authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}