Chung-In Won

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.

Sphericity of a protein via the β-complex

Molecular shape is a fundamental factor in determining the function of a molecule. As proteins tend to fold into globular shapes, the shape descriptor for protein sphericity is important in understanding molecular functions. In this paper, a definition of protein sphericity is introduced based on the recently developed geometric constructs of the beta-complex and beta-shape of a protein. The beta-complex represents the Euclidean proximity among all the atoms in a protein, and the beta-shape is the polyhedron contained within the boundary of the corresponding beta-complex. Hence, the beta-shape determines the proximity among the atoms on the boundary of a protein. Given the volume of a beta-shape, the ratio between the surface area of a sphere with this volume and the surface area of the beta-shape itself is a good measure to classify the sphericity of a protein, especially when the radius of a probe is 3.0 A. The presented measure is invariant to translation and rotation.

Optimal ligand descriptor for pocket recognition based on the Beta-shape.

Structure-based virtual screening is one of the most important and common computational methods for the identification of predicted hit at the beginning of drug discovery. Pocket recognition and definition is frequently a prerequisite of structure-based virtual screening, reducing the search space of the predicted protein-ligand complex. In this paper, we present an optimal ligand shape descriptor for a pocket recognition algorithm based on the beta-shape, which is a derivative structure of the Voronoi diagram of atoms. We investigate six candidates for a shape descriptor for a ligand using statistical analysis: the minimum enclosing sphere, three measures from the principal component analysis of atoms, the van der Waals volume, and the beta-shape volume. Among them, the van der Waals volume of a ligand is the optimal shape descriptor for pocket recognition and best tunes the pocket recognition algorithm based on the beta-shape for efficient virtual screening. The performance of the proposed algorithm is verified by a benchmark test.