Skip to main content
SpringerLink
Log in
Book cover

Transactions on Computational Science XX pp 92–111Cite as

Tunnels and Voids in Molecules via Voronoi Diagrams and Beta-Complexes

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 8110))

Abstract

Molecular external structure is important in understanding molecular interaction with its solvent environment and is useful in developing drugs. Important examples of external structures are tunnels, pockets, caves, clefts, voids, etc. This paper presents algorithms to extract tunnels and voids from molecular structures. The algorithms are based on the the Voronoi diagram of atoms in molecules and their time complexity are both O(m) time in the worst case, where m represents the number of entities in the Voronoi diagram. The algorithms are mathematically correct, computationally efficient, numerically robust, and easy to implement.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Voronoi Diagram Research Center (2011), http://voronoi.hanyang.ac.kr/

  2. Kim, D.S., Sugihara, K.: Tunnels and voids in molecules via voronoi diagram. In: 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering (2012)

    Google Scholar 

  3. Kim, D.S., Cho, C.H., Kim, D., Cho, Y.: Recognition of docking sites on a protein using β-shape based on Voronoi diagram of atoms. Computer-Aided Design 38(5), 431–443 (2006)

    Article  Google Scholar 

  4. Smart, O.S., Goodfellow, J.M., Wallace, B.A.: The pore dimensions of gramicidin a. Biophysical Journal 65(6), 2455–2460 (1993)

    Article  Google Scholar 

  5. Smart, O.S., Neduvelil, J.G., Wang, X., Wallace, B.A., Sansom, M.S.P.: HOLE: A program for the analysis of the pore dimensions of ion channel structural models. Journal of Molecular Graphics 14, 354–360 (1996)

    Article  Google Scholar 

  6. Kleywegt, G.J., Jones, T.A.: Detection, delineation, measurement and display of cavities in macromolecular structures. Acta Crystallographica Section D 50, 178–185 (1994)

    Article  Google Scholar 

  7. Laskowski, R.A.: SURFNET: A program for visualizing molecular surfaces, cavities, and intermolecular interactions. Journal of Molecular Graphics 13, 323–330 (1995)

    Article  Google Scholar 

  8. Voss, N.R., Gerstein, M., Steitz, T.A., Moore, P.B.: The geometry of the ribosomal polypeptide exit tunnel. Journal of Molecular Biology 260, 893–906 (2006)

    Article  Google Scholar 

  9. Petrek, M., Otyepka, M., Banas, P., Kosinova, P., Koca, J., Damborsky, J.: CAVER: A new tool to explore routes from protein clefts, pockets and cavities. BMC Bioinformatics 7(316) (2006)

    Google Scholar 

  10. DeLano, W.L.: Pymol: An open-source molecular graphics tool. CCP4 Newsletter (2002)

    Google Scholar 

  11. DeLano, W.L.: PyMOL molecular graphics system homepage (2002), http://pymol.org/

  12. Damborský, J., Petřek, M., Banáš, P., Otyepka, M.: Identification of tunnels in proteins, nucleic acids inorganic materials and molecular ensembles. Biotechnology Journal 2, 62–67 (2007)

    Article  Google Scholar 

  13. Petrek, M., Kosinova, P., Koca, J., Otyepka, M.: MOLE: A Voronoi diagram-based explorer of molecular channels, pores, and tunnels. Structure 15(11), 1357–1363 (2007)

    Article  Google Scholar 

  14. Medek, P., Beneš, P., Sochor, J.: Computation of tunnels in protein molecules using Delaunay triangulation. Journal of WSCG 15, 107–114 (2007)

    Google Scholar 

  15. Kozlílová, B., Andres, F., Sochor, J.: Visualization of tunnels in protein molecules. In: AfriGraph 2007, pp. 111–209 (2007)

    Google Scholar 

  16. Yaffe, E., Fishelovitch, D., Wolfson, H.J., Halperin, D., Nussinov, R.: MolAxis: a server for identification of channels in macromolecules. Nucleic Acids Research 36, W210–W215 (2008)

    Google Scholar 

  17. Yaffe, E., Fishelovitch, D., Wolfson, H.J., Halperin, D., Nussinov, R.: MolAxis: Efficient and accurate identification of channels in macromolecules. Proteins: Structure, Function, and Bioinformatics 73(1), 72–86 (2008)

    Google Scholar 

  18. Yaffe, E., Halperin, D.: Approximating the pathway axis and the persistence diagrams for a collection of balls in 3-space. Discrete & Computational Geometry 44, 660–685 (2010)

    Google Scholar 

  19. Ho, B.K., Gruswitz, F.: HOLLOW: Generating accurate representations of channel and interior surfaces in molecular structures. BMC Structural Biology 8(1),  49 (2008)

    Google Scholar 

  20. Coleman, R.G., Sharp, K.A.: Finding and characterizing tunnels in macromolecules with application to ion channels and pores. Biophysical Journal 96, 632–645 (2009)

    Article  Google Scholar 

  21. Norbert Lindow, D.B., Hege, H.C., Member, I.: Voronoi-based extraction and visualization of molecular paths. IEEE Transactions on Visualization and Computer Graphics 17(12), 2025–2034 (2011)

    Google Scholar 

  22. Anikeenko, A.V., Alinchenko, M.G., Voloshin, V.P., Medvedev, N.N., Gavrilova, M.L., Jedlovszky, P.: Implementation of the voronoi-delaunay method for analysis of intermolecular voids. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol. 3045, pp. 217–226. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  23. Goncalves, P.F.B., Stassen, H.: Free energy of solvation from molecular dynamics simulation applying voronoi-delaunay triangulation to the cavity creation. Journal of Chemical Physics 123(21), 214109 (2005)

    Article  Google Scholar 

  24. Kim, D.S., Cho, Y., Kim, D.: Euclidean Voronoi diagram of 3D balls and its computation via tracing edges. Computer-Aided Design 37(13), 1412–1424 (2005)

    Article  MATH  Google Scholar 

  25. Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley & Sons, Chichester (1999)

    Google Scholar 

  26. Kim, D.S., Cho, Y., Ryu, J., Kim, J.K., Kim, D.: Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules. Computer-Aided Design 45(1), 35–52 (2013)

    Article  MathSciNet  Google Scholar 

  27. Kim, D.S., Cho, Y., Sugihara, K.: Quasi-worlds and quasi-operators on quasi-triangulations. Computer-Aided Design 42(10), 874–888 (2010)

    Article  MATH  Google Scholar 

  28. Kim, D.S., Kim, D., Cho, Y., Sugihara, K.: Quasi-triangulation and interworld data structure in three dimensions. Computer-Aided Design 38(7), 808–819 (2006)

    Article  Google Scholar 

  29. Kim, D.S., Kim, J.K., Cho, Y., Kim, C.M.: Querying simplexes in quasi-triangulation. Computer-Aided Design 44(2), 85–98 (2012)

    Article  Google Scholar 

  30. Kim, D.S., Cho, Y., Sugihara, K., Ryu, J., Kim, D.: Three-dimensional beta-shapes and beta-complexes via quasi-triangulation. Computer-Aided Design 42(10), 911–929 (2010)

    Article  Google Scholar 

  31. Ryu, J., Cho, Y., Kim, D.S.: Triangulation of molecular surfaces. Computer-Aided Design 41(6), 463–478 (2009)

    Article  Google Scholar 

  32. Ryu, J., Park, R., Kim, D.S.: Molecular surfaces on proteins via beta shapes. Computer-Aided Design 39(12), 1042–1057 (2007)

    Article  Google Scholar 

  33. Kim, C.-M., Won, C.-I., Kim, J.-K., Ryu, J., Bhak, J., Kim, D.-S.: Protein-ligand docking based on beta-shape. In: Gavrilova, M.L., Tan, C.J.K., Anton, F. (eds.) Transactions on Computational Science IX. LNCS, vol. 6290, pp. 123–138. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  34. Kim, D.S., Kim, C.M., Won, C.I., Kim, J.K., Ryu, J., Cho, Y., Lee, C., Bhak, J.: Betadock: Shape-priority docking method based on beta-complex. Journal of Biomolecular Structure & Dynamics 29(1), 219–242 (2011)

    Article  Google Scholar 

  35. Kim, D.S., Ryu, J., Shin, H., Cho, Y.: Beta-decomposition for the volume and area of the union of three-dimensional balls and their offsets. Journal of Computational Chemistry 12(3), 1225–1283 (2012)

    Google Scholar 

  36. Kim, D.S., Kim, J.K., Won, C.I., Kim, C.M., Park, J.Y., Bhak, J.: Sphericity of a protein via the β-complex. Journal of Molecular Graphics and Modelling 28(7), 636–649 (2010)

    Article  Google Scholar 

  37. Lee, K.: Principles of CAD/CAM/CAE Systems. Addison Wesley (1999)

    Google Scholar 

  38. Bondi, A.: van der Waals volumes and radii. Journal of Physical Chemistry 68, 441–451 (1964)

    Article  Google Scholar 

  39. Boissonnat, J.D., Yvinec, M.: Algorithmic Geometry. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  40. Mäntylä, M.: An Introduction to Solid Modeling. Computer Science Press (1988)

    Google Scholar 

  41. RCSB Protein Data Bank (2009), http://www.rcsb.org/pdb/

Download references

Author information

Authors and Affiliations

  1. Voronoi Diagram Research Center, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul, 133-791, Korea

    Deok-Soo Kim

  2. Department of Industrial Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul, 133-791, Korea

    Deok-Soo Kim, Youngsong Cho & Jae-Kwan Kim

  3. Graduate School of Advanced Mathematical Sciences, Meiji University, Kawasaki, Japan

    Kokichi Sugihara

Authors
  1. Deok-Soo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youngsong Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jae-Kwan Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kokichi Sugihara
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina L. Gavrilova

  2. CloudFabriQ Ltd., Warnford Court, 29 Throgmorton Street, EC2N 2AT, London, UK

    C. J. Kenneth Tan

  3. Rutgers University, New Brunswick, NJ, USA

    Bahman Kalantari

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kim, DS., Cho, Y., Kim, JK., Sugihara, K. (2013). Tunnels and Voids in Molecules via Voronoi Diagrams and Beta-Complexes. In: Gavrilova, M.L., Tan, C.J.K., Kalantari, B. (eds) Transactions on Computational Science XX. Lecture Notes in Computer Science, vol 8110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41905-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41905-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41904-1

  • Online ISBN: 978-3-642-41905-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation