Molecular docking with Gaussian Boson Sampling

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Science Advances  05 Jun 2020:
Vol. 6, no. 23, eaax1950
DOI: 10.1126/sciadv.aax1950
  • Fig. 1 Construction of the labeled distance graph for a ligand molecule.

    (A) Planar structure of the ligand molecule. Pharmacophore points of the molecule (B) are identified, and their pairwise distance is measured using the known three-dimensional (3D) structure (C). This information is combined in the labeled distance graph for the ligand molecule (D), where vertices represent the pharmacophore points and edge weights of their respective pairwise distance [the complete weight matrix is on the right of (D)].

  • Fig. 2 Construction of the binding interaction graph.

    (A) Inputs for the construction of the binding interaction graph—two labeled graphs (one for the ligand and one for the receptor) and corresponding contact potential that captures the interaction strength between different types of vertex labels. We denote vertices on the ligand and receptor with uppercase and lowercase letters, respectively. The binding interaction graph is constructed (B) by creating a vertex for each possible contact between ligand and the receptor weighted by the contact potential. Pairs of vertices that represent compatible contacts [see (C) for various scenarios] are connected by an edge. The resulting graph is then used to search for potential binding poses (D). These are represented as complete subgraphs—also called cliques—of the graph, as they form a set of pairwise compatible contacts. The heaviest vertex-weighted cliques represent the most likely binding poses (maximum vertex-weighted clique depicted in orange).

  • Fig. 3 Schematics of the protocol.

    Squeezed light is injected from the left into a GBS device, which is programmed to sample from a vertex-weighted graph. The presence (star) or absence of photons is measured by detectors on the right. GBS random search (A): On the basis of the ports where photons have been detected, we construct a subgraph (yellow vertices and dark edges) and check if it is a clique. If it is not a clique, greedy shrinking (B) iteratively removes a vertex (red node with a cross) until the remaining ones form a clique. Two shrinking iterations are shown in (B) from left to right. In local search (C), the found clique is expanded by iteratively adding, as long as possible, a neighboring vertex (red node with a tick) to get a bigger clique.

  • Fig. 4 Graph-based molecular docking of an aryl sulfonamide compound to TACE.

    (A) Two labeled distance graphs—one for the aryl sulfonamide compound and one for the TACE receptor—and the resulting TACE-AS binding interaction graph. Construction of the labeled distance graph and binding interaction graph are described in Figs. 1 and 2. Pharmacophore points on the ligand and receptor are labeled with uppercase and lowercase letters, respectively. The search for the maximum vertex-weighted clique within the TACE-AS graph is illustrated in (B). Each clique in the TACE-AS graph corresponds to a different superposition of the ligand molecule and the TACE receptor. The correct ligand-receptor superposition corresponding to the maximum weighted clique in the TACE-AS graph is shown on the right. (C) Crystallographic structure of the TACE-AS complex with optimal ligand-receptor interactions correctly predicted by the maximum weighted clique. We omit the metal cofactor in the enzyme active site for visual clarity, as it was not considered as a pharmacophore point under our procedure.

  • Fig. 5 GBS random search sampling rate.

    Number of cliques sampled from a GBS device as a function of the total clique weight ∑jCwj. The GBS output has been post-selected to 105 samples with total number of detector clicks N = 8. With the same number of samples (each with N = 8 nodes), classical random search only found three cliques (not shown), none of them with maximum weight.

  • Fig. 6 Greedy shrinking success rate.

    Success rate in finding cliques of different sizes (N = 2, …, Nmax), when the max clique has size Nmax = 8, as a function of the total clique weight ∑jCwj. We used greedy shrinking over 104 GBS samples, ignoring trivial zero-photon outcomes. Outcomes with low (<0.5%) success rate are not shown.

  • Fig. 7 GBS versus classical success rate.

    Success rate in finding the maximum weighted clique after greedy shrinking and k expansion steps with local search. Samples are generated from either GBS or a purely classical approach. GBS maintains a significantly higher success rate over all iteration steps.

Supplementary Materials

  • Supplementary Materials

    Molecular docking with Gaussian Boson Sampling

    Leonardo Banchi, Mark Fingerhuth, Tomas Babej, Christopher Ing, Juan Miguel Arrazola

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