Quadratic Unconstrained Binary Optimization (QUBO) Problem Formulation of Fragment-Based Protein–Compound Flexible Docking

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1. Quadratic Unconstrained Binary Optimization (QUBO) Problem Formulation of Fragment-Based Protein–Compound Flexible Docking 1. Dept CS, Sch. Comput., Science Tokyo 2. Middle Molecule IT-Based Drug Discovery Laboratory (MIDL), Science Tokyo 3. Ahead Biocomputing, Co., Ltd. 4. Toshiba Digital Solutions Corporation 化合物ドッキングのQUBO（二次制約なし二値最適化）問題表現 This work was partly supported by NEDO Development of Quantum-Classical Hybrid Use-Case Technologies in Cyber-Physical Space (JPNP23003), JSPS KAKENHI (23K24939, 23K28185), NTT Research Inc., and AMED BINDS (JP24ama121026j0003, JP24ama121029j0003). Acknowledgements [1] Ali, A. M., Mencia, E. arXiv, 2024. DOI: 2410.06429 [2] Takabatake, K., Yanagisawa, K., Akiyama, Y. Entropy 24: 354, 2022. [3] Yanagisawa, K. et al. ACS Omega 7: 30265-74, 2022. References Keisuke Yanagisawa1,2 ◦ Takuya Fujie3 Kazuki Takabatake4 Yutaka Akiyama3 Quantum annealing efficiently solves QUBO (quadratic unconstrained binary optimization) problem. We formulated protein–compound flexible docking as a QUBO problem and implemented with SQBM+, a simulated quantum annealer. The redocking experiment indicates the validity of our formulation. Abstract Yanagisawa, K. et al., Entropy 26: 397, 2024. doi: 10.3390/e26050397 O=c1[nH]nc(c2c1cccc2)C Cc1nc2c(s1)cccc2 OC=O FC(F)F interaction energy scores of fragments covalent bonds between fragments clashes between fragments 𝐻 = 𝐴 ෍ 𝑖 Δ𝐺𝑖 𝑥𝑖 + 𝐵 ෍ 𝑖,𝑗 𝑏𝑖𝑗 𝑥𝑖 𝑥𝑗 + 𝐶 ෍ 𝑖,𝑗 𝑐𝑖𝑗 𝑥𝑖 𝑥𝑗 + 𝐷 2 ෍ 𝑘 𝐹 ෍ 𝑓𝑖=𝑘 𝑥𝑖 − 1 2 the constraint each fragment has a single placement Δ𝐺 = −5.2 kcal/mol 𝑐𝑜𝑛𝑛 𝑖, 𝑗 = −1 𝑐𝑙𝑎𝑠ℎ 𝑖, 𝑗 = 1 or or … QUBO problem formulation Experimental target Result and Discussion RMSD = 0.27 Å Background PDB ID: 2HV5 Zopolrestat (Inhibitor) Decomposed fragments Fragment-based protein–compound docking: Docks a compound by placing its substructures (fragments) Bottleneck: combinatorial optimization to reconstruct compound Quantum annealer: Efficiently solves combinatorial optimization which is formulated as a QUBO problem N-queen problem [1] Polyomino puzzle [2] 𝐻 = 𝐴 2 ෍ 𝑚=1 𝑀 ෍ 𝑖∈𝑃𝑚 𝑥𝑖 − 1 2 + 𝐵 2 ෍ 𝑛=1 𝑁 ෍ 𝑖∈𝐿𝑛 𝑥𝑖 − 1 2 + 𝐶 2 ෍ 𝑖=1 𝑄 ෍ 𝑗=1 𝑄 𝑓 𝑖, 𝑗 𝑥𝑖 𝑥𝑗 + ⋯ ⋮ consistency graph of fragment placements reconstructed binding pose Find consistent placements set NP-hard combi. opt. Experimental target: Aldose reductase (ALDR) Binary variables 𝒙𝒊 : enumerated fragment placements Fragment docking placements 𝒙 ligand fragments Objective function 𝑯: checking consistency as a compound Implementation Fragment placement enumeration: REstretto [3] 3005 placements with various positions and scores 0 -7 0 -7 -5 -5 binding free energy score [kcal/mol] 3005 placements Result 1: The best local solution has the best RMSD toward the co-crystalized ligand binding pose RMSD = 1.26 Å Objective function value -94 -86 2 10 Ligand RMSD [Å] optimal output RMSD distribution of top 1 000 local solutions Green: Purple: Cyan: The best output of our method Co-crystallized ligand structure Protein structure (ALDR) Result 2: Energy minimization removes bond distortions bonds are added between placements energy minimization with rigid protein long bond length unnatural angle Quantum annealer: SQBM+ (Simulated QA) 7298 local solutions were obtained in 5 min energy score distribution of all placements Journal paper Poster good bad Weight coefficients in this experiment: (A, B, C, D) = (1, 5, 5, 25)