Ligand Excluded Surface: A New Type of Molecular Surface

The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes - including visualization, analysis of molecular interactions and the study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation. Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.

[1]  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..

[2]  G. Schneider,et al.  PocketPicker: analysis of ligand binding-sites with shape descriptors , 2007, Chemistry Central Journal.

[3]  Markus Hadwiger,et al.  Real‐Time Ray‐Casting and Advanced Shading of Discrete Isosurfaces , 2005, Comput. Graph. Forum.

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

[5]  Andrea Brambilla,et al.  Fast Blending Scheme for Molecular Surface Representation , 2013, IEEE Transactions on Visualization and Computer Graphics.

[6]  Ivan Viola,et al.  Implicit representation of molecular surfaces , 2012, 2012 IEEE Pacific Visualization Symposium.

[7]  Pieter F. W. Stouten,et al.  Fast prediction and visualization of protein binding pockets with PASS , 2000, J. Comput. Aided Mol. Des..

[8]  M. Schroeder,et al.  LIGSITEcsc: predicting ligand binding sites using the Connolly surface and degree of conservation , 2006, BMC Structural Biology.

[9]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.

[10]  D. Levitt,et al.  POCKET: a computer graphics method for identifying and displaying protein cavities and their surrounding amino acids. , 1992, Journal of molecular graphics.

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

[12]  Frederick P. Brooks,et al.  Linearly Scalable Computation of Smooth Molecular Surfaces , 1997 .

[13]  Thomas Ertl,et al.  Parallel Contour-Buildup algorithm for the molecular surface , 2011, 2011 IEEE Symposium on Biological Data Visualization (BioVis)..

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

[15]  Jean-Claude Spehner,et al.  Fast and robust computation of molecular surfaces , 1995, SCG '95.

[16]  B. Bush,et al.  Macromolecular shape and surface maps by solvent exclusion. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

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

[18]  Bingding Huang,et al.  MetaPocket: a meta approach to improve protein ligand binding site prediction. , 2009, Omics : a journal of integrative biology.

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

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

[21]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.

[22]  Talha Bin Masood,et al.  Extraction of Robust Voids and Pockets in Proteins , 2013, Visualization in Medicine and Life Sciences III.

[23]  Daniel Baum,et al.  Exploring cavity dynamics in biomolecular systems , 2013, BMC Bioinformatics.

[24]  Nobuhiro Gō,et al.  Algorithm for rapid calculation of excluded volume of large molecules , 1989 .

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

[26]  John C. Hart,et al.  Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces , 1996, The Visual Computer.

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

[28]  Herbert Edelsbrunner,et al.  Measuring proteins and voids in proteins , 1995, Proceedings of the Twenty-Eighth Annual Hawaii International Conference on System Sciences.

[29]  Klaus Schulten,et al.  Fast Visualization of Gaussian Density Surfaces for Molecular Dynamics and Particle System Trajectories , 2012, EuroVis.

[30]  B. Fedorov,et al.  Improved technique for calculating X‐ray scattering intensity of biopolymers in solution: Evaluation of the form, volume, and surface of a particle , 1983 .

[31]  Laurence H. Pearl,et al.  Generation of molecular surfaces for graphic display , 1983 .

[32]  Maciej Haranczyk,et al.  Navigating molecular worms inside chemical labyrinths , 2009, Proceedings of the National Academy of Sciences.

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

[34]  M Hendlich,et al.  LIGSITE: automatic and efficient detection of potential small molecule-binding sites in proteins. , 1997, Journal of molecular graphics & modelling.

[35]  Kaspar Fischer,et al.  Smallest enclosing balls of balls , 2005 .

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

[37]  Chandrajit L. Bajaj,et al.  An Adaptive Grid Based Method for Computing Molecular Surfaces and Properties , 2006 .

[38]  Daniel Baum,et al.  Voronoi-Based Extraction and Visualization of Molecular Paths , 2011, IEEE Transactions on Visualization and Computer Graphics.

[39]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

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

[41]  G. Bowman,et al.  Equilibrium fluctuations of a single folded protein reveal a multitude of potential cryptic allosteric sites , 2012, Proceedings of the National Academy of Sciences.

[42]  Frederick P. Brooks,et al.  Computing smooth molecular surfaces , 1994, IEEE Computer Graphics and Applications.

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

[44]  R Abagyan,et al.  The contour-buildup algorithm to calculate the analytical molecular surface. , 1996, Journal of structural biology.

[45]  Michael L. Connolly,et al.  Molecular surface Triangulation , 1985 .

[46]  Jie Liang,et al.  CASTp: Computed Atlas of Surface Topography of proteins , 2003, Nucleic Acids Res..

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

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

[49]  Richard M. Jackson,et al.  Q-SiteFinder: an energy-based method for the prediction of protein-ligand binding sites , 2005, Bioinform..