International Tables for Crystallography (2012). Vol. F. ch. 22.1, pp. 703-712   | 1 | 2 |
https://doi.org/10.1107/97809553602060000885

Chapter 22.1. Protein geometry: volumes, areas and distances

Contents

  • 22.1. Protein geometry: volumes, areas and distances  (pp. 703-712) | html | pdf | chapter contents |
    M. Gerstein and F. M. Richards
    • 22.1.1. Introduction  (p. 703) | html | pdf |
    • 22.1.2. Definitions of protein volume  (pp. 703-706) | html | pdf |
      • 22.1.2.1. Volume in terms of Voronoi polyhedra: overview  (p. 703) | html | pdf |
      • 22.1.2.2. The basic Voronoi construction  (pp. 703-704) | html | pdf |
        • 22.1.2.2.1. Integrating on a grid  (pp. 703-704) | html | pdf |
        • 22.1.2.2.2. Finding polyhedron vertices  (p. 704) | html | pdf |
        • 22.1.2.2.3. Collecting vertices and calculating volumes   (p. 704) | html | pdf |
      • 22.1.2.3. Adapting Voronoi polyhedra to proteins  (pp. 704-705) | html | pdf |
        • 22.1.2.3.1. Method B and a simplification of it: the ratio method  (pp. 704-705) | html | pdf |
        • 22.1.2.3.2. Vertex error  (p. 705) | html | pdf |
        • 22.1.2.3.3. `Chopping-down' method of finding vertices  (p. 705) | html | pdf |
        • 22.1.2.3.4. Radical-plane method  (p. 705) | html | pdf |
      • 22.1.2.4. Delaunay triangulation  (pp. 705-706) | html | pdf |
    • 22.1.3. Definitions of protein surface  (pp. 706-708) | html | pdf |
      • 22.1.3.1. The problem of the protein surface  (p. 706) | html | pdf |
      • 22.1.3.2. Definitions of surface in terms of Voronoi polyhedra (the convex hull)  (p. 706) | html | pdf |
      • 22.1.3.3. Definitions of surface in terms of a probe sphere  (pp. 707-708) | html | pdf |
        • 22.1.3.3.1. van der Waals surface (VDWS)  (p. 707) | html | pdf |
        • 22.1.3.3.2. Solvent-accessible surface (SAS)  (p. 707) | html | pdf |
        • 22.1.3.3.3. Molecular surface as the sum of the contact and re-entrant surfaces (MS = CS + RS)  (pp. 707-708) | html | pdf |
        • 22.1.3.3.4. Further points  (p. 708) | html | pdf |
    • 22.1.4. Definitions of atomic radii  (pp. 708-709) | html | pdf |
      • 22.1.4.1. van der Waals radii  (pp. 708-709) | html | pdf |
      • 22.1.4.2. The probe radius  (p. 709) | html | pdf |
    • 22.1.5. Application of geometry calculations: the measurement of packing  (pp. 709-711) | html | pdf |
      • 22.1.5.1. Using volume to measure packing efficiency  (pp. 709-710) | html | pdf |
      • 22.1.5.2. The tight packing of the protein core  (pp. 710-711) | html | pdf |
      • 22.1.5.3. Looser packing on the surface  (p. 711) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 22.1.2.1. The Voronoi construction in two and three dimensions  (p. 703) | html | pdf |
      • Fig. 22.1.2.2. Labelling parts of Voronoi polyhedra  (p. 704) | html | pdf |
      • Fig. 22.1.2.3. Positioning of the dividing plane  (p. 704) | html | pdf |
      • Fig. 22.1.2.4. The `chopping-down' method of polyhedra construction  (p. 705) | html | pdf |
      • Fig. 22.1.2.5. Delaunay triangulation and its relation to the Voronoi construction  (p. 706) | html | pdf |
      • Fig. 22.1.3.1. The problem of the protein surface  (p. 706) | html | pdf |
      • Fig. 22.1.3.2. Definitions of the protein surface  (p. 707) | html | pdf |
      • Fig. 22.1.5.1. Packing efficiency  (p. 709) | html | pdf |
    • Tables
      • Table 22.1.4.1. Standard atomic radii (Å)  (p. 708) | html | pdf |
      • Table 22.1.4.2. Probe radii and their relation to surface definition  (p. 709) | html | pdf |
      • Table 22.1.5.1. Standard residue volumes  (p. 710) | html | pdf |
      • Table 22.1.5.2. Standard atomic volumes  (p. 710) | html | pdf |