Voronoi-Based Extraction and Visualization of Molecular Paths

Visual analysis is widely used to study the behavior of molecules. Of particular interest are the analysis of molecular interactions and the investigation of binding sites. For large molecules, however, it is difficult to detect possible binding sites and paths leading to these sites by pure visual inspection. In this paper, we present new methods for the computation and visualization of potential molecular paths. Using a novel filtering method, we extract the significant paths from the Voronoi diagram of spheres. For the interactive visualization of molecules and their paths, we present several methods using deferred shading and other state-of-theart techniques. To allow for a fast overview of reachable regions of the molecule, we illuminate the molecular surface using a large number of light sources placed on the extracted paths. We also provide a method to compute the extension surface of selected paths and visualize it using the skin surface. Furthermore, we use the extension surface to clip the molecule to allow easy visual tracking of even deeply buried paths. The methods are applied to several proteins to demonstrate their usefulness.

[1]  Jaroslav Koca,et al.  CAVER: a new tool to explore routes from protein clefts, pockets and cavities , 2006, BMC Bioinformatics.

[2]  Marina L. Gavrilova,et al.  Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space , 2003, Comput. Aided Geom. Des..

[3]  R. Laskowski SURFNET: a program for visualizing molecular surfaces, cavities, and intermolecular interactions. , 1995, Journal of molecular graphics.

[4]  Thomas Ertl,et al.  Visual Abstractions of Solvent Pathlines near Protein Cavities , 2008, Comput. Graph. Forum.

[5]  H. Edelsbrunner,et al.  Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design , 1998, Protein science : a publication of the Protein Society.

[6]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[7]  Matthias Keil,et al.  Identifification of Substrate Channels and Protein Cavities , 1998 .

[8]  Deok-Soo Kim,et al.  Euclidean Voronoi diagram of 3D balls and its computation via tracing edges , 2005, Comput. Aided Des..

[9]  Kengo Kinoshita,et al.  Development of new indices to evaluate protein-protein interfaces: assembling space volume, assembling space distance, and global shape descriptor. , 2009, Journal of molecular graphics & modelling.

[10]  Daniel Baum,et al.  Accelerated Visualization of Dynamic Molecular Surfaces , 2010, Comput. Graph. Forum.

[11]  Ivana Kolingerová,et al.  Fast Discovery of Voronoi Vertices in the Construction of Voronoi Diagram of 3D Balls , 2010, 2010 International Symposium on Voronoi Diagrams in Science and Engineering.

[12]  Jaroslav Koca,et al.  MOLE: a Voronoi diagram-based explorer of molecular channels, pores, and tunnels. , 2007, Structure.

[13]  Mark Gerstein,et al.  3V: cavity, channel and cleft volume calculator and extractor , 2010, Nucleic Acids Res..

[14]  H. Wolfson,et al.  MolAxis: Efficient and accurate identification of channels in macromolecules , 2008, Proteins.

[15]  S. LaValle Rapidly-exploring random trees : a new tool for path planning , 1998 .

[16]  Marina L. Gavrilova,et al.  An algorithm for three‐dimensional Voronoi S‐network , 2006, J. Comput. Chem..

[17]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[18]  Franz Aurenhammer,et al.  Power Diagrams: Properties, Algorithms and Applications , 1987, SIAM J. Comput..

[19]  D. Siersma Voronoi diagrams and Morse theory of the distance function , 1996 .

[20]  Tim Weyrich,et al.  Eurographics Symposium on Point-based Graphics (2006) Gpu-based Ray-casting of Quadratic Surfaces , 2022 .

[21]  Yong Zhou,et al.  Roll: a new algorithm for the detection of protein pockets and cavities with a rolling probe sphere , 2010, Bioinform..

[22]  Thierry Siméon,et al.  Encoding molecular motions in voxel maps , 2009, ICRA.

[23]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[24]  Thierry Siméon,et al.  A path planning approach for computing large-amplitude motions of flexible molecules , 2005, ISMB.

[25]  Takafumi Saito,et al.  Comprehensible rendering of 3-D shapes , 1990, SIGGRAPH.

[26]  Andrew Gillette,et al.  Topology Based Selection and Curation of Level Sets , 2009, Topology-Based Methods in Visualization II.

[27]  Martin Falk,et al.  Interactive Exploration of Protein Cavities , 2011, Comput. Graph. Forum.

[28]  Matthieu Chavent,et al.  MetaMol: high-quality visualization of molecular skin surface. , 2008, Journal of molecular graphics & modelling.

[29]  Janet M. Thornton,et al.  PoreWalker: A Novel Tool for the Identification and Characterization of Channels in Transmembrane Proteins from Their Three-Dimensional Structure , 2009, PLoS Comput. Biol..

[30]  Deok-Soo Kim,et al.  Reduction of the Search Space in the Edge-Tracing Algorithm for the Voronoi Diagram of 3D Balls , 2006, ICCSA.

[31]  Kwan-Liu Ma,et al.  Visualizing Flow Trajectories Using Locality-based Rendering and Warped Curve Plots , 2010, IEEE Transactions on Visualization and Computer Graphics.

[32]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[33]  Thomas Ertl,et al.  Interactive Visualization of Molecular Surface Dynamics , 2009, IEEE Transactions on Visualization and Computer Graphics.

[34]  G J Kleywegt,et al.  Detection, delineation, measurement and display of cavities in macromolecular structures. , 1994, Acta crystallographica. Section D, Biological crystallography.

[35]  Georg Tamm Deferred Shading , 2009, Informatiktage.

[36]  Bosco K. Ho,et al.  HOLLOW: Generating Accurate Representations of Channel and Interior Surfaces in Molecular Structures , 2008, BMC Structural Biology.

[37]  K. Sharp,et al.  Finding and characterizing tunnels in macromolecules with application to ion channels and pores. , 2009, Biophysical journal.

[38]  B. Wallace,et al.  HOLE: a program for the analysis of the pore dimensions of ion channel structural models. , 1996, Journal of molecular graphics.

[39]  Deok-Soo Kim,et al.  Quasi-worlds and quasi-operators on quasi-triangulations , 2010, Comput. Aided Des..

[40]  Jirí Sochor,et al.  Computation of Tunnels in Protein Molecules using Delaunay Triangulation , 2007, J. WSCG.

[41]  Randi J. Rost OpenGL(R) Shading Language (2nd Edition) , 2005 .

[42]  Tobias Blaschke,et al.  Nanoparticles for skin penetration enhancement--a comparison of a dendritic core-multishell-nanotransporter and solid lipid nanoparticles. , 2009, European journal of pharmaceutics and biopharmaceutics : official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V.

[43]  Louis Bavoil,et al.  Image-space horizon-based ambient occlusion , 2008, SIGGRAPH '08.

[44]  Deok-Soo Kim,et al.  Quasi-triangulation and interworld data structure in three dimensions , 2006, Comput. Aided Des..

[45]  Christian Kandt,et al.  dxTuber: detecting protein cavities, tunnels and clefts based on protein and solvent dynamics. , 2011, Journal of molecular graphics & modelling.

[46]  Herbert Edelsbrunner,et al.  Deformable Smooth Surface Design , 1999, Discret. Comput. Geom..

[47]  Paolo Cignoni,et al.  Ambient Occlusion and Edge Cueing for Enhancing Real Time Molecular Visualization , 2006, IEEE Transactions on Visualization and Computer Graphics.