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This methodology aims to estimate the binding mode and binding free energy between the drug-targeted protein and candidate chemical compounds, utilizing protein tertiary structure information. Reformulation of this docking as a quadratic unconstrained binary optimization (QUBO) problem to obtain solutions via quantum annealing has been attempted. However, previous studies did not consider the internal degrees of freedom of the compound that is mandatory and essential. In this study, we formulated fragment-based protein\u2013ligand flexible docking, considering the internal degrees of freedom of the compound by focusing on fragments (rigid chemical substructures of compounds) as a QUBO problem. We introduced four factors essential for fragment\u2013based docking in the Hamiltonian: (1) interaction energy between the target protein and each fragment, (2) clashes between fragments, (3) covalent bonds between fragments, and (4) the constraint that each fragment of the compound is selected for a single placement. We also implemented a proof-of-concept system and conducted redocking for the protein\u2013compound complex structure of Aldose reductase (a drug target protein) using SQBM+, which is a simulated quantum annealer. The predicted binding pose reconstructed from the best solution was near-native (RMSD = 1.26 \u00c5), which can be further improved (RMSD = 0.27 \u00c5) using conventional energy minimization. The results indicate the validity of our QUBO problem formulation.<\/jats:p>","DOI":"10.3390\/e26050397","type":"journal-article","created":{"date-parts":[[2024,5,3]],"date-time":"2024-05-03T08:02:22Z","timestamp":1714723342000},"page":"397","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["QUBO Problem Formulation of Fragment-Based Protein\u2013Ligand Flexible Docking"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-0224-0035","authenticated-orcid":false,"given":"Keisuke","family":"Yanagisawa","sequence":"first","affiliation":[{"name":"Department of Computer Science, School of Computing, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan"},{"name":"Middle Molecule IT-Based Drug Discovery Laboratory (MIDL), Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-2103-6195","authenticated-orcid":false,"given":"Takuya","family":"Fujie","sequence":"additional","affiliation":[{"name":"Ahead Biocomputing, Co., Ltd., Kawasaki-shi 210-0007, Kanagawa, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-1138-2599","authenticated-orcid":false,"given":"Kazuki","family":"Takabatake","sequence":"additional","affiliation":[{"name":"Toshiba Digital Solutions Corporation, Kawasaki-shi 212-8585, Kanagawa, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-2863-8703","authenticated-orcid":false,"given":"Yutaka","family":"Akiyama","sequence":"additional","affiliation":[{"name":"Ahead Biocomputing, Co., Ltd., Kawasaki-shi 210-0007, Kanagawa, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1006\/jmbi.1996.0897","article-title":"Development and validation of a genetic algorithm for flexible docking","volume":"267","author":"Jones","year":"1997","journal-title":"J. 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