Dynamic channels in biomolecular systems: Path analysis and visualization

Analysis of protein dynamics suggests that internal cavities and channels can be rather dynamic structures. Here, we present a Voronoi-based algorithm to extract the geometry and the dynamics of cavities and channels from a molecular dynamics trajectory. The algorithm requires a pre-processing step in which the Voronoi diagram of the van der Waals spheres is used to calculate the cavity structure for each coordinate set of the trajectory. In the next step, we interactively compute dynamic channels by analyzing the time evolution of components of the cavity structure. Tracing of the cavity dynamics is supported by timeline visualization tools that allow the user to select specific components of the cavity structures for detailed exploration. All visualization methods are interactive and enable the user to animate the time-dependent molecular structure together with its cavity structure. To facilitate a comprehensive overview of the dynamics of a channel, we have also developed a visualization technique that renders a dynamic channel in a single image and color-codes time on its extension surface. We illustrate the usefullness of our tools by inspecting the structure and dynamics of internal cavities in the bacteriorhodopsin proton pump.

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

[2]  Stefan Fischer,et al.  Mechanism of a molecular valve in the halorhodopsin chloride pump. , 2005, Structure.

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

[4]  M. Klein,et al.  Constant pressure molecular dynamics algorithms , 1994 .

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

[6]  H Luecke,et al.  Structure of bacteriorhodopsin at 1.55 A resolution. , 1999, Journal of molecular biology.

[7]  Alexander D. MacKerell,et al.  An Improved Empirical Potential Energy Function for Molecular Simulations of Phospholipids , 2000 .

[8]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

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

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

[11]  Stefan Fischer,et al.  Water Pathways in the Bacteriorhodopsin Proton Pump , 2010, The Journal of Membrane Biology.

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

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

[14]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[15]  Laxmikant V. Kale,et al.  NAMD2: Greater Scalability for Parallel Molecular Dynamics , 1999 .

[16]  Ron O. Dror,et al.  Exploring atomic resolution physiology on a femtosecond to millisecond timescale using molecular dynamics simulations , 2010, The Journal of general physiology.

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

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

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

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

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

[22]  B. Brooks,et al.  Constant pressure molecular dynamics simulation: The Langevin piston method , 1995 .

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

[24]  Ana-Nicoleta Bondar,et al.  Coupling of retinal, protein, and water dynamics in squid rhodopsin. , 2010, Biophysical journal.

[25]  Jeremy C. Smith,et al.  Functional interactions in bacteriorhodopsin: a theoretical analysis of retinal hydrogen bonding with water. , 1995, Biophysical journal.

[26]  Laxmikant V. Kalé,et al.  Scalable molecular dynamics with NAMD , 2005, J. Comput. Chem..

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

[28]  Michael Wulff,et al.  Structural dynamics of light-driven proton pumps. , 2009, Structure.

[29]  Barbara Tversky,et al.  Animation: can it facilitate? , 2002, Int. J. Hum. Comput. Stud..

[30]  W. Marsden I and J , 2012 .

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

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

[33]  G. Ullmann,et al.  McVol - A program for calculating protein volumes and identifying cavities by a Monte Carlo algorithm , 2010, Journal of molecular modeling.

[34]  Alexander D. MacKerell,et al.  All-atom empirical potential for molecular modeling and dynamics studies of proteins. , 1998, The journal of physical chemistry. B.

[35]  Michael Gleicher,et al.  Ieee Transactions on Visualization and Computer Graphics Automated Illustration of Molecular Flexibility , 2022 .

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

[37]  Johannes Schmidt-Ehrenberg Analysis and Visualization of Molecular Conformations , 2008 .

[38]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[39]  Klaus Schulten,et al.  Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions , 1991 .

[40]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .

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

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

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

[44]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

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

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

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

[48]  V. Gordeliy,et al.  Water molecules and hydrogen-bonded networks in bacteriorhodopsin--molecular dynamics simulations of the ground state and the M-intermediate. , 2005, Biophysical journal.

[49]  K Schulten,et al.  Molecular dynamics study of the nature and origin of retinal's twisted structure in bacteriorhodopsin. , 2000, Biophysical journal.

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

[51]  M. Melamed Detection , 2021, SETI: Astronomy as a Contact Sport.

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

[53]  Ana-Nicoleta Bondar,et al.  Extended protein/water H-bond networks in photosynthetic water oxidation. , 2012, Biochimica et biophysica acta.

[54]  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.

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

[56]  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..

[57]  J. Lansing,et al.  Magnetic resonance studies of the bacteriorhodopsin pump cycle. , 2002, Annual review of biophysics and biomolecular structure.

[58]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

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

[60]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[61]  C Menzel,et al.  Protein, lipid and water organization in bacteriorhodopsin crystals: a molecular view of the purple membrane at 1.9 A resolution. , 1999, Structure.

[62]  Hans-Christian Hege,et al.  amira: A Highly Interactive System for Visual Data Analysis , 2005, The Visualization Handbook.

[63]  Daniel Baum,et al.  Visualizing dynamic molecular conformations , 2002, IEEE Visualization, 2002. VIS 2002..

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