BetaDock: Shape-Priority Docking Method Based on Beta-Complex

Abstract

This paper presents an approach and a software, BetaDock, to the docking problem by putting the priority on shape complementarity between a receptor and a ligand. The approach is based on the theory of the β-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the β-complex corresponding to water molecule is computed. Then, the boundary of the β-complex defines the β-shape which has the complete proximity information among all atoms on the receptor boundary. From the β-shape, we first compute pockets where the ligand may bind. Then, we quickly place the ligand within each pocket by solving the singular value decomposition problem and the assignment problem. Using the conformations of the ligands within the pockets as the initial solutions, we run the genetic algorithm to find the optimal solution for the docking problem. The performance of the proposed algorithm was verified through a benchmark test and showed that BetaDock is superior to a popular docking software AutoDock 4.

BetaVoid: Molecular voids via beta-complexes and Voronoi diagrams

“…This approach, called the QTDB‐approach, is significant because the quasi‐triangulation and the Voronoi diagram are used not only for extracting voids but also for many other problems related to the geometry of molecules. Some applications are as follows: the computation of the Connolly surface, docking simulation, computation of molecular volume, computation of molecular sphericity, etc. We anticipate that many more shape‐related problems that are not known today will also be solved efficiently using the quasi‐triangulation of molecules.…”

Three-Dimensional Compound Comparison Methods and Their Application in Drug Discovery

“…BetaDock [33] uses another surface representation called the β-shape that is generated also from a Voronoi diagram. β-shape uses similar procedure as α-shape but their differences include that β-shape is able to robustly construct surface for a set of spheres of different radii, e.g.…”

“…The 3D Zernike function is defined as follows: $${\mathrm{normalZ}}_{\mathrm{nl}}^{\mathrm{normalm}}(\mathrm{r},\theta ,\phi )={\mathrm{normalR}}_{\mathrm{nl}}\left(\mathrm{r}\right){\mathrm{normalY}}_{\mathrm{normall}}^{\mathrm{normalm}}(\theta ,\phi )$$ where Y m l is the spherical harmonics and R nl (r) is the radial function. m and l are integers that have ranges −1 < m < 1 and 0 ≤ 1 ≤ n. After generating Connolly surface of a molecule [33], the surface is mapped on the 3D grid and voxelized, which is considered as the 3D function f(x) to be expanded. Then, 3D Zernike moments of surface shape, f(x) , are computed as Equation 2.3.4.…”

Tunnels and Voids in Molecules via Voronoi Diagram

“…For example, the binding of a compound to a pocket of target protein is fundamental for drug design [1], [2], [3]; docking simulation frequently uses pockets as a potential binding site in the computation of binding affinity; an ion channel is a passage in plasma membrane through which ions pass and is a type of tunnel formed by proteins.…”