{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:59:20Z","timestamp":1776841160428,"version":"3.51.2"},"reference-count":25,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,13]],"date-time":"2016-10-13T00:00:00Z","timestamp":1476316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002770","name":"Cabinet Office, Government of Japan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002770","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A structure-based lead optimization procedure is an essential step to finding appropriate ligand molecules binding to a target protein structure in order to identify drug candidates. This procedure takes a known structure of a protein-ligand complex as input, and structurally similar compounds with the query ligand are designed in consideration with all possible combinations of atomic species. This task is, however, computationally hard since such combinatorial optimization problems belong to the non-deterministic nonpolynomial-time hard (NP-hard) class. In this paper, we propose the structure-based lead generation and optimization procedures by a degenerate optical parametric oscillator (DOPO) network. Results of numerical simulation demonstrate that the DOPO network efficiently identifies a set of appropriate ligand molecules according to the Boltzmann sampling law.<\/jats:p>","DOI":"10.3390\/e18100365","type":"journal-article","created":{"date-parts":[[2016,10,13]],"date-time":"2016-10-13T10:33:10Z","timestamp":1476354790000},"page":"365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Boltzmann Sampling by Degenerate Optical Parametric Oscillator Network for Structure-Based Virtual Screening"],"prefix":"10.3390","volume":"18","author":[{"given":"Hiromasa","family":"Sakaguchi","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Information Systems, The University of Tokyo, Tokyo 113-8654, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9002-9621","authenticated-orcid":false,"given":"Koji","family":"Ogata","sequence":"additional","affiliation":[{"name":"RIKEN Innovation Center, Saitama 351-0198, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7075-7779","authenticated-orcid":false,"given":"Tetsu","family":"Isomura","sequence":"additional","affiliation":[{"name":"The KAITEKI Institute, Inc.,Tokyo 100-8251, Japan"}]},{"given":"Shoko","family":"Utsunomiya","sequence":"additional","affiliation":[{"name":"National Institute of Informatics, Tokyo 101-8403, Japan"}]},{"given":"Yoshihisa","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"ImPACT Program, The Japan Science and Technology Agency, Tokyo 102-0076, Japan"}]},{"given":"Kazuyuki","family":"Aihara","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Information Systems, The University of Tokyo, Tokyo 113-8654, Japan"},{"name":"Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/(SICI)1098-1128(199601)16:1<3::AID-MED1>3.0.CO;2-6","article-title":"The art and practice of structure-based drug design: A molecular modeling perspective","volume":"16","author":"Bohacek","year":"1996","journal-title":"Med. Res. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.chembiol.2003.09.002","article-title":"The process of structure-based drug design","volume":"10","author":"Anderson","year":"2003","journal-title":"Chem. Biol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5936\/csbj.201302011","article-title":"Current progress in structure-based rational drug design marks a new mindset in drug discovery","volume":"5","author":"Lounnas","year":"2013","journal-title":"Comput. Struct. Biotechnol. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1016\/j.bmcl.2005.11.046","article-title":"Identification of phosphodiesterase-1 and 5 dual inhibitors by a ligand-based virtual screening optimized for lead evolution","volume":"16","author":"Yamazaki","year":"2006","journal-title":"Bioorg. Med. Chem. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1991","DOI":"10.1016\/j.bmcl.2007.01.024","article-title":"Thiazolone-acylsulfonamides as novel HCV NS5B polymerase allosteric inhibitors: Convergence of structure-based drug design and X-ray crystallographic study","volume":"17","author":"Yan","year":"2007","journal-title":"Bioorg. Med. Chem. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.1021\/jm061440p","article-title":"Virtual screening for novel openers of pancreatic K(ATP) channels","volume":"50","author":"Carosati","year":"2007","journal-title":"J. Med. Chem."},{"key":"ref_7","first-page":"596","article-title":"A quantitative approach to the estimation of chemical space from a given geometry by the combination of atomic species","volume":"26","author":"Ogata","year":"2007","journal-title":"Mol. Inform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4382","DOI":"10.3390\/molecules15064382","article-title":"Lead generation and optimization based on protein-ligand complementarity","volume":"15","author":"Ogata","year":"2010","journal-title":"Molecules"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1038\/nature10012","article-title":"Quantum annealing with manufactured spins","volume":"473","author":"Johnson","year":"2011","journal-title":"Nature"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yamaoka, M., Yoshimura, C., Hayashi, M., Okuyama, T., Aoki, H., and Mizuno, H. (2015, January 22\u201326). 20k-spin Ising Chip for Combinational Optimization Problem with CMOS Annealing. Proceedings of the IEEE International Solid-State Circuits Conference, San Francisco, CA, USA.","DOI":"10.1109\/ISSCC.2015.7063111"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"18091","DOI":"10.1364\/OE.19.018091","article-title":"Mapping of Ising models onto injection-locked laser systems","volume":"19","author":"Utsunomiya","year":"2011","journal-title":"Opt. Express"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lucas, A. (2014). Ising formulations of many NP problems. Front. Phys., 2.","DOI":"10.3389\/fphy.2014.00005"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-014-0892-x","article-title":"A case study in programming a quantum annealer for hard operational planning problems","volume":"14","author":"Rieffel","year":"2014","journal-title":"Quantum Inf. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1038\/srep00571","article-title":"Finding low-energy conformations of lattice protein models by quantum annealing","volume":"2","author":"Dickson","year":"2012","journal-title":"Sci. Rep."},{"key":"ref_15","unstructured":"Denil, N., and Fretias, N. (2011, January 16). Toward the Implementation of a Quantum RBM. Proceedings of the NIPS 2011 Deep Learning and Unsupervised Feature Learning Workshop, Cranada, Spain."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dumoulin, V., Goodfellow, I.J., Courville, A., and Bengio, Y. (2014, January 27\u201331). On the Challenges of Physical Implementations of RBMs. Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, Qu\u00e9bec, QC, Canada.","DOI":"10.1609\/aaai.v28i1.8924"},{"key":"ref_17","unstructured":"Adachi, S.H., and Henderson, M.P. (2015). Application of Quantum Annealing to Training of Deep Neural Networks."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"063853","DOI":"10.1103\/PhysRevA.88.063853","article-title":"Coherent Ising machine based on degenerate optical parametric oscillators","volume":"88","author":"Wang","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1038\/nphoton.2014.249","article-title":"Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine","volume":"8","author":"Marandi","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1038\/nphoton.2016.68","article-title":"Large-scale Ising spin network based on degenerate optical parametric oscillators","volume":"10","author":"Inagaki","year":"2016","journal-title":"Nat. Photonics"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Haribara, Y., Utsunomiya, S., and Yamamoto, Y. (2016). Computational principle and performance evaluation of coherent Ising machine based on degenerate optical parametric oscillator network. Entropy, 18.","DOI":"10.3390\/e18040151"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"043821","DOI":"10.1103\/PhysRevA.92.043821","article-title":"Quantum correlation in degenerate optical parametric oscillators with mutual injections","volume":"92","author":"Takata","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"083010","DOI":"10.1088\/0031-8949\/91\/8\/083010","article-title":"Truncated Wigner theory of coherent Ising machines based on degenerate optical parametric oscillator","volume":"91","author":"Maruo","year":"2016","journal-title":"Phys. Scr."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1017\/S0305004100030401","article-title":"A generalized inverse for matrices","volume":"51","author":"Penrose","year":"1955","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Moln\u00e1r, B., and Ercsey-Ravasz, M. (2013). Asymmetric Continuous-Time Neural Networks without Local Traps for Solving Constraint Satisfaction Problems. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0073400"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/365\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:32:55Z","timestamp":1760211175000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,13]]},"references-count":25,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["e18100365"],"URL":"https:\/\/doi.org\/10.3390\/e18100365","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,13]]}}}