International Tables for Crystallography (2006). Vol. F. ch. 22.1, pp. 531-545   | 1 | 2 |
https://doi.org/10.1107/97809553602060000710

Chapter 22.1. Protein surfaces and volumes: measurement and use

Contents

  • 22.1. Protein surfaces and volumes: measurement and use  (pp. 531-545) | html | pdf | chapter contents |
    M. Gerstein, F. M. Richards, M. S. Chapman and M. L. Connolly
    • 22.1.1. Protein geometry: volumes, areas and distances  (pp. 531-539) | html | pdf |
      M. Gerstein and F. M. Richards
      • 22.1.1.1. Introduction  (p. 531) | html | pdf |
      • 22.1.1.2. Definitions of protein volume  (pp. 531-533) | html | pdf |
        • 22.1.1.2.1. Volume in terms of Voronoi polyhedra: overview  (p. 531) | html | pdf |
        • 22.1.1.2.2. The basic Voronoi construction  (pp. 531-532) | html | pdf |
          • 22.1.1.2.2.1. Integrating on a grid  (pp. 531-532) | html | pdf |
          • 22.1.1.2.2.2. Finding polyhedron vertices  (p. 532) | html | pdf |
          • 22.1.1.2.2.3. Collecting vertices and calculating volumes   (p. 532) | html | pdf |
        • 22.1.1.2.3. Adapting Voronoi polyhedra to proteins  (pp. 532-533) | html | pdf |
          • 22.1.1.2.3.1. Method B and a simplification of it: the ratio method  (pp. 532-533) | html | pdf |
          • 22.1.1.2.3.2. Vertex error  (p. 533) | html | pdf |
          • 22.1.1.2.3.3. `Chopping-down' method of finding vertices  (p. 533) | html | pdf |
          • 22.1.1.2.3.4. Radical-plane method  (p. 533) | html | pdf |
        • 22.1.1.2.4. Delaunay triangulation  (p. 533) | html | pdf |
      • 22.1.1.3. Definitions of protein surface  (pp. 534-536) | html | pdf |
        • 22.1.1.3.1. The problem of the protein surface  (p. 534) | html | pdf |
        • 22.1.1.3.2. Definitions of surface in terms of Voronoi polyhedra (the convex hull)  (p. 534) | html | pdf |
        • 22.1.1.3.3. Definitions of surface in terms of a probe sphere  (pp. 534-536) | html | pdf |
          • 22.1.1.3.3.1. van der Waals surface (VDWS)  (p. 535) | html | pdf |
          • 22.1.1.3.3.2. Solvent-accessible surface (SAS)  (p. 535) | html | pdf |
          • 22.1.1.3.3.3. Molecular surface as the sum of the contact and re-entrant surfaces (MS = CS + RS)  (p. 535) | html | pdf |
          • 22.1.1.3.3.4. Further points  (pp. 535-536) | html | pdf |
      • 22.1.1.4. Definitions of atomic radii  (pp. 536-537) | html | pdf |
        • 22.1.1.4.1. van der Waals radii  (pp. 536-537) | html | pdf |
        • 22.1.1.4.2. The probe radius  (p. 537) | html | pdf |
      • 22.1.1.5. Application of geometry calculations: the measurement of packing  (pp. 537-539) | html | pdf |
        • 22.1.1.5.1. Using volume to measure packing efficiency  (pp. 537-538) | html | pdf |
        • 22.1.1.5.2. The tight packing of the protein core  (p. 538) | html | pdf |
        • 22.1.1.5.3. Looser packing on the surface  (pp. 538-539) | html | pdf |
    • 22.1.2. Molecular surfaces: calculations, uses and representations  (pp. 539-545) | html | pdf |
      M. S. Chapman and M. L. Connolly
      • 22.1.2.1. Introduction  (pp. 539-540) | html | pdf |
        • 22.1.2.1.1. Uses of surface-area calculations  (p. 539) | html | pdf |
        • 22.1.2.1.2. Molecular, solvent-accessible and occluded surface areas  (pp. 539-540) | html | pdf |
        • 22.1.2.1.3. Hydration surface  (p. 540) | html | pdf |
        • 22.1.2.1.4. Hydrophobicity  (p. 540) | html | pdf |
      • 22.1.2.2. Calculation of surface area and energies of interaction  (pp. 540-541) | html | pdf |
        • 22.1.2.2.1. Introduction  (pp. 540-541) | html | pdf |
        • 22.1.2.2.2. Lee & Richards planar slices  (p. 541) | html | pdf |
        • 22.1.2.2.3. Connolly dot surface algorithm  (p. 541) | html | pdf |
        • 22.1.2.2.4. Marching-cube algorithm  (p. 541) | html | pdf |
        • 22.1.2.2.5. Complete and connected rolling algorithms  (p. 541) | html | pdf |
        • 22.1.2.2.6. Analytic surface calculations and the Gauss–Bonnet theorem  (p. 541) | html | pdf |
        • 22.1.2.2.7. Approximations to the surface  (p. 541) | html | pdf |
        • 22.1.2.2.8. Extended atoms account for missing hydrogen atoms  (p. 541) | html | pdf |
      • 22.1.2.3. Estimation of binding energies  (pp. 542-543) | html | pdf |
        • 22.1.2.3.1. Hydrophobicity  (p. 542) | html | pdf |
        • 22.1.2.3.2. Estimates of binding energies  (p. 542) | html | pdf |
        • 22.1.2.3.3. Other non-graphical interpretive methods using surface area  (pp. 542-543) | html | pdf |
      • 22.1.2.4. Graphical representations of shape and properties  (pp. 543-545) | html | pdf |
        • 22.1.2.4.1. Realistic  (pp. 543-544) | html | pdf |
          • 22.1.2.4.1.1. Shaded backbone  (p. 543) | html | pdf |
          • 22.1.2.4.1.2. `Connolly' and solid polyhedral surfaces  (p. 543) | html | pdf |
          • 22.1.2.4.1.3. Photorealistic rendering  (p. 543) | html | pdf |
          • 22.1.2.4.1.4. GRASP surfaces  (pp. 543-544) | html | pdf |
          • 22.1.2.4.1.5. Implementations in popular packages  (p. 544) | html | pdf |
        • 22.1.2.4.2. Schematic and two-dimensional representations such as `roadmap'  (pp. 544-545) | html | pdf |
      • 22.1.2.5. Conclusion  (p. 545) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 22.1.1.1. The Voronoi construction in two and three dimensions  (p. 531) | html | pdf |
      • Fig. 22.1.1.2. Labelling parts of Voronoi polyhedra  (p. 532) | html | pdf |
      • Fig. 22.1.1.3. Positioning of the dividing plane  (p. 532) | html | pdf |
      • Fig. 22.1.1.4. The `chopping-down' method of polyhedra construction  (p. 533) | html | pdf |
      • Fig. 22.1.1.5. Delaunay triangulation and its relation to the Voronoi construction  (p. 534) | html | pdf |
      • Fig. 22.1.1.6. The problem of the protein surface  (p. 534) | html | pdf |
      • Fig. 22.1.1.7. Definitions of the protein surface  (p. 535) | html | pdf |
      • Fig. 22.1.1.8. Packing efficiency  (p. 537) | html | pdf |
      • Fig. 22.1.2.1. Surfaces in a plane cut through a hypothetical molecule  (p. 540) | html | pdf |
      • Fig. 22.1.2.2. GRASP example  (p. 543) | html | pdf |
      • Fig. 22.1.2.3. (a) Solvent-accessible surface topology of a rhinovirus 14–drug complex (Kim et al  (p. 544) | html | pdf |
      • Fig. 22.1.2.4. Different projections illustrated with lysozyme  (p. 545) | html | pdf |
    • Tables
      • Table 22.1.1.1. Standard atomic radii (Å)  (p. 536) | html | pdf |
      • Table 22.1.1.2. Probe radii and their relation to surface definition  (p. 537) | html | pdf |
      • Table 22.1.1.3. Standard residue volumes  (p. 538) | html | pdf |
      • Table 22.1.1.4. Standard atomic volumes  (p. 539) | html | pdf |
      • Table 22.1.2.1. The atomic solvation parameters of Eisenberg & McLachlan (1986)  (p. 542) | html | pdf |