A Dynamic Substrate Pool Revealed by cryo-EM of a Lipid-Preserved Respiratory Supercomplex.

Aims: Mitochondrial respiratory supercomplexes mediate redox electron transfer, generating a proton gradient for ATP synthesis. To provide structural information on the function of supercomplexes in physiologically relevant conditions, we conducted cryoelectron microscopy studies with supercomplexes in a lipid-preserving state. Results: Here, we present cryoelectron microscopy structures of bovine respiratory supercomplex I1III2IV1 by using a lipid-preserving sample preparation. The preparation greatly enhances the intercomplex quinone transfer activity. The structures reveal large intercomplex motions that result in different shapes and sizes of the intercomplex space between complexes I and III, forming a dynamic substrate pool. Biochemical and structural analyses indicated that intercomplex phospholipids mediate the intercomplex motions. An analysis of the different classes of focus-refined complex I showed that structural switches due to quinone reduction led to the formation of a novel channel that could transfer reduced quinones to the intercomplex substrate pool. Innovation and Conclusion: Our results indicate potential mechanism for the facilitated electron transfer involving a dynamic substrate pool and intercomplex movement by which supercomplexes play an active role in the regulation of metabolic flux and reactive oxygen species.

Benchmark dataset for the convex hull of 2D disks.

In this paper, we present a benchmark dataset which can be used to evaluate the algorithms to construct the convex hull of 2D disks. The dataset contains disk arrangements including general and extremely biased cases, which are generated by a C++ program. The dataset is related to an article: "QuickhullDisk: A Faster Convex Hull Algorithm for Disks" in which the QuickhullDisk algorithm is presented and compared to the incremental algorithm which was reported by Devillers and Golin in 1995 [1].

BetaSCPWeb: side-chain prediction for protein structures using Voronoi diagrams and geometry prioritization.

Many applications, such as protein design, homology modeling, flexible docking, etc. require the prediction of a protein's optimal side-chain conformations from just its amino acid sequence and backbone structure. Side-chain prediction (SCP) is an NP-hard energy minimization problem. Here, we present BetaSCPWeb which efficiently computes a conformation close to optimal using a geometry-prioritization method based on the Voronoi diagram of spherical atoms. Its outputs are visual, textual and PDB file format. The web server is free and open to all users at http://voronoi.hanyang.ac.kr/betascpweb with no login requirement.

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.

The effects of railroad ballast surface and slope on rearfoot motion in walking.

The purpose of this study was to investigate the effects of transversely sloped ballasted walking surface on gait and rearfoot motion (RFM) parameters. Motion analysis was performed with 20 healthy participants (15 male and 5 female) walking in six surface-slope conditions: two surfaces (solid and ballasted) by three slopes (0, 5, and 10 degrees). The gait parameters (walking velocity, step length, step rate, step width, stance time, and toe-out angle) showed significant surface effect (p = .004) and surface-slope interaction (p = .017). The RFM motion parameters (peak everted/inverted position, eversion/inversion velocity, and acceleration) revealed significant surface (p = .004) and slope (p = .024) effects. The ballasted conditions showed more cautious gait patterns with lower walk velocity, step length, and step rate and longer stance time. In the RFM parameters, the slope effect was more notable in the solid conditions due to the gait adaptations in the ballasted conditions. Ballast conditions showed reduced inversion and increased eversion and RFM range. The RFM data were comparable to other typical walking conditions but smaller than those from running.

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.

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.