Molecular Docking via Weighted Subgraph Isomorphism on Quantum Annealers

TL;DR

The paper addresses molecular docking by reframing shape complementarity as a weighted subgraph isomorphism problem, enabling a purely QUBO-based formulation suitable for quantum annealing. Ligand geometry is encoded as a weighted graph and a protein pocket as a weighted space-grid, with an injective mapping objective that preserves edge weights, expressed as $\mathcal{H}_{qubo} = A H_{iso} + H_{opt}$ using hard constraints $H_{iso}$ and a geometry-compatibility term $H_{opt}$. The authors analyze problem size, hardware embedding on D-Wave devices, and compare quantum annealers (2000Q and Advantage) to simulated annealing, finding that QPUs can sample poses with lower ABD/RMSD but often produce fewer valid solutions and that SA yields superior Time To Solution in many scenarios. Overall, the work demonstrates the feasibility of geometry-preserving docking on quantum hardware, provides detailed embedding and parameter-tuning guidance, and highlights the trade-offs between quantum-sampled pose quality and solution throughput.

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 QUBO 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. Results and performance obtained with quantum annealers are compared with classical simulated annealing solvers.

Figures (14)

• Figure 1: Complete workflow: the approach addresses the SC search via QA which outputs a sample of valid configurations. The pose filter, in the BA evaluation, selects the most promising poses based on chemical score.
• Figure 2: Plot of the functions $A(t)$ (blue line) and $B(t)$ (light blue line) defining the annealing schedule.
• Figure 3: From the molecular pocket we select the pocket points that are used to construct the 3D space grid inside the pocket.
• Figure 4: Three different pre-processing approximations: No fragment simplification, Center of mass simplification, and Internal Fragments removal
• Figure 5: Example of graph construction. On the left, the original molecule obtained after preprocessing, rotatable bonds are identified with arrows. On the right, the graph structure obtained: $e^{bond}_{i,j}$, $e^{angle}_{i,j}$ and $e^{dih}_{i,j}$ are respectively depicted in black, blue and red in the figure.