Ray-representation formalism for geometric computations on protein solid models

  • Michael G. Prisant
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1148)


Ray-representation or ray-rep formalism provides a comprehensive and simple approach for geometric computations on molecular solid models. These methods allow model formulation in terms of simple constructive solid geometry. In particular, the van der Waals exclusion volume is described by computing the ray-representation of a union of spheres and the solvent exclusion volume is computed by Minkowski dilation and erosion. Volume and area properties are calculated, respectively, by a ”pile-of-bricks” and ”collocation-of-tiles” interpretation of the rayrep. Labeling the chemical character of surface patches is facilitated by the intrinsic point ordering of the ray-rep. Definition of internal cavities can be accomplished by equivalence-set clustering of internal void segments. Finally, a Boolean intersection procedure determines placement of crystallographic waters with respect to the protein solvent excluded volume.


Molecular Surface Exit Point Probe Sphere Constructive Solid Geometry Compound Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    F. M. Richards. Folded and unfolded proteins: An introduction. In Thomas E. Creighton, editor, Protein Folding, pages 1–58. W. H. Freeman and Company, New York, 1992.Google Scholar
  2. 2.
    J. L. Finney. Volume occupation, environment and accessibility in proteins, the problem of the protein surface. J. Mol. Biol., 96:721–732, 1975.CrossRefGoogle Scholar
  3. 3.
    Cyrus Chothia. The nature of the accessible and buried surfaces in proteins. J. Mol. Biol., 105:1–14, 1976.CrossRefPubMedGoogle Scholar
  4. 4.
    C. Frommel. The apolar surface area of amino acids and its empirical correlation with hydrophobic free energy. J. Theor. Biol., 111:247–260, 1984.PubMedGoogle Scholar
  5. 5.
    D. Eisenberg and A. D. McLachlan. Solvation energy in protein folding and binding. Nature, 319:199–203, 1986.CrossRefPubMedGoogle Scholar
  6. 6.
    Irwin D. Kuntz. Structure-based strategies for drug design and discovery. Science, 257:1078–1082, 1992.PubMedGoogle Scholar
  7. 7.
    A. A. G. Requicha. Mathematical models of solid objects. Technical Report Technical Memorandum 28, Production Automation Project, University of Rochester, Available from CPA/COMEPP, Cornell University, Ithaca, NY 14853-7501, November 1977.Google Scholar
  8. 8.
    A. A. G. Requicha and R. B. Tilove. Mathematical foundations of constructive solid geometry: general topology of closed regular sets. Technical Report Technical Memorandum 27, Production Automation Project, University of Rochester, Available from CPA/COMEPP, Cornell University, Ithaca, NY 14853-7501, June 1978.Google Scholar
  9. 9.
    J. P. Menon, R. J. Marisa, and J. Zagajac. More powerful solid modeling through ray representations. Technical Report CPA92-4, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, 1992.Google Scholar
  10. 10.
    J. P. Menon and H. B. Voelcker. Mathematical foundations: set theoretic properties of ray representations and minkowski operations on solids. Technical Report CPA92-9, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, January 1992.Google Scholar
  11. 11.
    John Ellis, Gershon Kedem, Richard Marisa, Jai Menon, and Herbert Voelcker. Breaking barriers in solid modeling. Mechanical Engineering, pages 28–34, February 1991.Google Scholar
  12. 12.
    M. S. Head, G. Kedem, and M. G. Prisant. Application of the ray representation and a massively parallel special purpose computer to problems of protein structure and function: I. Methodology for calculation of molecular contact surface, volume and internal free space. Technical Report CS-1994-31, Department of Computer Science, Duke University, 1994.Google Scholar
  13. 13.
    Lawrence R. Dodd and Doros N. Theodorou. Analytical treatment of the volume and surface area of molecules formed by an arbitrary collection of unequal spheres intersected by planes. Mol. Phys., 72(6):1313–1345, 1991.Google Scholar
  14. 14.
    Frederic M. Richards. Areas, volumes, packing, and protein structure. Ann. Rev. Biophys. Bioeng., 6:151–176, 1977.CrossRefGoogle Scholar
  15. 15.
    Michael L. Connolly. Solvent-accessible surfaces of proteins and nucleic acids. Science, 221(4612):709–713, August 1983.PubMedGoogle Scholar
  16. 16.
    Michael L. Connolly. Analytical molecular surface calculation. J. Appl. Crystallogr., 16:548–558, 1983.CrossRefGoogle Scholar
  17. 17.
    Michael L. Connolly. The molecular surface package. J. Mol. Graphics, 11:139–141, 1993.CrossRefGoogle Scholar
  18. 18.
    Juan Luis Pascual-Ahuir and Estanislao Silla. GEPOL: An improved description of molecular surface. I. building the spherical surface set. J. Comp. Chem., 11(9):1047–1060, 1990.CrossRefGoogle Scholar
  19. 19.
    W. Heiden, T. Goetze, and J. Brickmann. Fast generation of molecular surfaces from 3D data fields with an enhanced ”marching cube” algorithm. J. Comp. Chem., 14(2):246–250, 1993.CrossRefGoogle Scholar
  20. 20.
    Michel Sanner, Arthur J. Olson, and Jean Claude Spehner. Fast and robust computation of molecular surfaces. In Proc. 11th ACM Symp. Comp. Geom, C6-C7. ACM, 1995.Google Scholar
  21. 21.
    H. Edelsbrunner and E. Mucke. Three-dimensional alpha shapes. ACM Transactions on Graphics, 13(1):43–72, 1994.CrossRefGoogle Scholar
  22. 22.
    Amitabh Varshney, Frederick P. Brooks Jr., and William V. Wright. Linearly scalable computation of smooth molecular surfaces. IEEE Computer Graphics and Applications, 14(5):19–25, 1994.CrossRefGoogle Scholar
  23. 23.
    H. J. A. Heijmans and C. Ronse. The algebraic basis of mathematical morphology: I. dilations and erosions. Computer Vision, Graphics, and Image Processing, 50:245–295, 1990.Google Scholar
  24. 24.
    Jean-Paul Serra. Image Analysis and Mathematical Morphology. Academic Press, New York, 1982.Google Scholar
  25. 25.
    Benoit E. Mandelbroit. The Fractal Geometry of Nature. Freeman, New York, 1983.Google Scholar
  26. 26.
    Dietrich Stauffer and Amnon Aharony. Introduction to Percolation Theory. Taylor and Francis, Washington, DC, 1992.Google Scholar
  27. 27.
    J. Hoshen and R. Kopelman. Percolation and cluster distribution. I. cluster multiple labeling technique and critical concentration algorithm. Phys. Rev. B., 14(8):3438–3435, 1976.CrossRefGoogle Scholar
  28. 28.
    R. Varadarajan and F. M. Richards. Crystallographic structures of ribonuclease s variants with nonpolar substitution at position 13: Packing and cavities. Biochemistry, 31:12315–12327, 1992.CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Michael G. Prisant
    • 1
  1. 1.Departments of Chemistry and Computer ScienceDuke UniversityDurham

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