Advertisement

Decomposition of a Protein Solution into Voronoi Shells and Delaunay Layers: Calculation of the Volumetric Properties

  • Alexandra V. Kim
  • Vladimir P. Voloshin
  • Nikolai N. Medvedev
  • Alfons Geiger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8110)

Abstract

A simple formalism is proposed for a quantitative analysis of interatomic voids inside and outside a solute molecule in solution. It can be applied for the interpretation of volumetric data, obtained in studies of protein folding and unfolding in water. In particular, it helps to divide the partial molar volume of the solute into several components. The method is based on the Voronoi-Delaunay tessellation of molecular-dynamic models of solutions. It is suggested to select successive Voronoi shells, starting from the interface between the solute molecule and the solvent, and continuing to the outside (into the solvent) as well as into the inner of the molecule. Similarly, successive Delaunay layers, consisting of Delaunay simplexes, can also be constructed. Geometrical properties of the selected shells and layers are discussed. The temperature behavior of inner, boundary and outer shells is discussed by the example of a molecular-dynamic model of an aqueous solution of the polypeptide hIAPP.

Keywords

Voronoi diagram solvation shell molecular dynamics of solutions Voronoi cells Delaunay simplexes partial molar volume 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chalikian, T.V.: Volumetric properties of proteins: Annu. Rev. Biophys. Biomol. Struct. 32, 207–235 (2003)CrossRefGoogle Scholar
  2. 2.
    Van der Spoel, D., Lindahl, E., Hess, B., Groenhof, G., Mark, A.E., Berendsen, H.J.C.: GROMACS: Fast, Flexible, and Free. J. Comp. Chem. 26(16), 1701–1718 (2005)CrossRefGoogle Scholar
  3. 3.
    Medvedev, N.N.: Computational porosimetry. In: Engel, P., Syta, H. (eds.) Voronoi’s Impact on Modern Science, pp. 165–175. Institute of Math National Acad. of Sciences of Ukraine, Kiev (1998)Google Scholar
  4. 4.
    Sastry, S., Truskett, T.M., Debenedetti, P.G., Torquato, S., Stillinger, F.H.: Free Volume in the Hard-Sphere Liquid. Molecular Physics 95, 289–297 (1998)CrossRefGoogle Scholar
  5. 5.
    Malavasi, G., Menziani, M.C., Pedone, A., Segre, U.: Void size distribution in MD-modelled silica glass structures. Journal of Non-Crystalline Solids 352, 285–296 (2006)CrossRefGoogle Scholar
  6. 6.
    Luchnikov, V.A., Gavrilova, M.L., Medvedev, N.N., Voloshin, V.P.: The Voronoi-Delaunay approach for the free volume analysis of a packing of balls in a cylindrical container. Future Generation Computer Systems, Special Issue on Computer Modeling, Algorithms and Supporting Environments 18, 673–679 (2002)CrossRefzbMATHGoogle Scholar
  7. 7.
    Rémond, S., Gallias, J.L., Mizrahi, A.: Characterization of voids in spherical particle systems by Delaunay empty spheres. Granular Matter 10, 329–334 (2008)CrossRefzbMATHGoogle Scholar
  8. 8.
    Haw, M.D.: Void structure and cage fluctuations in simulations of concentrated suspensions. Soft Matter 2, 950–956 (2006)CrossRefGoogle Scholar
  9. 9.
    Sung, B.J., Yethiraj, A.: Structure of void space in polymer solutions. Phys. Rev. E 81, 031801 (2010)Google Scholar
  10. 10.
    Alinchenko, M.G., Anikeenko, A.V., Medvedev, N.N., Voloshin, V.P., Mezei, M., Jedlovszky, P.: Morphology of voids in molecular systems. A Voronoi-Delaunay analysis of a simulated DMPC membrane. J. Phys. Chem. B 108(49), 19056–19067 (2004)Google Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Edelsbrunner, H., Facello, M., Liang, J.: On the definition and construction of pockets in macromolecules. Discr. Appl. Math. 88, 83–102 (1998)Google Scholar
  13. 13.
    Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P., Subramaniam, S.: Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins. Proteins: Struct. Func. Genet. 33, 18–29 (1998)Google Scholar
  14. 14.
    Kim, D., Cho, C.-H., Cho, Y., Ryu, J., Bhak, J., Kim, D.-S.: Pocket extraction on proteins via the Voronoi diagram of spheres. Journal of Molecular Graphics and Modelling 26(7), 1104–1112 (2008)CrossRefGoogle Scholar
  15. 15.
    Raschke, T.M., Levitt, M.: Nonpolar solutes enhance water structure within hydration shells while reducing interactions between them. PNAS 102(19), 6777–6782 (2005)CrossRefGoogle Scholar
  16. 16.
    Schröder, C., Rudas, T., Boresch, S., Steinhausera, O.: Simulation studies of the protein-water interface. I.Properties at the molecular resolution. J. Chem. Phys. 124, 234907 (2006)CrossRefGoogle Scholar
  17. 17.
    Bouvier, B., Grünberg, R., Nilges, M., Cazals, F.: Shelling the Voronoi interface of protein-protein complexes predicts residue activity and conservation. Proteins: Structure, Function, and Bioinformatics 76(3), 677–692 (2008)CrossRefGoogle Scholar
  18. 18.
    Neumayr, G., Rudas, T., Steinhausera, O.: Global and local Voronoi analysis of solvation shells of proteins. J. Chem. Phys. 133, 084108 (2010)Google Scholar
  19. 19.
    Voloshin, V.P., Medvedev, N.N., Andrews, M.N., Burri, R.R., Winter, R., Geiger, A.: Volumetric Properties of Hydrated Peptides: Voronoi-Delaunay Analysis of Molecular Simulation Runs. J. Phys. Chem. B 115(48), 14217–14228 (2011)CrossRefGoogle Scholar
  20. 20.
    Okabe, A., Boots, B., Sugihara, K., Chiu, S.: Spatial tessellations - concepts and applications of Voronoi diagrams. John Wiley & Sons, New York (2000)CrossRefzbMATHGoogle Scholar
  21. 21.
    Medvedev, N.N.: Voronoi-Delaunay method for non-crystalline structures. SB of Russian Academy of Science, Novosibirsk (2000) (in Russian)Google Scholar
  22. 22.
    Richards, F.M.: Calculation of molecular volumes and areas for structures of known geo-metry. Methods in Enzymology 115, 440–464 (1985)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Gellatly, B.J., Finney, J.L.: Calculation of protein volumes: an alternative to the Voronoi procedure. J. Mol. Biol. 161, 305–322 (1982)CrossRefGoogle Scholar
  24. 24.
    Anishchik, S.V., Medvedev, N.N.: Three-dimensional Apollonian packing as a model for dense granular systems. Phys.Rev.Lett. 75(23), 4314–4317 (1995)CrossRefGoogle Scholar
  25. 25.
    Medvedev, N.N., Voloshin, V.P., Luchnikov, V.A., Gavrilova, M.L.: An algorithm for three-dimensional Voronoi S-network. J. Comput. Chem. 27, 1676–1692 (2006)CrossRefGoogle Scholar
  26. 26.
    Aurenhammer, F.: Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16, 78–96 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Kim, D.-S., Cho, Y., Sugihara, K.: Quasi-worlds and Quasi-operators on Quasi-triangulations. Computer-Aided Design 42(10), 874–888 (2010)CrossRefzbMATHGoogle Scholar
  28. 28.
    Aste, T., Szeto, K.Y., Tam, W.Y.: Statistical properties and shell analysis in random cellular structures. Phys.Rev.E 54(5), 5482–5492 (1996)CrossRefGoogle Scholar
  29. 29.
    Andrews, M.N., Winter, R.: Comparing the Structural Properties of Human and Rat Islet Amyloid Polypeptide by MD Computer Simulations. Biophys. Chem. 156, 43–50 (2011)CrossRefGoogle Scholar
  30. 30.
    Mitra, L., Smolin, N., Ravindra, R., Royer, C., Winter, R.: Pressure perturbation calorimetric study of the solvation properties and the thermal unfolding of proteins in solution - experiment and theoretical interpretation. Phys.Chem. Chem. Phys. 8, 1249–1265 (2006)CrossRefGoogle Scholar
  31. 31.
    Imai, T.: Molecular theory of partial molar volume and its application to biomolecular systems. Cond. Matter Physics 10, 3(51), 343–361 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alexandra V. Kim
    • 1
  • Vladimir P. Voloshin
    • 1
  • Nikolai N. Medvedev
    • 1
    • 2
  • Alfons Geiger
    • 3
  1. 1.Institute of Chemical Kinetics and CombustionSB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Physikalische Chemie, Technische Universität DortmundDortmundGermany

Personalised recommendations