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Abstract

The area of molecular biology opens new applications for the communities of computer graphics, geometric modeling and computational geometry. It has been a usual understanding that the structure of a molecule is one of the major factors determining the functions of the molecule and therefore the efforts to better understand the molecular structure have been made.

It turns out that the analysis and the prediction of the spatial structure of a molecule usually takes a significant amount of computation even though the number of atoms involved in the molecule is relatively small. Examples are the protein-ligand docking, protein folding, etc.

In many molecules, however, the number of atoms is quite large. The number of atoms in the system varies from hundreds to thousands of thousand. The problem size gets even larger by both incorporating more details of a model and expanding the scope of the model from a single protein to a whole cell. This trend will continue as the computational resource gets more powerful and therefore the computational requirement will always remain critical.

In this paper, we propose a multi-resolution model for a protein (MRPM) to find a seemingly optimal trade-off between the computational requirement and the solution quality. There are two aspects of the proposal: The avoidance of computation and the delay of computation until it is really necessary.

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References

  1. Bernal, J.D., Finney, J.L.: Random close-packed hard-sphere model ii. Geometry of random packing of hard spheres. Discussions of the Faraday Society 43, 62–69 (1967)

    Article  Google Scholar 

  2. Richards, F.M.: The interpretation of protein structures: Total volume, group volume distributions and packing density. Journal of Molecular Biology 82, 1–14 (1974)

    Article  Google Scholar 

  3. Zimmer, R., Wöhler, M., Thiele, R.: New scoring schemes for protein fold recognition based on Voronoi contacts. Bioinformatics 14(3), 295–308 (1998)

    Article  Google Scholar 

  4. Angelov, B., Sadoc, J.F., Jullien, R., Soyer, A., Mornon, J.P., Chomilier, J.: Nonatomic solvent-driven Voronoi tessellation of proteins: An open tool to analyze protein folds. Proteins: Structure, Function, and Genetics 49(4), 446–456 (2002)

    Article  Google Scholar 

  5. Tsai, J., Taylor, R., Chothia, C., Gerstein, M.: The packing density in proteins: Standard radii and voulmes. J. Mol. Biol. 290, 253–266 (1999)

    Article  Google Scholar 

  6. Pontius, J., Richelle, J., Wodak, S.J.: Deviations from standard atomic volumes as a quality measure for protein crystal structures. Journal of Molecular Biology 264(1), 121–136 (1996)

    Article  Google Scholar 

  7. Dupuis, F., Sadoc, J.F., Mornon, J.P.: Protein secondary structure assignment through Voronoi tessellation. Proteins: Structure, Function, and Bioinformatics 55, 519–528 (2004)

    Article  Google Scholar 

  8. Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P.V., Subramaniam, S.: Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape. Proteins: Structure, Function, and Genetics 33, 1–17 (1998)

    Article  Google Scholar 

  9. Edelsbrunner, H., Facello, M., Liang, J.: On the definition and the construction of pockets in macromolecules. Discrete Applied Mathematics 88, 83–102 (1998)

    Article  MATH  Google Scholar 

  10. Will, H.M.: Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology. PhD thesis, Swiss Federal Institute of Technology, Zurich (1999)

    Google Scholar 

  11. 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  Google Scholar 

  12. Kim, D.S., Kim, D., Cho, Y.: Euclidean Voronoi diagrams of 3D spheres: Their construction and related problems from biochemistry. In: Martin, R., Bez, H., Sabin, M.A. (eds.) Mathematics of Surfaces XI. LNCS, vol. 3604, pp. 255–271. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Kim, D., Kim, D.S.: Region-expansion for the Voronoi diagram of 3D spheres. Computer-Aided Design 38(5), 417–430 (2006)

    Article  Google Scholar 

  14. 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 

  15. Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.P.: Interactive multi-resolution modeling on arbitrary meshes. In: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pp. 105–114. ACM Press, New York (1998)

    Chapter  Google Scholar 

  16. Rusinkiewicz, S., Levoy, M.: QSplat: A multiresolution point rendering system for large meshes. In: Proceedings of the SIGGRAPH 2000 (2000)

    Google Scholar 

  17. Bajaj, C.L., Pascucci, V., Shamir, A., Holt, R.J., Netravali, A.N.: Multiresolution molecular shapes. Technical report, TICAM, University of Texas at Austin (December 1999)

    Google Scholar 

  18. Zhang, G., Kazanielz, M.G., Blumberg, P.M., Hurley, J.H.: Crystal structure of the cys2 activator-binding domain of protein kinase cδ in complex with phorbol ester. Cell 81, 917–924 (1995)

    Article  Google Scholar 

  19. Cramer, P., Bushnell, D.A., Kornberg, R.D.: Structural basis of transcription: RNA polymerase II at 2.8 ångstrom resolution. Science 292(8), 1863–1876 (2007)

    Google Scholar 

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

    Article  Google Scholar 

  21. Hopfinger, A.J.: Conformational Properties of Macromolecules. Academic Press, London (1973)

    Google Scholar 

  22. Bourne, P.E., Weissig, H.: Structural Bioinformatics. Wiley-Liss, Chichester (2003)

    Google Scholar 

  23. Ghose, A.K., Viswanadhan, V.N., Wendoloski, J.J.: Prediction of hydrophobic (lipophilic) properties of small organic molecules using fragmental methods: An analysis of ALOGP and CLOGP methods. The Journal of Physical Chemistry A 102, 3762–3772 (1998)

    Article  Google Scholar 

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

    Google Scholar 

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Osvaldo Gervasi Marina L. Gavrilova

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Kim, DS. et al. (2007). Multi-Resolution Protein Model. In: Gervasi, O., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2007. ICCSA 2007. Lecture Notes in Computer Science, vol 4706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74477-1_59

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  • DOI: https://doi.org/10.1007/978-3-540-74477-1_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74475-7

  • Online ISBN: 978-3-540-74477-1

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