Changhee Lee

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.

Manifoldization of β-shapes by topology operators

It is well known that the geometric structure of a protein is an important factor to determine its functions. In particular, the atoms located at the boundary of a protein are more important since various physicochemical reactions happen in the boundary of the protein. The β-shape is a powerful tool for the analysis of atoms located at the boundary since it provides the complete information of the proximity among these atoms. However, β-shapes are difficult to handle and require heavy weight data structures since they form non-manifold structure. In this paper, we propose topology operators for converting a β-shape into a manifold. Once it is converted, compact data structures for representing a manifold are available. In addition, general topology operators used for manifold structures can also be available for various applications.

Manifoldization of β-shapes in O(n) time

The ββ-shape and the ββ-complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the ββ-shape is inconvenient for reasoning about the surface structure of a sphere set. In this paper, we present an algorithm to transform a ββ-shape from being non-manifold to manifold without altering any of the geometric characteristics of the model. After locating the simplexes where the non-manifoldness is defined on the ββ-shape, the algorithm augments the ββ-complex which corresponds to the ββ-shape so that all the non-manifoldness is resolved on such simplexes. The algorithm runs in O(n)O(n) time, without any floating-point operation, in the worst case for protein models where nn is the number of spherical atoms. We also provide some experimental results obtained from real protein models available from the Protein Data Bank.

Trash removal algorithm for fast construction of the elliptic Gabriel graph using Delaunay triangulation

Given a set of points P, finding near neighbors among the points is an important problem in many applications in CAD/CAM, computer graphics, computational geometry, etc. In this paper, we propose an efficient algorithm for constructing the elliptic Gabriel graph (EGG), which is a generalization of the well-known Gabriel graph and parameterized by a non-negative value @a. Our algorithm is based on the observation that a candidate point which may define an edge of an EGG with a given point p@?P is always in the scaled Voronoi region of p with a scale factor 2/@a^2 when the parameter @a =1, due to the fact that EGG is a subgraph of the Delaunay graph of P, EGG can be efficiently computed by watching the validity of each edge in the Delaunay graph. The proposed algorithm is shown to have its time complexity as O(n^3) in the worst case and O(n) in the average case when @a is moderately close to unity. The idea presented in this paper may similarly apply to other problems for the proximity search for point sets.

Efficient computation of elliptic gabriel graph

Searching neighboring points around a point in a point set has been important for various applications and there have been extensive studies such as the minimum spanning tree, relative neighborhood graph, Delaunay triangulation, Gabriel graph, and so on. n nObserving the fact that the previous approaches of neighbor search may possibly sample severely biased neighbors in a set of unevenly distributed points, an elliptic Gabriel graph has recently been proposed. By extending the influence region from a circle to an ellipse, the elliptic Gabriel graph generalizes the ordinary Gabriel graph. Hence, the skewness in the sampled neighbors is rather reduced. n nIn this paper, we present a simple observation which allows to compute the correct elliptic Gabriel graph efficiently by reducing the search space.

Manifoldization of ββ-shapes in O(n)O(n) time

The ββ-shape and the ββ-complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the ββ-shape is inconvenient for reasoning about the surface structure of a sphere set. In this paper, we present an algorithm to transform a ββ-shape from being non-manifold to manifold without altering any of the geometric characteristics of the model. After locating the simplexes where the non-manifoldness is defined on the ββ-shape, the algorithm augments the ββ-complex which corresponds to the ββ-shape so that all the non-manifoldness is resolved on such simplexes. The algorithm runs in O(n)O(n) time, without any floating-point operation, in the worst case for protein models where nn is the number of spherical atoms. We also provide some experimental results obtained from real protein models available from the Protein Data Bank.

Manifoldization of -shapes in time

The ββ-shape and the ββ-complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the ββ-shape is inconvenient for reasoning about the surface structure of a sphere set. In this paper, we present an algorithm to transform a ββ-shape from being non-manifold to manifold without altering any of the geometric characteristics of the model. After locating the simplexes where the non-manifoldness is defined on the ββ-shape, the algorithm augments the ββ-complex which corresponds to the ββ-shape so that all the non-manifoldness is resolved on such simplexes. The algorithm runs in O(n)O(n) time, without any floating-point operation, in the worst case for protein models where nn is the number of spherical atoms. We also provide some experimental results obtained from real protein models available from the Protein Data Bank.