A Co-Design Approach to Physically-Informed Molecular Docking for Quantum Annealers
Francesco Micucci, Matteo Barbieri, Gabriella Bettonte, Domenico Bonanni, Anita Camillini, Anna Fava, Daniele Gregori, Andrea R. Beccari, Gianluca Palermo
Molecular docking is a crucial step in computer- aided drug design, involving the identification of ligand poses that are physically plausible within a protein pocket. Recent studies have shown that this problem can be formulated as a geometric weighted subgraph isomorphism, which can then be encoded as a QUBO and thus solved on D-Wave quantum annealers. In this work, we adopt a co-design approach, addressing molecular docking at the formulation and encoding levels, and examining how hardware topology affects solution quality on current quantum annealers. We propose new QUBO formulations that extend the state-of-the-art ones by including van der Waals, Coulomb, hydrogen bonding, and hydrophobic interactions. Experimental results show that incorporating physicochemical terms improves the average docking quality by more than 18% compared to the purely geometric baseline on D-Wave quantum annealers with the Pegasus topology, and by up to 29% on those with the Zephyr topology. The choice of topology, along with an improved encoding design, yields significant gains in embedding efficiency and the number of valid solutions. Our designs reduce the number of physical qubits required by up to 14.5% and decrease the chain break fraction by an order of magnitude, thereby enhancing confidence in the resulting solutions.
Molecular docking is a crucial step in computer- aided drug design, involving the identification of ligand poses that are physically plausible within a protein pocket. Recent studies have shown that this problem can be formulated as a geometric weighted subgraph isomorphism, which can then be encoded as a QUBO and thus solved on D-Wave quantum annealers. In this work, we adopt a co-design approach, addressing molecular docking at the formulation and encoding levels, and examining how hardware topology affects solution quality on current quantum annealers. We propose new QUBO formulations that extend the state-of-the-art ones by including van der Waals, Coulomb, hydrogen bonding, and hydrophobic interactions. Experimental results show that incorporating physicochemical terms improves the average docking quality by more than 18% compared to the purely geometric baseline on D-Wave quantum annealers with the Pegasus topology, and by up to 29% on those with the Zephyr topology. The choice of topology, along with an improved encoding design, yields significant gains in embedding efficiency and the number of valid solutions. Our designs reduce the number of physical qubits required by up to 14.5% and decrease the chain break fraction by an order of magnitude, thereby enhancing confidence in the resulting solutions.
Abstract Molecular docking is an essential step in the drug discovery process involving the detection of three-dimensional poses of a ligand inside the active site of the protein. In this paper, we address the Molecular Docking search phase by formulating the problem in quadratic unconstrained binary optimization terms, suitable for an annealing approach. We propose a problem formulation as a weighted subgraph isomorphism between the ligand graph and the grid of the target protein pocket. In particular, we applied a graph representation to the ligand embedding all the geometrical properties of the molecule including its flexibility, and we created a weighted spatial grid to the 3D space region inside the pocket. The proposed quantum annealing-based method for molecular docking achieves valid ligand placements. Compared to simulated annealing, quantum solvers sampled fewer but higher-quality solutions with lower root-mean-square deviation, demonstrating competitive performance within hardware limits.
With the continuous growth of quantum hardware and its increasing accessibility, there is a shift away from theoretical research towards real-world problems. One of the most promising applications of quantum computing is drug discovery, which is a complex and multi-disciplinary process. To increase the success probability of finding new drugs, we can introduce an in-silico step to virtual screen the drug candidates. In this paper, we address the molecular docking problem of virtual screening. In particular, we analyze the performance of a molecular docking application, which is modeled as a Quadratic Unconstrained Binary Optimization (QUBO) instance. We leveraged the computational power offered by different quantum computing models, gate-based and quantum annealing, to speed the solution of the QUBO formulation. Experimental results show how quantum annealer is still the best in class for our case study. Moreover, we report here the experience and the takeaways we obtained by executing quantum molecular docking on publicly accessible quantum hardware and software.
Molecular docking is a crucial phase in drug discovery, involving the precise determination of the optimal spatial arrangement between two molecules when they bind. The such analysis, the 3D structure of molecules is a fundamental consideration, involving the manipulation of molecular representations based on their degrees of freedom, including rigid roto-translation and fragment rotations along rotatable bonds, to determine the preferred spatial arrangement when molecules bind to each other. In this paper, quantum annealing based solution to solve Molecular unfolding (MU) problem, a specific phase within molecular docking, is explored and compared with a state-of-the-art classical algorithm named "GeoDock". Molecular unfolding focuses on expanding a molecule to an unfolded state to simplify manipulation within the target cavity and optimize its configuration, typically by maximizing molecular area or internal atom distances. Molecular unfolding problem aims to find the torsional configuration that increases the inter-atomic distance within a molecule, which also increases the molecular area. Quantum annealing approach first encodes the problem into a Higher-order Unconstrained Binary Optimization (HUBO) equation which is pruned to an arbitrary percentage to improve the time efficiency and to be able to solve the equation using any quantum annealer. The resultant HUBO is then converted to a Quadratic Unconstrained Binary Optimization equation (QUBO), which is easily embedded on a D-wave annealing Quantum processor.
Molecular docking, which aims to find the most stable interacting configuration of a set of molecules, is of critical importance to drug discovery. Although a considerable number of classical algorithms have been developed to carry out molecular docking, most focus on the limiting case of docking two molecules. Since the number of possible configurations of N molecules is exponential in N, those exceptions which permit docking of more than two molecules scale poorly, requiring exponential resources to find high-quality solutions. Here, we introduce a one-hot encoded quadratic unconstrained binary optimization formulation (QUBO) of the multibody molecular docking problem, which is suitable for solution by quantum annealer. Our approach involves a classical pre-computation of pairwise interactions, which scales only quadratically in the number of bodies while permitting well-vetted scoring functions like the Rosetta REF2015 energy function to be used. In a second step, we use the quantum annealer to sample low-energy docked configurations efficiently, considering all possible docked configurations simultaneously through quantum superposition. We show that we are able to minimize the time needed to find diverse low-energy docked configurations by tuning the strength of the penalty used to enforce the one-hot encoding, demonstrating a 3-4 fold improvement in solution quality and diversity over performance achieved with conventional penalty strengths. By mapping the configurational search to a form compatible with current- and future-generation quantum annealers, this work provides an alternative means of solving multibody docking problems that may prove to have performance advantages for large problems, potentially circumventing the exponential scaling of classical approaches and permitting a much more efficient solution to a problem central to drug discovery and validation pipelines.
Molecular docking (MD) is a crucial task in drug design, which predicts the position, orientation, and conformation of the ligand when it is bound to a target protein. It can be interpreted as a combinatorial optimization problem, where quantum annealing (QA) has shown a promising advantage for solving combinatorial optimization. In this work, we propose a novel quantum molecular docking (QMD) approach based on a QA-inspired algorithm. We construct two binary encoding methods to efficiently discretize the degrees of freedom with an exponentially reduced number of bits and propose a smoothing filter to rescale the rugged objective function. We propose a new quantum-inspired algorithm, hopscotch simulated bifurcation (hSB), showing great advantages in optimizing over extremely rugged energy landscapes. This hSB can be applied to any formulation of an objective function under binary variables. An adaptive local continuous search is also introduced for further optimization of the discretized solution from hSB. Concerning the stability of docking, we propose a perturbation detection method to help rank the candidate poses. We demonstrate our approach on a typical data set. QMD has shown advantages over the search-based Autodock Vina and the deep-learning DIFFDOCK in both redocking and self-docking scenarios. These results indicate that quantum-inspired algorithms can be applied to solve practical problems in drug discovery even before quantum hardware become mature.
Molecular docking is a vital computational task in drug discovery, wherein the objective is to efficiently identify optimal binding poses between a ligand and a target receptor protein. Due to the combinatorial explosion of possible binding configurations, docking of large and flexible molecules remains a computationally intensive problem, especially at scale. Early studies have revealed that the molecular docking can be re-cast as a maximum vertex-weighted clique problem (MVWCP) problem on a compatibility graph to be solved classically. In this work, we proposed a hybrid quantum-classical approach for molecular docking leveraging the MVWCP formalism with a variational full-basis encoding (FBE) strategy, which enables efficient encoding of classical binary variables with Bloch sphere vectors. We further prove that a global minimizer of the FBE objective can always be chosen to be a pure product state, thereby providing a rigorous justification for its optimization using a unitary variational circuit. The molecular docking problem is first mapped to a cost Hamiltonian that is minimized within a variational framework, optimized via a randomized imaginary time evolution (ITE)-inspired warm start, and gradient-based techniques. Finally, we also executed the circuit on an IBM quantum computer, underlying the feasibility and of quantum-assisted optimization for structure-based drug design and point towards the broader utility of advanced encoding techniques in quantum optimization for computational biology.