BetaCavityWeb: a webserver for molecular voids and channels.

Molecular cavities, which include voids and channels, are critical for molecular function. We present a webserver, BetaCavityWeb, which computes these cavities for a given molecular structure and a given spherical probe, and reports their geometrical properties: volume, boundary area, buried area, etc. The server's algorithms are based on the Voronoi diagram of atoms and its derivative construct: the beta-complex. The correctness of the computed result and computational efficiency are both mathematically guaranteed. BetaCavityWeb is freely accessible at the Voronoi Diagram Research Center (VDRC) (http://voronoi.hanyang.ac.kr/betacavityweb).

BetaVoid: molecular voids via beta-complexes and Voronoi diagrams.

Molecular external structure is important for molecular function, with voids on the surface and interior being one of the most important features. Hence, recognition of molecular voids and accurate computation of their geometrical properties, such as volume, area and topology, are crucial, yet most popular algorithms are based on the crude use of sampling points and thus are approximations even with a significant amount of computation. In this article, we propose an analytic approach to the problem using the Voronoi diagram of atoms and the beta-complex. The correctness and efficiency of the proposed algorithm is mathematically proved and experimentally verified. The benchmark test clearly shows the superiority of BetaVoid to two popular programs: VOIDOO and CASTp. The proposed algorithm is implemented in the BetaVoid program which is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

Beta-decomposition for the volume and area of the union of three-dimensional balls and their offsets.

Given a set of spherical balls, called atoms, in three-dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well-solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta-decomposition, based on the recent theory of the beta-complex. Given the beta-complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta-complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta-complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ℝ(3) that m = O(n) on average for biomolecules and m = O(n(2)) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ℝ(2) and extended to ℝ(3). The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site.

Beta-complex versus Alpha-complex: Similarities and Dissimilarities.

The beta-complex is a construct derived from the Voronoi diagram of spherical balls of arbitrary radii and has proven a powerful capability for proximity reasoning among spherical balls in three-dimensional space. Important applications related to molecular shapes in structural/computational molecular biology have been correctly, efficiently, and conveniently solved in the unified framework of the beta-complex and the Voronoi diagram. The beta-complex is a generalization of the ordinary alpha-complex. However, there are similarities and dissimilarities between the two complexes and it is necessary to correctly understand these similarities and dissimilarities to choose the right complex to solve application problems at hand. This paper presents the similarities and dissimilarities between these constructs and illustrates the consequence of the dissimilarity in application problems from both theoretical and practical points of view using examples of atomic arrangements.

Innovative platform for transmission localized surface plasmon transducers and its application in detecting heavy metal Pd(II).

Transmission localized surface plasmon resonance (T-LSPR) transducers based on the characteristic surface plasmon absorption band of Au island films have become increasingly attractive. The first and main bottleneck hampering the development of T-LSPR sensors is instability, manifested as change in the surface plasmon absorbance band following immersion in organic solvents and aqueous solutions. In this paper, we innovate the platform for T-LSPR transducer by using remarkably stable and highly adhesive Au/Al(2)O(3) nanocomposite film. Isolated Au nanoparticles embedded in dielectric matrix Al(2)O(3) were prepared by a simple one-step radio frequency magnetron cosputtering technique. The obtained nanocomposite film is exceedingly stable during immersion in solvents, drying, and binding of different molecules; it successfully passes the adhesive tape test and sonication treatment. The superior stability and adhesion, obtained without the use of any intermediate adhesion layer or protective overlayer, is attributed to (1) the Au nanoparticles embedment and Al(2)O(3) rim formation during the sputtering process and (2) the resistance of element Al in matrix to the nucleophilic attack by the solvent molecules. Given this success, we believe that the Au/Al(2)O(3) nanocomposite film holds promise as an innovative sensing platform in T-LSPR detection technology, as demonstrated here for the Pd(II) sensing process with excellent sensitivity and low detection limit.

Pocket extraction on proteins via the Voronoi diagram of spheres.

Proteins consist of atoms. Given a protein, the automatic recognition of depressed regions, called pockets, on the surface of proteins is important for protein-ligand docking and facilitates fast development of new drugs. Recently, computational approaches have emerged for recognizing pockets from the geometrical point of view. Presented in this paper is a geometric method for the pocket recognition which is based on the Voronoi diagram for atoms. Given a Voronoi diagram, the proposed algorithm transforms the atomic structure to meshes which contain the information of the proximity among atoms, and then recognizes depressions on the surface of a protein using the meshes.

BetaDock: shape-priority docking method based on beta-complex.

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 ß-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the ß-complex corresponding to water molecule is computed. Then, the boundary of the ß-complex defines the ß-shape which has the complete proximity information among all atoms on the receptor boundary. From the ß-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.