(International Tables) Crystallography of biological macromolecules

International Tables for Crystallography
Volume F: Crystallography of biological macromolecules

First online edition (2006) ISBN: 978-0-7923-6857-1 eISBN: 978-1-4020-5416-7 doi: 10.1107/97809553602060000106

Edited by M. G. Rossmann and E. Arnold

Preface (p. xxiii) | html | pdf |
E. Arnold and M. G. Rossmann

Part 1. Introduction
- 1.1. Overview (pp. 1-3) | html | pdf | chapter contents |
  E. Arnold and M. G. Rossmann
- 1.2. Historical background (pp. 4-9) | html | pdf | chapter contents |
  M. G. Rossmann
  - 1.2.1. Introduction (p. 4) | html | pdf |
  - 1.2.2. 1912 to the 1950s (pp. 4-5) | html | pdf |
  - 1.2.3. The first investigations of biological macromolecules (p. 5) | html | pdf |
  - 1.2.4. Globular proteins in the 1950s (pp. 5-7) | html | pdf |
  - 1.2.5. The first protein structures (1957 to the 1970s) (pp. 7-8) | html | pdf |
  - 1.2.6. Technological developments (1958 to the 1980s) (pp. 8-9) | html | pdf |
  - 1.2.7. Meetings (p. 9) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.2.4.1. Change of structure amplitude for horse haemoglobin as a function of salt concentration in the suspension medium of the low-order h 0 l reflections at various lattice shrinkage stages (C, C′, D, E, F, G, H, J) (p. 6) | html | pdf |
    - Fig. 1.2.5.1. A model of the myoglobin molecule at 6 Å resolution (p. 7) | html | pdf |
    - Fig. 1.2.5.2. Cylindrical sections through a helical segment of a myoglobin polypeptide chain (p. 7) | html | pdf |
    - Fig. 1.2.6.1. The 2 Å-resolution map of sperm-whale myoglobin was represented by coloured Meccano-set clips on a forest of vertical rods (p. 8) | html | pdf |
- 1.3. Macromolecular crystallography and medicine (pp. 10-25) | html | pdf | chapter contents |
  W. G. J. Hol and C. L. M. J. Verlinde
  - 1.3.1. Introduction (p. 10) | html | pdf |
  - 1.3.2. Crystallography and medicine (pp. 10-11) | html | pdf |
  - 1.3.3. Crystallography and genetic diseases (pp. 11-12) | html | pdf |
  - 1.3.4. Crystallography and development of novel pharmaceuticals (pp. 12-24) | html | pdf |
    - 1.3.4.1. Infectious diseases (pp. 13-15) | html | pdf |
      - 1.3.4.1.1. Viral diseases (p. 13) | html | pdf |
      - 1.3.4.1.2. Bacterial diseases (p. 13) | html | pdf |
      - 1.3.4.1.3. Protozoan infections (pp. 13-15) | html | pdf |
      - 1.3.4.1.4. Fungi (p. 15) | html | pdf |
      - 1.3.4.1.5. Helminths (p. 15) | html | pdf |
    - 1.3.4.2. Resistance (pp. 15-21) | html | pdf |
    - 1.3.4.3. Non-communicable diseases (pp. 21-24) | html | pdf |
      - 1.3.4.3.1. Cancers (p. 21) | html | pdf |
      - 1.3.4.3.2. Diabetes (p. 21) | html | pdf |
      - 1.3.4.3.3. Blindness (p. 21) | html | pdf |
      - 1.3.4.3.4. Cardiovascular disorders (p. 21) | html | pdf |
      - 1.3.4.3.5. Neurological disorders (p. 24) | html | pdf |
    - 1.3.4.4. Drug metabolism and crystallography (p. 24) | html | pdf |
    - 1.3.4.5. Drug manufacturing and crystallography (p. 24) | html | pdf |
  - 1.3.5. Vaccines, immunology and crystallography (pp. 24-25) | html | pdf |
  - 1.3.6. Outlook and dreams (p. 25) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.3.4.1. The structure-based drug design cycle (p. 13) | html | pdf |
  - Tables
    - Table 1.3.3.1. Crystal structures and genetic diseases (p. 11) | html | pdf |
    - Table 1.3.4.1. Important human pathogenic viruses and their proteins (pp. 14-15) | html | pdf |
    - Table 1.3.4.2. Protein structures of important human pathogenic bacteria (pp. 16-18) | html | pdf |
    - Table 1.3.4.3. Protein structures of important human pathogenic protozoa, fungi and helminths (pp. 19-20) | html | pdf |
    - Table 1.3.4.4. Mechanisms of resistance (p. 20) | html | pdf |
    - Table 1.3.4.5. Important human protein structures in drug design (pp. 22-23) | html | pdf |
- 1.4. Perspectives for the future (pp. 26-43) | html | pdf | chapter contents |
  E. Arnold and M. G. Rossmann
  - 1.4.1. Gazing into the crystal ball (pp. 26-27) | html | pdf |
    E. Arnold
    - 1.4.1.1. What can we expect to see in the future of science and technology in general? (p. 26) | html | pdf |
    - 1.4.1.2. How will crystallography change in the future? (pp. 26-27) | html | pdf |
  - 1.4.2. Brief comments on Gazing into the crystal ball (p. 27) | html | pdf |
    M. G. Rossmann

Part 2. Basic crystallography
- 2.1. Introduction to basic crystallography (pp. 45-63) | html | pdf | chapter contents |
  J. Drenth
  - 2.1.1. Crystals (pp. 45-46) | html | pdf |
  - 2.1.2. Symmetry (pp. 46-47) | html | pdf |
  - 2.1.3. Point groups and crystal systems (pp. 47-52) | html | pdf |
  - 2.1.4. Basic diffraction physics (pp. 52-57) | html | pdf |
    - 2.1.4.1. Diffraction by one electron (pp. 52-53) | html | pdf |
    - 2.1.4.2. Scattering by a system of two electrons (p. 53) | html | pdf |
    - 2.1.4.3. Scattering by atoms (pp. 53-54) | html | pdf |
      - 2.1.4.3.1. Scattering by one atom (pp. 53-54) | html | pdf |
      - 2.1.4.3.2. Scattering by a plane of atoms (p. 54) | html | pdf |
    - 2.1.4.4. Anomalous dispersion (pp. 54-55) | html | pdf |
    - 2.1.4.5. Scattering by a crystal (pp. 55-56) | html | pdf |
    - 2.1.4.6. The structure factor (pp. 56-57) | html | pdf |
  - 2.1.5. Reciprocal space and the Ewald sphere (pp. 57-58) | html | pdf |
  - 2.1.6. Mosaicity and integrated reflection intensity (pp. 58-59) | html | pdf |
  - 2.1.7. Calculation of electron density (pp. 59-60) | html | pdf |
  - 2.1.8. Symmetry in the diffraction pattern (pp. 60-61) | html | pdf |
  - 2.1.9. The Patterson function (pp. 61-62) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.1.1.1. One unit cell with axes a , b and c (p. 45) | html | pdf |
    - Fig. 2.1.1.2. A set of $[5 \times 3 \times 3]$ unit cells (p. 45) | html | pdf |
    - Fig. 2.1.1.3. A two-dimensional lattice with $[3 \times 3]$ unit cells (p. 46) | html | pdf |
    - Fig. 2.1.1.4. Non-centred and centred unit cells (p. 46) | html | pdf |
    - Fig. 2.1.3.1. How to construct a stereographic projection (p. 47) | html | pdf |
    - Fig. 2.1.3.2. A rhombohedral unit cell (p. 47) | html | pdf |
    - Fig. 2.1.3.3. The 14 Bravais lattices (p. 52) | html | pdf |
    - Fig. 2.1.4.1. The electric vector of a monochromatic and polarized X-ray beam is in the plane (p. 53) | html | pdf |
    - Fig. 2.1.4.2. The black dots are electrons (p. 53) | html | pdf |
    - Fig. 2.1.4.3. The direction of the incident wave is indicated by $[{\bf s}_{o}]$ and that of the scattered wave by s (p. 53) | html | pdf |
    - Fig. 2.1.4.4. An Argand diagram for the scattering by two electrons (p. 54) | html | pdf |
    - Fig. 2.1.4.5. The atomic scattering factor f for carbon as a function of $[\sin \theta /\lambda]$ , expressed in units of the scattering by one electron (p. 54) | html | pdf |
    - Fig. 2.1.4.6. S is the X-ray source and D is the detector (p. 54) | html | pdf |
    - Fig. 2.1.4.7. Schematic picture of the Argand diagram for the scattering by atoms in a plane (p. 55) | html | pdf |
    - Fig. 2.1.4.8. The atomic scattering factor as a vector in the Argand diagram (p. 55) | html | pdf |
    - Fig. 2.1.4.9. X-ray diffraction by a crystal is, in Bragg's conception, reflection by lattice planes (p. 56) | html | pdf |
    - Fig. 2.1.4.10. The Wilson plot for phospholipase A ₂ with data to 1.7 Å resolution (p. 57) | html | pdf |
    - Fig. 2.1.5.1. A two-dimensional real unit cell is drawn together with its reciprocal unit cell (p. 58) | html | pdf |
    - Fig. 2.1.5.2. The circle is, in fact, a sphere with radius $[1/\lambda]$ (p. 58) | html | pdf |
    - Fig. 2.1.7.1. An Argand diagram for the structure factors of the two members of a Friedel pair (p. 60) | html | pdf |
    - Fig. 2.1.9.1. ( a ) A two-dimensional unit cell with two atoms (p. 62) | html | pdf |
  - Tables
    - Table 2.1.2.1. The most common space groups for protein crystals (p. 46) | html | pdf |
    - Table 2.1.3.1. The 11 enantiomorphic point groups (pp. 48-49) | html | pdf |
    - Table 2.1.3.2. The 11 point groups with a centre of symmetry (pp. 50-51) | html | pdf |
    - Table 2.1.3.3. The icosahedral point group 532 (p. 51) | html | pdf |
    - Table 2.1.3.4. The seven crystal systems (p. 52) | html | pdf |
    - Table 2.1.4.1. The position of the K α edge of different elements (p. 54) | html | pdf |

Part 3. Techniques of molecular biology
- 3.1. Preparing recombinant proteins for X-ray crystallography (pp. 65-80) | html | pdf | chapter contents |
  S. H. Hughes and A. M. Stock
  - 3.1.1. Introduction (p. 65) | html | pdf |
  - 3.1.2. Overview (p. 65) | html | pdf |
  - 3.1.3. Engineering an expression construct (pp. 66-67) | html | pdf |
    - 3.1.3.1. Choosing an expression system (p. 66) | html | pdf |
    - 3.1.3.2. Creating an expression construct (p. 66) | html | pdf |
    - 3.1.3.3. Addition of tags or domains (p. 67) | html | pdf |
  - 3.1.4. Expression systems (pp. 67-74) | html | pdf |
    - 3.1.4.1. E. coli (pp. 67-71) | html | pdf |
    - 3.1.4.2. Yeast (pp. 71-72) | html | pdf |
    - 3.1.4.3. Baculoviruses and insect cells (pp. 72-73) | html | pdf |
    - 3.1.4.4. Mammalian cells (pp. 73-74) | html | pdf |
  - 3.1.5. Protein purification (pp. 75-77) | html | pdf |
    - 3.1.5.1. Conventional protein purification (pp. 75-76) | html | pdf |
    - 3.1.5.2. Affinity purification (pp. 76-77) | html | pdf |
    - 3.1.5.3. Purifying and refolding denatured proteins (p. 77) | html | pdf |
  - 3.1.6. Characterization of the purified product (pp. 77-78) | html | pdf |
    - 3.1.6.1. Assessment of sample homogeneity (pp. 77-78) | html | pdf |
    - 3.1.6.2. Protein storage (p. 78) | html | pdf |
  - 3.1.7. Reprise (pp. 78-79) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.1.3.1. Creating an expression construct (p. 67) | html | pdf |
    - Fig. 3.1.5.1. Protein purification strategy (p. 75) | html | pdf |
  - Tables
    - Table 3.1.4.1. Strategies for improving expression in E. coli (p. 68) | html | pdf |

Part 4. Crystallization
- 4.1. General methods (pp. 81-93) | html | pdf | chapter contents |
  R. Giegé and A. McPherson
  - 4.1.1. Introduction (p. 81) | html | pdf |
  - 4.1.2. Crystallization arrangements and methodologies (pp. 81-86) | html | pdf |
    - 4.1.2.1. General considerations (p. 81) | html | pdf |
    - 4.1.2.2. Batch crystallizations (pp. 81-82) | html | pdf |
    - 4.1.2.3. Dialysis methods (p. 82) | html | pdf |
    - 4.1.2.4. Vapour diffusion methods (pp. 82-84) | html | pdf |
    - 4.1.2.5. Interface diffusion and the gel acupuncture method (p. 84) | html | pdf |
    - 4.1.2.6. Crystallization in gelled media (pp. 84-86) | html | pdf |
    - 4.1.2.7. Miscellaneous crystallization methods (p. 86) | html | pdf |
    - 4.1.2.8. Seeding (p. 86) | html | pdf |
  - 4.1.3. Parameters that affect crystallization of macromolecules (pp. 86-88) | html | pdf |
    - 4.1.3.1. Crystallizing agents (pp. 86-87) | html | pdf |
    - 4.1.3.2. Other chemical, physical and biochemical variables (pp. 87-88) | html | pdf |
    - 4.1.3.3. Additives (p. 88) | html | pdf |
  - 4.1.4. How to crystallize a new macromolecule (pp. 88-89) | html | pdf |
    - 4.1.4.1. Rules and general principles (p. 88) | html | pdf |
    - 4.1.4.2. Purity and homogeneity (p. 88) | html | pdf |
    - 4.1.4.3. Sample preparation (pp. 88-89) | html | pdf |
    - 4.1.4.4. Strategic concerns: a summary (p. 89) | html | pdf |
  - 4.1.5. Techniques for physical characterization of crystallization (pp. 89-91) | html | pdf |
    - 4.1.5.1. Techniques for studying prenucleation and nucleation (pp. 89-90) | html | pdf |
    - 4.1.5.2. Techniques for studying growth mechanisms (pp. 90-91) | html | pdf |
    - 4.1.5.3. Techniques for evaluating crystal perfection (p. 91) | html | pdf |
  - 4.1.6. Use of microgravity (pp. 91-93) | html | pdf |
    - 4.1.6.1. Why microgravity? (p. 91) | html | pdf |
    - 4.1.6.2. Instrumentation (p. 91) | html | pdf |
    - 4.1.6.3. Present results: a summary (pp. 91-92) | html | pdf |
    - 4.1.6.4. Interpretation of data (pp. 92-93) | html | pdf |
    - 4.1.6.5. The future of crystallization under microgravity (p. 93) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 4.1.2.1. Principles of the major methods currently used to crystallize biological macromolecules (p. 82) | html | pdf |
    - Fig. 4.1.2.2. Two versions of boxes for vapour diffusion crystallization (p. 83) | html | pdf |
    - Fig. 4.1.2.3. Principle of the gel acupuncture method for the crystallization of proteins by counter-diffusion (p. 84) | html | pdf |
    - Fig. 4.1.5.1. Visualization of the surface of yeast tRNA ^Phe crystals by AFM (p. 90) | html | pdf |
  - Tables
    - Table 4.1.2.1. Factors affecting crystallization (p. 83) | html | pdf |
    - Table 4.1.2.2. Crystallizing agents for protein crystallization (pp. 85-86) | html | pdf |
- 4.2. Crystallization of membrane proteins (pp. 94-99) | html | pdf | chapter contents |
  H. Michel
  - 4.2.1. Introduction (p. 94) | html | pdf |
  - 4.2.2. Principles of membrane-protein crystallization (p. 94) | html | pdf |
  - 4.2.3. General properties of detergents relevant to membrane-protein crystallization (pp. 94-98) | html | pdf |
  - 4.2.4. The `small amphiphile concept' (p. 98) | html | pdf |
  - 4.2.5. Membrane-protein crystallization with the help of antibody Fv fragments (pp. 98-99) | html | pdf |
  - 4.2.6. Membrane-protein crystallization using cubic bicontinuous lipidic phases (p. 99) | html | pdf |
  - 4.2.7. General recommendations (p. 99) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 4.2.1.1. Compilation of membrane proteins with known structures, including crystallization conditions and key references for the structure determinations (pp. 95-96) | html | pdf |
    - Table 4.2.2.1. Potentially useful detergents for membrane-protein crystallizations with molecular weights and CMCs [in water, from Michel (1991) or as provided by the vendor] (p. 97) | html | pdf |
    - Table 4.2.3.1. Summary of the results of attempts to crystallize the two-subunit cytochrome c oxidase from the soil bacterium Paracoccus denitrificans using different detergents (after Ostermeier et al. , 1997) (p. 98) | html | pdf |
- 4.3. Application of protein engineering to improve crystal properties (pp. 100-110) | html | pdf | chapter contents |
  D. R. Davies and A. Burgess Hickman
  - 4.3.1. Introduction (p. 100) | html | pdf |
  - 4.3.2. Improving solubility (pp. 100-101) | html | pdf |
  - 4.3.3. Use of fusion proteins (p. 101) | html | pdf |
  - 4.3.4. Mutations to accelerate crystallization (p. 101) | html | pdf |
  - 4.3.5. Mutations to improve diffraction quality (pp. 101-102) | html | pdf |
  - 4.3.6. Avoiding protein heterogeneity (p. 102) | html | pdf |
  - 4.3.7. Engineering crystal contacts to enhance crystallization in a particular crystal form (pp. 102-103) | html | pdf |
  - 4.3.8. Engineering heavy-atom sites (p. 103) | html | pdf |
  - References | html | pdf |

Part 5. Crystal properties and handling
- 5.1. Crystal morphology, optical properties of crystals and crystal mounting (pp. 111-116) | html | pdf | chapter contents |
  H. L. Carrell and J. P. Glusker
  - 5.1.1. Crystal morphology and optical properties (pp. 111-114) | html | pdf |
    - 5.1.1.1. Crystal growth habits (pp. 111-112) | html | pdf |
      - 5.1.1.1.1. The shape of a crystal – growth habits (p. 111) | html | pdf |
      - 5.1.1.1.2. Quality of protein crystals (p. 111) | html | pdf |
      - 5.1.1.1.3. Polymorphism (pp. 111-112) | html | pdf |
      - 5.1.1.1.4. Twinning (p. 112) | html | pdf |
    - 5.1.1.2. Properties of crystal faces (pp. 112-113) | html | pdf |
      - 5.1.1.2.1. Indexing crystal faces (pp. 112-113) | html | pdf |
      - 5.1.1.2.2. Measurement of crystal habit (p. 113) | html | pdf |
    - 5.1.1.3. Optical properties (p. 113) | html | pdf |
      - 5.1.1.3.1. Crystals between crossed polarizers (p. 113) | html | pdf |
      - 5.1.1.3.2. Refractive indices and what they tell us about structure (p. 113) | html | pdf |
    - 5.1.1.4. Packing of molecules in crystals (p. 114) | html | pdf |
  - 5.1.2. Crystal mounting (pp. 114-116) | html | pdf |
    - 5.1.2.1. Introduction to crystal mounting (p. 114) | html | pdf |
    - 5.1.2.2. Tools for crystal mounting (pp. 114-115) | html | pdf |
      - 5.1.2.2.1. Microscope (p. 114) | html | pdf |
      - 5.1.2.2.2. Capillaries (pp. 114-115) | html | pdf |
      - 5.1.2.2.3. Thumb pump (p. 115) | html | pdf |
      - 5.1.2.2.4. Heater (p. 115) | html | pdf |
    - 5.1.2.3. Capillary mounting (pp. 115-116) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 5.1.1.1. Crystal faces (p. 112) | html | pdf |
    - Fig. 5.1.2.1. Tools commonly used for mounting crystals (p. 114) | html | pdf |
    - Fig. 5.1.2.2. Mounting a crystal in a capillary (p. 115) | html | pdf |
- 5.2. Crystal-density measurements (pp. 117-123) | html | pdf | chapter contents |
  E. M. Westbrook
  - 5.2.1. Introduction (p. 117) | html | pdf |
  - 5.2.2. Solvent in macromolecular crystals (p. 117) | html | pdf |
  - 5.2.3. Matthews number (p. 117) | html | pdf |
  - 5.2.4. Algebraic concepts (pp. 117-118) | html | pdf |
  - 5.2.5. Experimental estimation of hydration (p. 118) | html | pdf |
  - 5.2.6. Methods for measuring crystal density (pp. 118-121) | html | pdf |
    - 5.2.6.1. Pycnometry (pp. 118-119) | html | pdf |
    - 5.2.6.2. Volumenometry (p. 119) | html | pdf |
    - 5.2.6.3. The method of Archimedes (p. 119) | html | pdf |
    - 5.2.6.4. Immersion microbalance (p. 119) | html | pdf |
    - 5.2.6.5. Flotation (p. 119) | html | pdf |
    - 5.2.6.6. Tomographic crystal-volume measurement (pp. 119-120) | html | pdf |
    - 5.2.6.7. Gradient-tube method (pp. 120-121) | html | pdf |
  - 5.2.7. How to handle the solvent density (p. 121) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 5.2.6.1. Organic liquids for density determinations (p. 120) | html | pdf |
    - Table 5.2.6.2. Inorganic salts for density determinations (p. 120) | html | pdf |

Part 6. Radiation sources and optics
- 6.1. X-ray sources (pp. 125-132) | html | pdf | chapter contents |
  U. W. Arndt
  - 6.1.1. Overview (p. 125) | html | pdf |
  - 6.1.2. Generation of X-rays (pp. 125-127) | html | pdf |
    - 6.1.2.1. Stationary-target X-ray tubes (p. 125) | html | pdf |
    - 6.1.2.2. Rotating-anode X-ray tubes (pp. 125-126) | html | pdf |
    - 6.1.2.3. Microfocus X-ray tubes (p. 126) | html | pdf |
    - 6.1.2.4. Synchrotron-radiation sources (pp. 126-127) | html | pdf |
  - 6.1.3. Properties of the X-ray beam (pp. 127-129) | html | pdf |
    - 6.1.3.1. Beam size (p. 128) | html | pdf |
    - 6.1.3.2. X-ray wavelength (p. 128) | html | pdf |
    - 6.1.3.3. Spectral composition (p. 128) | html | pdf |
    - 6.1.3.4. Intensity (pp. 128-129) | html | pdf |
    - 6.1.3.5. Cross fire (p. 129) | html | pdf |
    - 6.1.3.6. Beam stability (p. 129) | html | pdf |
  - 6.1.4. Beam conditioning (pp. 129-132) | html | pdf |
    - 6.1.4.1. X-ray mirrors (pp. 129-131) | html | pdf |
    - 6.1.4.2. Focusing collimators for microfocus sources (p. 131) | html | pdf |
    - 6.1.4.3. Other focusing collimators (p. 131) | html | pdf |
    - 6.1.4.4. Crystal monochromators (pp. 131-132) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 6.1.2.1. Section through a sealed X-ray tube (p. 125) | html | pdf |
    - Fig. 6.1.2.2. Synchrotron radiation emitted by a relativistic electron travelling in a curved trajectory (p. 126) | html | pdf |
    - Fig. 6.1.2.3. Comparison of the spectra from the storage ring SPEAR (p. 127) | html | pdf |
    - Fig. 6.1.2.4. Main components of a dedicated electron storage-ring synchrotron-radiation source (p. 127) | html | pdf |
    - Fig. 6.1.2.5. Electron trajectory within a multipole wiggler or undulator (p. 127) | html | pdf |
    - Fig. 6.1.2.6. Spectral distribution and critical wavelengths for ( a ) a dipole magnet, ( b ) a wavelength shifter and ( c ) a multipole wiggler at the ESRF (p. 128) | html | pdf |
    - Fig. 6.1.4.1. Production of a point focus by successive reflections at two orthogonal curved mirrors (p. 130) | html | pdf |
    - Fig. 6.1.4.2. The `catamegonic' arrangement of Montel (1957), in which two confocal mirrors with orthogonal curvatures lie side-by-side (p. 130) | html | pdf |
    - Fig. 6.1.4.3. Mirror bender (after Franks, 1955) (p. 130) | html | pdf |
    - Fig. 6.1.4.4. Triangular mirror bender as described by Lemonnier et al (p. 130) | html | pdf |
    - Fig. 6.1.4.5. Mirror holder with machined slots for two orthogonal pairs of curved mirrors (after Arndt, Duncumb et al (p. 130) | html | pdf |
    - Fig. 6.1.4.6. Ellipsoidal mirror for use with a microfocus X-ray tube, where x ₁ is ∼15 mm (p. 131) | html | pdf |
    - Fig. 6.1.4.7. A polycapillary collimator (after Bly & Gibson, 1996) (p. 131) | html | pdf |
  - Tables
    - Table 6.1.2.1. Standard X-ray tube inserts (p. 125) | html | pdf |
- 6.2. Neutron sources (pp. 133-142) | html | pdf | chapter contents |
  B. P. Schoenborn and R. Knott
  - 6.2.1. Reactors (pp. 133-137) | html | pdf |
    - 6.2.1.1. Basic reactor physics (p. 133) | html | pdf |
    - 6.2.1.2. Moderators for neutron scattering (pp. 133-134) | html | pdf |
      - 6.2.1.2.1. Thermal moderators (p. 134) | html | pdf |
      - 6.2.1.2.2. Cold moderators (p. 134) | html | pdf |
    - 6.2.1.3. Beamline components (pp. 134-136) | html | pdf |
      - 6.2.1.3.1. Collimators and filters (p. 135) | html | pdf |
      - 6.2.1.3.2. Crystal monochromators (p. 135) | html | pdf |
      - 6.2.1.3.3. Multilayer monochromators and supermirrors (pp. 135-136) | html | pdf |
      - 6.2.1.3.4. Velocity selectors (p. 136) | html | pdf |
      - 6.2.1.3.5. Neutron guides (p. 136) | html | pdf |
    - 6.2.1.4. Detectors (pp. 136-137) | html | pdf |
      - 6.2.1.4.1. Multiwire proportional counters (p. 136) | html | pdf |
      - 6.2.1.4.2. Image plates (pp. 136-137) | html | pdf |
    - 6.2.1.5. Instrument resolution functions (p. 137) | html | pdf |
  - 6.2.2. Spallation neutron sources (pp. 137-139) | html | pdf |
    - 6.2.2.1. Spallation neutron production (pp. 137-138) | html | pdf |
    - 6.2.2.2. Moderators (pp. 138-139) | html | pdf |
    - 6.2.2.3. Beamline optics (p. 139) | html | pdf |
    - 6.2.2.4. Time-of-flight techniques (p. 139) | html | pdf |
    - 6.2.2.5. Data-collection considerations (p. 139) | html | pdf |
  - 6.2.3. Summary (p. 139) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 6.2.1.1. Schematic of the High Flux Beam Reactor at the Brookhaven National Laboratory (USA) (p. 133) | html | pdf |
    - Fig. 6.2.1.2. Neutron wavelength distributions for a thermal (310 K) and a cold (30 K) neutron moderator in a `typical' dedicated beam reactor (p. 134) | html | pdf |
    - Fig. 6.2.1.3. ( a ) Schematic vector diagram for an elastic neutron-scattering event (p. 134) | html | pdf |
    - Fig. 6.2.1.4. A generic neutron-scattering instrument illustrating the classes of facilities and operators important to instrument design and assessment (p. 135) | html | pdf |
    - Fig. 6.2.2.1. Schematic presentation of the various nuclear processes encountered in spallation (p. 137) | html | pdf |
    - Fig. 6.2.2.2. Schematic diagram of a spallation target module depicting the inner Be and outer Pb reflector (p. 138) | html | pdf |
    - Fig. 6.2.2.3. Neutron flux given as a time–wavelength spectrum for ( a ) a fully decoupled system and ( b ) for a fully coupled system (p. 138) | html | pdf |

Part 7. X-ray detectors
- 7.1. Comparison of X-ray detectors (pp. 143-147) | html | pdf | chapter contents |
  S. M. Gruner, E. F. Eikenberry and M. W. Tate
  - 7.1.1. Commonly used detectors: general considerations (pp. 143-144) | html | pdf |
  - 7.1.2. Evaluating and comparing detectors (pp. 144-145) | html | pdf |
  - 7.1.3. Characteristics of different detector approaches (pp. 145-147) | html | pdf |
    - 7.1.3.1. Point versus linear versus area detection (p. 145) | html | pdf |
    - 7.1.3.2. Counting and integrating detectors (pp. 145-147) | html | pdf |
      - 7.1.3.2.1. Photon-counting detectors (pp. 145-146) | html | pdf |
      - 7.1.3.2.2. Integrating detectors (pp. 146-147) | html | pdf |
  - 7.1.4. Future detectors (p. 147) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 7.1.1.1. X-ray detectors for crystallography (p. 143) | html | pdf |
- 7.2. CCD detectors (pp. 148-153) | html | pdf | chapter contents |
  M. W. Tate, E. F. Eikenberry and S. M. Gruner
  - 7.2.1. Overview (p. 148) | html | pdf |
  - 7.2.2. CCD detector assembly (pp. 148-149) | html | pdf |
  - 7.2.3. Calibration and correction (pp. 149-151) | html | pdf |
    - 7.2.3.1. Dark-current subtraction (p. 149) | html | pdf |
    - 7.2.3.2. Removal of radioactive decay events (pp. 149-150) | html | pdf |
    - 7.2.3.3. Geometric distortion (p. 150) | html | pdf |
    - 7.2.3.4. Flat-field corrections (pp. 150-151) | html | pdf |
    - 7.2.3.5. Obliquity correction (p. 151) | html | pdf |
    - 7.2.3.6. Modular images (p. 151) | html | pdf |
  - 7.2.4. Detector system integration (pp. 151-152) | html | pdf |
  - 7.2.5. Applications to macromolecular crystallography (p. 152) | html | pdf |
  - 7.2.6. Future of CCD detectors (p. 152) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 7.2.1.1. Schematic of a single-module CCD detector (p. 148) | html | pdf |

Part 8. Synchrotron crystallography
- 8.1. Synchrotron-radiation instrumentation, methods and scientific utilization (pp. 155-166) | html | pdf | chapter contents |
  J. R. Helliwell
  - 8.1.1. Introduction (p. 155) | html | pdf |
  - 8.1.2. The physics of SR (p. 155) | html | pdf |
  - 8.1.3. Insertion devices (IDs) (pp. 155-156) | html | pdf |
  - 8.1.4. Beam characteristics delivered at the crystal sample (pp. 156-158) | html | pdf |
  - 8.1.5. Evolution of SR machines and experiments (pp. 158-161) | html | pdf |
    - 8.1.5.1. First-generation SR machines (pp. 158-159) | html | pdf |
    - 8.1.5.2. Second-generation dedicated machines (p. 160) | html | pdf |
    - 8.1.5.3. Third-generation high-brilliance machines (pp. 160-161) | html | pdf |
    - 8.1.5.4. New national SR machines (p. 161) | html | pdf |
    - 8.1.5.5. X-ray free electron laser (XFEL) (p. 161) | html | pdf |
  - 8.1.6. SR instrumentation (pp. 161-162) | html | pdf |
  - 8.1.7. SR monochromatic and Laue diffraction geometry (pp. 162-164) | html | pdf |
    - 8.1.7.1. Laue geometry: sources, optics, sample reflection bandwidth and spot size (p. 162) | html | pdf |
    - 8.1.7.2. Monochromatic SR beams: optical configurations and sample rocking width (pp. 162-164) | html | pdf |
      - 8.1.7.2.1. Curved single-crystal monochromator (pp. 162-163) | html | pdf |
      - 8.1.7.2.2. Double-crystal monochromator (p. 163) | html | pdf |
      - 8.1.7.2.3. Crystal sample rocking width (pp. 163-164) | html | pdf |
  - 8.1.8. Scientific utilization of SR in protein crystallography (pp. 164-166) | html | pdf |
    - 8.1.8.1. Atomic and ultra high resolution macromolecular crystallography (p. 165) | html | pdf |
    - 8.1.8.2. Small crystals (p. 165) | html | pdf |
    - 8.1.8.3. Time-resolved macromolecular crystallography (p. 165) | html | pdf |
    - 8.1.8.4. Multi-macromolecular complexes (p. 165) | html | pdf |
    - 8.1.8.5. Optimized anomalous dispersion (MAD), improved MIR data and `structural genomics' (pp. 165-166) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 8.1.2.1. ( a ) Evolution of X-ray source brilliance (p. 156) | html | pdf |
    - Fig. 8.1.2.2. Overall layout of the Daresbury SRS facility (p. 157) | html | pdf |
    - Fig. 8.1.2.3. The ring tunnel and part of the machine lattice at the ESRF, Grenoble, France (p. 158) | html | pdf |
    - Fig. 8.1.2.4. SR spectra (p. 158) | html | pdf |
    - Fig. 8.1.4.1. Common beamline optics modes (p. 159) | html | pdf |
    - Fig. 8.1.4.2. Single-crystal SR diffraction patterns (p. 159) | html | pdf |
    - Fig. 8.1.5.1. Anomalous dispersion (p. 160) | html | pdf |
    - Fig. 8.1.7.1. Single-crystal monochromator illuminated by SR (p. 163) | html | pdf |
    - Fig. 8.1.7.2. Double-crystal monochromator illuminated by SR (p. 163) | html | pdf |
    - Fig. 8.1.7.3. The rocking width of an individual reflection for the case of Fig. 8.1.7.1( c ) and a vertical rotation axis (p. 164) | html | pdf |
    - Fig. 8.1.8.1. Determination of the protonation states of carboxylic acid side chains in proteins via hydrogen atoms and resolved single and double bond lengths (p. 164) | html | pdf |
    - Fig. 8.1.8.2. A view of SV40 virus (p. 164) | html | pdf |
    - Fig. 8.1.8.3. The protein crystal structure of F ₁ ATPase (p. 164) | html | pdf |
  - Tables
    - Table 8.1.4.1. Internet addresses of SR facilities with macromolecular crystallography beamlines (p. 157) | html | pdf |
    - Table 8.1.5.1. A comparison of the parameter list for the 2 GeV SRS, 1997, and the new higher-energy machine for the UK, DIAMOND (p. 160) | html | pdf |
- 8.2. Laue crystallography: time-resolved studies (pp. 167-176) | html | pdf | chapter contents |
  K. Moffat
  - 8.2.1. Introduction (p. 167) | html | pdf |
  - 8.2.2. Principles of Laue diffraction (pp. 167-168) | html | pdf |
  - 8.2.3. Practical considerations in the Laue technique (pp. 168-170) | html | pdf |
  - 8.2.4. The time-resolved experiment (pp. 170-171) | html | pdf |
  - 8.2.5. Conclusions (p. 171) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 8.2.2.1. Laue diffraction geometry (p. 167) | html | pdf |
    - Fig. 8.2.3.1. Flow chart of typical Laue data processing (p. 169) | html | pdf |
  - Tables
    - Table 8.2.2.1. Advantages and disadvantages of the Laue technique (p. 169) | html | pdf |
    - Table 8.2.5.1. Time-resolved Laue diffraction experiments (p. 171) | html | pdf |

Part 9. Monochromatic data collection
- 9.1. Principles of monochromatic data collection (pp. 177-195) | html | pdf | chapter contents |
  Z. Dauter and K. S. Wilson
  - 9.1.1. Introduction (p. 177) | html | pdf |
  - 9.1.2. The components of a monochromatic X-ray experiment (p. 177) | html | pdf |
  - 9.1.3. Data completeness (p. 177) | html | pdf |
  - 9.1.4. X-ray sources (pp. 177-178) | html | pdf |
    - 9.1.4.1. Conventional sources (pp. 177-178) | html | pdf |
    - 9.1.4.2. Synchrotron storage rings (p. 178) | html | pdf |
  - 9.1.5. Goniostat geometry (pp. 178-179) | html | pdf |
    - 9.1.5.1. Overview (p. 178) | html | pdf |
    - 9.1.5.2. Film methods: the precession and Weissenberg methods (p. 178) | html | pdf |
    - 9.1.5.3. Single-counter diffractometers (pp. 178-179) | html | pdf |
    - 9.1.5.4. 2D detectors (p. 179) | html | pdf |
  - 9.1.6. Basis of the rotation method (pp. 179-183) | html | pdf |
    - 9.1.6.1. Rotation geometry (p. 179) | html | pdf |
    - 9.1.6.2. Diffraction pattern at a single orientation: the `still' image (pp. 179-180) | html | pdf |
    - 9.1.6.3. Rocking curve: crystal mosaicity and beam divergence (p. 180) | html | pdf |
    - 9.1.6.4. Rotation images and lunes (pp. 180-181) | html | pdf |
    - 9.1.6.5. Partially and fully recorded reflections (p. 181) | html | pdf |
    - 9.1.6.6. The width of the rotation range per image: fine ϕ slicing (pp. 181-182) | html | pdf |
    - 9.1.6.7. Wide slicing (pp. 182-183) | html | pdf |
    - 9.1.6.8. The Weissenberg camera (p. 183) | html | pdf |
  - 9.1.7. Rotation method: geometrical completeness (pp. 183-188) | html | pdf |
    - 9.1.7.1. Total rotation range for non-anomalous data (pp. 183-186) | html | pdf |
    - 9.1.7.2. Total rotation range for anomalous-dispersion data (p. 186) | html | pdf |
    - 9.1.7.3. Blind region (pp. 186-187) | html | pdf |
    - 9.1.7.4. Alternative indexing (pp. 187-188) | html | pdf |
  - 9.1.8. Crystal-to-detector distance (p. 188) | html | pdf |
  - 9.1.9. Wavelength (pp. 188-189) | html | pdf |
  - 9.1.10. Lysozyme as an example (pp. 189-190) | html | pdf |
  - 9.1.11. Rotation method: qualitative factors (pp. 190-191) | html | pdf |
    - 9.1.11.1. Inspection of reflection profiles (p. 190) | html | pdf |
    - 9.1.11.2. Exposure time (p. 190) | html | pdf |
    - 9.1.11.3. Overloads (pp. 190-191) | html | pdf |
    - 9.1.11.4. R factor, I /σ( I ) ratio and estimated uncertainties (p. 191) | html | pdf |
  - 9.1.12. Radiation damage (pp. 191-192) | html | pdf |
    - 9.1.12.1. Historical perspective (pp. 191-192) | html | pdf |
    - 9.1.12.2. Cryogenic freezing (p. 192) | html | pdf |
    - 9.1.12.3. Ultra high intensity SR sources (p. 192) | html | pdf |
  - 9.1.13. Relating data collection to the problem in hand (pp. 192-194) | html | pdf |
    - 9.1.13.1. Isomorphous-anomalous derivatives (pp. 192-193) | html | pdf |
    - 9.1.13.2. Anomalous scattering, MAD and SAD (p. 193) | html | pdf |
    - 9.1.13.3. Molecular replacement (p. 193) | html | pdf |
    - 9.1.13.4. Definitive data on relevant biological structures (p. 193) | html | pdf |
    - 9.1.13.5. A series of mutant or complex structures (pp. 193-194) | html | pdf |
    - 9.1.13.6. Atomic resolution applications (p. 194) | html | pdf |
  - 9.1.14. The importance of low-resolution data (p. 194) | html | pdf |
  - 9.1.15. Data quality over the whole resolution range (p. 194) | html | pdf |
  - 9.1.16. Final remarks (pp. 194-195) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 9.1.6.1. The Ewald-sphere construction (p. 179) | html | pdf |
    - Fig. 9.1.6.2. The plane of reflections in the reciprocal sphere that is approximately perpendicular to the X-ray beam gives rise to an ellipse of reflections on the detector (p. 180) | html | pdf |
    - Fig. 9.1.6.3. Schematic representation of beam divergence (δ) and crystal mosaicity (η) (p. 180) | html | pdf |
    - Fig. 9.1.6.4. A single lune on two consecutive exposures (p. 181) | html | pdf |
    - Fig. 9.1.6.5. Appearance of a lune for ( a ) a crystal of low mosaicity and ( b ) a highly mosaic crystal (p. 181) | html | pdf |
    - Fig. 9.1.6.6. The width of the lunes is proportional to the rotation range per image, Δϕ, which increases from ( a ) to ( c ) (p. 182) | html | pdf |
    - Fig. 9.1.6.7. The largest allowed rotation range per exposure depends on the dimension of the primitive unit cell oriented along the X-ray beam; this is diminished by high mosaicity (p. 183) | html | pdf |
    - Fig. 9.1.6.8. If the crystal lattice is centred or if its orientation is non-axial, the reflections do not overlap in spite of overlapping lunes (p. 183) | html | pdf |
    - Fig. 9.1.7.1. Rotation of a triclinic crystal by 180° in the X-ray beam, represented as rotating the Ewald sphere with a stationary crystal, projected along the rotation axis (p. 184) | html | pdf |
    - Fig. 9.1.7.2. Rotation of a triclinic crystal by 135° is not sufficient to obtain totally complete data (p. 184) | html | pdf |
    - Fig. 9.1.7.3. After a 90° rotation out of a required 180°, the overall completeness is higher than 50% (p. 185) | html | pdf |
    - Fig. 9.1.7.4. For an orthorhombic crystal, a 90° rotation is sufficient provided the starting or final orientation is along the major axis (p. 185) | html | pdf |
    - Fig. 9.1.7.5. Rotation of an orthorhombic crystal by 90° between two diagonal orientations leaves a part of the reciprocal space unmeasured (p. 185) | html | pdf |
    - Fig. 9.1.7.6. For data containing an anomalous signal, when both Bijvoet mates have to be measured, 180° rotation of a triclinic crystal is not sufficient and at least an additional $[2\theta_{\max}]$ is required (p. 186) | html | pdf |
    - Fig. 9.1.7.7. Rotation by 360° leaves the part of the reciprocal space in the blind region unmeasured, since the reflections near the rotation axis do not cross the surface of the Ewald sphere (p. 186) | html | pdf |
    - Fig. 9.1.7.8. Dependence of the total fraction of reflections in the blind region on the resolution for three different wavelengths: 1.54, 1 and 0.71 Å (p. 187) | html | pdf |
    - Fig. 9.1.7.9. For shorter wavelengths the blind region is narrower, since the Ewald sphere is flatter (p. 187) | html | pdf |
    - Fig. 9.1.7.10. If the crystal has a symmetry axis, it should be skewed from the rotation axis by at least $[\theta_{\max}]$ to be able to collect the reflections equivalent to those in the blind region (p. 187) | html | pdf |
    - Fig. 9.1.10.1. Images recorded from a crystal of lysozyme (p. 189) | html | pdf |
  - Tables
    - Table 9.1.1.1. Size of the unit cell and number of reflections (p. 177) | html | pdf |
    - Table 9.1.7.1. Standard choice of asymmetric unit in reciprocal space for different point groups from the CCP4 program suite (p. 184) | html | pdf |
    - Table 9.1.7.2. Rotation range (°) required in different crystal classes (p. 186) | html | pdf |
    - Table 9.1.7.3. Space groups with alternative, non-equivalent indexing schemes (p. 188) | html | pdf |

Part 10. Cryocrystallography
- 10.1. Introduction to cryocrystallography (pp. 197-201) | html | pdf | chapter contents |
  H. Hope
  - 10.1.1. Utility of low-temperature data collection (p. 197) | html | pdf |
    - 10.1.1.1. Prevention of radiation damage (p. 197) | html | pdf |
    - 10.1.1.2. Mechanical stability of the crystal mount (p. 197) | html | pdf |
    - 10.1.1.3. Effect on resolution (p. 197) | html | pdf |
  - 10.1.2. Cooling of biocrystals (pp. 197-199) | html | pdf |
    - 10.1.2.1. Physical chemistry of biocrystals (pp. 197-198) | html | pdf |
    - 10.1.2.2. Internal ice or phase transition (p. 198) | html | pdf |
    - 10.1.2.3. Removal of the solvent layer (p. 198) | html | pdf |
    - 10.1.2.4. Cooling rates (pp. 198-199) | html | pdf |
  - 10.1.3. Principles of cooling equipment (p. 199) | html | pdf |
    - 10.1.3.1. Cold gas supply (p. 199) | html | pdf |
    - 10.1.3.2. Frost prevention (p. 199) | html | pdf |
  - 10.1.4. Operational considerations (pp. 199-201) | html | pdf |
    - 10.1.4.1. Dual-stream instruments (pp. 199-200) | html | pdf |
    - 10.1.4.2. Electrically heated nozzle (pp. 200-201) | html | pdf |
    - 10.1.4.3. Temperature calibration (p. 201) | html | pdf |
    - 10.1.4.4. Transfer of the crystal to the diffractometer (p. 201) | html | pdf |
  - 10.1.5. Concluding note (p. 201) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 10.1.4.1. Schematic drawing of a dual-stream setup with the streams parallel to the diffractometer ϕ axis (p. 199) | html | pdf |
    - Fig. 10.1.4.2. Schematic drawing of a dual-stream setup with the streams angled relative to the diffractometer ϕ axis (p. 200) | html | pdf |
    - Fig. 10.1.4.3. Schematic drawing of a single-stream setup with the stream parallel to the diffractometer ϕ axis (p. 200) | html | pdf |
    - Fig. 10.1.4.4. Schematic drawing of a single-stream setup with the stream angled relative to the diffractometer ϕ axis (p. 200) | html | pdf |
- 10.2. Cryocrystallography techniques and devices (pp. 202-208) | html | pdf | chapter contents |
  D. W. Rodgers
  - 10.2.1. Introduction (p. 202) | html | pdf |
  - 10.2.2. Crystal preparation (pp. 202-203) | html | pdf |
  - 10.2.3. Crystal mounting (pp. 203-204) | html | pdf |
  - 10.2.4. Flash cooling (pp. 205-206) | html | pdf |
  - 10.2.5. Transfer and storage (pp. 206-207) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 10.2.2.1. Recommended pathway for optimizing cryoprotectant conditions and flash cooling (p. 203) | html | pdf |
    - Fig. 10.2.3.1. Different crystal mounts for flash cooling and cryogenic data collection (p. 204) | html | pdf |
    - Fig. 10.2.3.2. Mounting a crystal in a loop (p. 204) | html | pdf |
    - Fig. 10.2.3.3. Photograph of a flash-cooled crystal mounted in a nylon loop (p. 204) | html | pdf |
    - Fig. 10.2.3.4. Arrangement for using the loop-mounting technique at non-cryogenic temperatures (p. 204) | html | pdf |
    - Fig. 10.2.4.1. Flash cooling a crystal in the cold gas stream from a cryostat (p. 205) | html | pdf |
    - Fig. 10.2.4.2. Flash cooling in a liquid cryogen (p. 205) | html | pdf |
    - Fig. 10.2.5.1. Transfer of the flash-cooled crystal and loop assembly to a goniometer using a cryovial (p. 206) | html | pdf |
    - Fig. 10.2.5.2. Transfer using an alternative device for achieving the correct magnetic mount orientation (p. 207) | html | pdf |
    - Fig. 10.2.5.3. Transfer using tongs (p. 207) | html | pdf |
  - Tables
    - Table 10.2.2.1. List of cryoprotectants used successfully for flash cooling macromolecular crystals (p. 202) | html | pdf |
    - Table 10.2.2.2. Methods for introducing the cryoprotectants needed for flash cooling (p. 202) | html | pdf |

Part 11. Data processing
- 11.1. Automatic indexing of oscillation images (pp. 209-211) | html | pdf | chapter contents |
  M. G. Rossmann
  - 11.1.1. Introduction (p. 209) | html | pdf |
  - 11.1.2. The crystal orientation matrix (p. 209) | html | pdf |
  - 11.1.3. Fourier analysis of the reciprocal-lattice vector distribution when projected onto a chosen direction (pp. 209-210) | html | pdf |
  - 11.1.4. Exploring all possible directions to find a good set of basis vectors (p. 210) | html | pdf |
  - 11.1.5. The program (p. 211) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 11.1.3.1. Frequency distribution of the projected reciprocal-lattice vectors for a suitably chosen direction of a diffraction pattern from a fibritin crystal (Tao et al (p. 210) | html | pdf |
    - Fig. 11.1.3.2. Fourier analysis of the distribution shown in Fig. 11.1.3.1 (p. 210) | html | pdf |
- 11.2. Integration of macromolecular diffraction data (pp. 212-217) | html | pdf | chapter contents |
  A. G. W. Leslie
  - 11.2.1. Introduction (p. 212) | html | pdf |
  - 11.2.2. Prerequisites for accurate integration (p. 212) | html | pdf |
    - 11.2.2.1. Crystal parameters (p. 212) | html | pdf |
    - 11.2.2.2. Detector parameters (p. 212) | html | pdf |
  - 11.2.3. Methods of integration (p. 212) | html | pdf |
  - 11.2.4. The measurement box (pp. 212-213) | html | pdf |
  - 11.2.5. Integration by simple summation (pp. 213-214) | html | pdf |
    - 11.2.5.1. Determination of the best background plane (p. 213) | html | pdf |
      - 11.2.5.1.1. Outlier rejection (p. 213) | html | pdf |
    - 11.2.5.2. Evaluating the integrated intensity and standard deviation (pp. 213-214) | html | pdf |
    - 11.2.5.3. The effect of instrument or detector errors (p. 214) | html | pdf |
  - 11.2.6. Integration by profile fitting (pp. 214-217) | html | pdf |
    - 11.2.6.1. Forming the standard profiles (pp. 214-215) | html | pdf |
    - 11.2.6.2. Evaluation of the profile-fitted intensity (p. 215) | html | pdf |
    - 11.2.6.3. Modifications for very close spots (pp. 215-216) | html | pdf |
    - 11.2.6.4. Profile fitting very strong reflections (p. 216) | html | pdf |
    - 11.2.6.5. Profile fitting very weak reflections (p. 216) | html | pdf |
    - 11.2.6.6. Improvement provided by profile fitting weak reflections (p. 216) | html | pdf |
    - 11.2.6.7. Other benefits of profile fitting (pp. 216-217) | html | pdf |
      - 11.2.6.7.1. Incompletely resolved spots (p. 216) | html | pdf |
      - 11.2.6.7.2. Elimination of peak pixel outliers (p. 216) | html | pdf |
      - 11.2.6.7.3. Estimation of overloaded reflections (pp. 216-217) | html | pdf |
    - 11.2.6.8. Profile fitting partially recorded reflections (p. 217) | html | pdf |
    - 11.2.6.9. Systematic errors in profile-fitted intensities (p. 217) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 11.2.4.1. The measurement-box definition used in MOSFLM (p. 213) | html | pdf |
- 11.3. Integration, scaling, space-group assignment and post refinement (pp. 218-225) | html | pdf | chapter contents |
  W. Kabsch
  - 11.3.1. Introduction (p. 218) | html | pdf |
  - 11.3.2. Modelling rotation images (pp. 218-221) | html | pdf |
    - 11.3.2.1. Coordinate systems and parameters (p. 218) | html | pdf |
    - 11.3.2.2. Spot prediction (pp. 218-219) | html | pdf |
    - 11.3.2.3. Standard spot shape (p. 219) | html | pdf |
    - 11.3.2.4. Spot centroids and partiality (p. 219) | html | pdf |
    - 11.3.2.5. Localizing diffraction spots (pp. 219-220) | html | pdf |
    - 11.3.2.6. Basis extraction (p. 220) | html | pdf |
    - 11.3.2.7. Indexing (p. 220) | html | pdf |
    - 11.3.2.8. Refinement (pp. 220-221) | html | pdf |
  - 11.3.3. Integration (pp. 221-222) | html | pdf |
    - 11.3.3.1. Spot extraction (p. 221) | html | pdf |
    - 11.3.3.2. Background (pp. 221-222) | html | pdf |
    - 11.3.3.3. Standard profiles (p. 222) | html | pdf |
    - 11.3.3.4. Intensity estimation (p. 222) | html | pdf |
  - 11.3.4. Scaling (pp. 222-223) | html | pdf |
  - 11.3.5. Post refinement (pp. 223-224) | html | pdf |
  - 11.3.6. Space-group assignment (pp. 224-225) | html | pdf |
    - 11.3.6.1. Determination of the Bravais lattice (p. 224) | html | pdf |
    - 11.3.6.2. Finding possible space groups (pp. 224-225) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 11.3.6.1. Rating of lattice types implied by a given reduced cell (p. 225) | html | pdf |
- 11.4. DENZO and SCALEPACK (pp. 226-235) | html | pdf | chapter contents |
  Z. Otwinowski and W. Minor
  - 11.4.1. Introduction (p. 226) | html | pdf |
  - 11.4.2. Diffraction from a perfect crystal lattice (pp. 226-227) | html | pdf |
  - 11.4.3. Autoindexing (pp. 227-228) | html | pdf |
    - 11.4.3.1. Lattice symmetry (p. 227) | html | pdf |
    - 11.4.3.2. Lattice pseudosymmetry (p. 227) | html | pdf |
    - 11.4.3.3. Data-collection requirements (pp. 227-228) | html | pdf |
    - 11.4.3.4. Misindexing (p. 228) | html | pdf |
    - 11.4.3.5. Twins (p. 228) | html | pdf |
  - 11.4.4. Coordinate systems (pp. 228-229) | html | pdf |
    - 11.4.4.1. Beam–gravity (p. 228) | html | pdf |
    - 11.4.4.2. Data (p. 228) | html | pdf |
    - 11.4.4.3. Beam–spindle (p. 228) | html | pdf |
    - 11.4.4.4. Beam–2θ (pp. 228-229) | html | pdf |
  - 11.4.5. Experimental assumptions (pp. 229-231) | html | pdf |
    - 11.4.5.1. Crystal diffraction (p. 229) | html | pdf |
    - 11.4.5.2. Data model (p. 229) | html | pdf |
    - 11.4.5.3. Data-model refinement (pp. 229-230) | html | pdf |
    - 11.4.5.4. Correlation between parameters (p. 230) | html | pdf |
    - 11.4.5.5. Single- and multiframe refinement (p. 230) | html | pdf |
    - 11.4.5.6. Active area (p. 230) | html | pdf |
    - 11.4.5.7. Flood field (p. 230) | html | pdf |
    - 11.4.5.8. Absolute configuration (p. 230) | html | pdf |
    - 11.4.5.9. Correcting diffraction images (p. 230) | html | pdf |
    - 11.4.5.10. Detector goniostat (pp. 230-231) | html | pdf |
    - 11.4.5.11. Crystal goniostat (p. 231) | html | pdf |
    - 11.4.5.12. Crystal orthogonalization convention (p. 231) | html | pdf |
    - 11.4.5.13. Refinement and calibration (p. 231) | html | pdf |
  - 11.4.6. Prediction of the diffraction pattern (pp. 231-232) | html | pdf |
    - 11.4.6.1. Refinement of crystal and detector parameters (p. 232) | html | pdf |
    - 11.4.6.2. Bragg's law for non-ideal conditions: mosaicity (p. 232) | html | pdf |
    - 11.4.6.3. Detector distortions (p. 232) | html | pdf |
  - 11.4.7. Detector diagnostics (p. 233) | html | pdf |
  - 11.4.8. Multiplicative corrections (scaling) (p. 233) | html | pdf |
    - 11.4.8.1. Polarization (p. 233) | html | pdf |
  - 11.4.9. Global refinement or post refinement (p. 233) | html | pdf |
  - 11.4.10. Graphical command centre (pp. 233-235) | html | pdf |
  - 11.4.11. Final note (p. 235) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 11.4.5.1. The transformations in DENZO applied to APS-1 detector data (p. 231) | html | pdf |
    - Fig. 11.4.10.1. The strategy program as implemented in the HKL package (p. 234) | html | pdf |
    - Fig. 11.4.10.2. The scaling window of the graphical user interface (p. 234) | html | pdf |
- 11.5. The use of partially recorded reflections for post refinement, scaling and averaging X-ray diffraction data (pp. 236-245) | html | pdf | chapter contents |
  C. G. van Beek, R. Bolotovsky and M. G. Rossmann
  - 11.5.1. Introduction (p. 236) | html | pdf |
  - 11.5.2. Generalization of the Hamilton, Rollett and Sparks equations to take into account partial reflections (pp. 236-237) | html | pdf |
  - 11.5.3. Selection of reflections useful for scaling (p. 237) | html | pdf |
  - 11.5.4. Restraints and constraints (p. 237) | html | pdf |
  - 11.5.5. Generalization of the procedure for averaging reflection intensities (p. 238) | html | pdf |
  - 11.5.6. Estimating the quality of data scaling and averaging (p. 238) | html | pdf |
  - 11.5.7. Experimental results (pp. 238-241) | html | pdf |
    - 11.5.7.1. Variation of scale factors versus frame number (pp. 238-239) | html | pdf |
    - 11.5.7.2. R factor as a function of `sum-of-partialities' (method 1) (p. 239) | html | pdf |
    - 11.5.7.3. Statistics for rejecting reflections and data quality as a function of frame number (p. 240) | html | pdf |
    - 11.5.7.4. Observed versus calculated partiality (p. 240) | html | pdf |
    - 11.5.7.5. Anisotropic mosaicity (p. 240) | html | pdf |
    - 11.5.7.6. Anomalous dispersion (p. 241) | html | pdf |
  - 11.5.8. Conclusions (p. 241) | html | pdf |
  - Appendix 11.5.1. Partiality model (Rossmann, 1979; Rossmann et al. , 1979) (pp. 241-242) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 11.5.7.1. Linear scale factors as a function of frame number for a ϕX174 data set (Dokland et al (p. 239) | html | pdf |
    - Fig. 11.5.7.2. Linear scale factor as a function of frame number for an HRV14 data set (Rossmann et al (p. 239) | html | pdf |
    - Fig. 11.5.7.3. Linear scale factor determined by method 2 as a function of frame number for an SCP(114–264) data set (Choi et al (p. 239) | html | pdf |
    - Fig. 11.5.7.4. R factor as a function of the difference of calculated `sum-of-partialities' and unity for the estimates of full reflections when method 1 is used for the scaling and averaging of a ϕX174 data set (Dokland et al (p. 240) | html | pdf |
    - Fig. 11.5.7.5. R factor per frame as a function of frame number for a ϕX174 data set (Dokland et al (p. 240) | html | pdf |
    - Fig. 11.5.7.6. The observed partialities plotted against calculated partialities for a ϕX174 data set (Dokland et al (p. 240) | html | pdf |
    - Fig. 11.5.7.7. Variation of (unconstrained) mosaicity for a monoclinic crystal of the bacterial virus alpha3 (Bernal et al (p. 240) | html | pdf |
    - Fig. 11.5.7.8. Quality of anomalous-dispersion data for an SeMet derivative of dioxygenase Rieske ferredoxin (Colbert & Bolin, 1999) (p. 240) | html | pdf |
    - Fig. A11.5.1.1. Penetration of a reciprocal-lattice point P into the sphere of reflection by rotation around Oy (p. 241) | html | pdf |
    - Fig. A11.5.1.2. Relationship between the fraction of the path travelled, q , by a reciprocal-lattice point across an Ewald sphere of finite thickness and the fraction of the total scattered intensity, p (p. 242) | html | pdf |
    - Fig. A11.5.1.3. The four conditions 1, 2, 3 and 4 for partial reflections corresponding to Table A11.5.1.1 (p. 242) | html | pdf |
  - Tables
    - Table 11.5.3.1. Hierarchy of criteria for selecting reflections for scaling and averaging procedures (p. 237) | html | pdf |
    - Table A11.5.1.1. Calculation of the degree of penetration of the Ewald sphere, q (p. 242) | html | pdf |

Part 12. Isomorphous replacement
- 12.1. The preparation of heavy-atom derivatives of protein crystals for use in multiple isomorphous replacement and anomalous scattering (pp. 247-255) | html | pdf | chapter contents |
  D. Carvin, S. A. Islam, M. J. E. Sternberg and T. L. Blundell
  - 12.1.1. Introduction (p. 247) | html | pdf |
  - 12.1.2. Heavy-atom data bank (pp. 247-248) | html | pdf |
  - 12.1.3. Properties of heavy-atom compounds and their complexes (pp. 248-250) | html | pdf |
    - 12.1.3.1. Stability (p. 248) | html | pdf |
    - 12.1.3.2. Lability (p. 248) | html | pdf |
    - 12.1.3.3. Oxidation state of metal ions in protein crystals (p. 248) | html | pdf |
    - 12.1.3.4. Effect of pH (pp. 248-249) | html | pdf |
    - 12.1.3.5. Effect of precipitants and buffers on heavy-atom binding (p. 249) | html | pdf |
    - 12.1.3.6. Solubility of heavy-atom compounds (p. 249) | html | pdf |
    - 12.1.3.7. Effect of concentration, time of soak and temperature on heavy-atom binding (p. 250) | html | pdf |
  - 12.1.4. Amino acids as ligands (p. 250) | html | pdf |
  - 12.1.5. Protein chemistry of heavy-atom reagents (pp. 250-254) | html | pdf |
    - 12.1.5.1. Hard cations (p. 251) | html | pdf |
    - 12.1.5.2. Thallium and lead ions (p. 251) | html | pdf |
    - 12.1.5.3. B-metal reagents (pp. 251-253) | html | pdf |
    - 12.1.5.4. Electrostatic binding of heavy-atom anions (p. 253) | html | pdf |
    - 12.1.5.5. Hydrophobic heavy-atom reagents (pp. 253-254) | html | pdf |
    - 12.1.5.6. Iodine (p. 254) | html | pdf |
    - 12.1.5.7. Polynuclear reagents (p. 254) | html | pdf |
  - 12.1.6. Metal-ion replacement in metalloproteins (pp. 254-255) | html | pdf |
  - 12.1.7. Analogues of amino acids (p. 255) | html | pdf |
  - 12.1.8. Use of the heavy-atom data bank to select derivatives (p. 255) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 12.1.5.1. The binding site for uranyl ions in cytochrome b 5 (oxidized: 3B5C) (p. 252) | html | pdf |
    - Fig. 12.1.5.2. Mercuric ions replace zinc in thermolysin (3TLN) (p. 252) | html | pdf |
    - Fig. 12.1.5.3. The binding of a silver ion to immunoglobulin Fab (2FB4) (p. 252) | html | pdf |
    - Fig. 12.1.5.4. The binding of $[\hbox{PtCl}_{4}^{2-}]$ through a methionine in azurin (1AZU) (p. 252) | html | pdf |
    - Fig. 12.1.5.5. The relative positions of methionine side chains (carbon: green; sulfur: yellow) in the parent crystals to the binding of platinum (pink) of $[\hbox{PtCl}_{4}^{2-}]$ (p. 252) | html | pdf |
    - Fig. 12.1.5.6. The relative positions of cystine disulfide bridges (carbon: green; sulfur: yellow) in the parent crystals to the binding of platinum (pink) of $[\hbox{PtCl}_{4}^{2-}]$ (p. 253) | html | pdf |
    - Fig. 12.1.5.7. The binding of $[\hbox{Pt(CN)}_{4}^{2-}]$ to aldose dehydrogenase (8ADH) (p. 253) | html | pdf |
    - Fig. 12.1.6.1. The displacement of calcium by samarium in thermolysin (p. 254) | html | pdf |
  - Tables
    - Table 12.1.3.1. Useful pH ranges of some heavy-atom reagents derived from the heavy-atom data bank (p. 249) | html | pdf |
    - Table 12.1.5.1. The 23 most commonly used heavy-atom reagents (p. 251) | html | pdf |
    - Table 12.1.5.2. The five most popular uranium derivatives (p. 251) | html | pdf |
    - Table 12.1.5.3. The five most popular mercury derivatives (p. 251) | html | pdf |
    - Table 12.1.5.4. The five most popular platinum derivatives (p. 253) | html | pdf |
- 12.2. Locating heavy-atom sites (pp. 256-262) | html | pdf | chapter contents |
  M. T. Stubbs and R. Huber
  - 12.2.1. The origin of the phase problem (pp. 256-257) | html | pdf |
  - 12.2.2. The Patterson function (pp. 257-258) | html | pdf |
  - 12.2.3. The difference Fourier (p. 258) | html | pdf |
  - 12.2.4. Reality (pp. 258-259) | html | pdf |
    - 12.2.4.1. Treatment of errors (pp. 258-259) | html | pdf |
    - 12.2.4.2. Automated search procedures (p. 259) | html | pdf |
  - 12.2.5. Special complications (pp. 259-260) | html | pdf |
    - 12.2.5.1. Lack of isomorphism (pp. 259-260) | html | pdf |
    - 12.2.5.2. Space-group problems (p. 260) | html | pdf |
    - 12.2.5.3. High levels of substitution; noncrystallographic symmetry (p. 260) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 12.2.1.1. Relationships in diffraction space (p. 256) | html | pdf |
    - Fig. 12.2.1.2. The effect of introducing a heavy atom or anomalous scatterer (p. 257) | html | pdf |
    - Fig. 12.2.2.1. The Patterson map with symmetry (p. 257) | html | pdf |
    - Fig. 12.2.2.2. The vector superposition method (p. 258) | html | pdf |
    - Fig. 12.2.4.1. The treatment of phase errors (p. 258) | html | pdf |

Part 13. Molecular replacement
- 13.1. Noncrystallographic symmetry (pp. 263-268) | html | pdf | chapter contents |
  D. M. Blow
  - 13.1.1. Introduction (p. 263) | html | pdf |
  - 13.1.2. Definition of noncrystallographic symmetry (p. 263) | html | pdf |
    - 13.1.2.1. Standard noncrystallographic symmetry (p. 263) | html | pdf |
    - 13.1.2.2. Generalized noncrystallographic symmetry (p. 263) | html | pdf |
    - 13.1.2.3. Exploitation of noncrystallographic symmetry (p. 263) | html | pdf |
  - 13.1.3. Use of the Patterson function to interpret noncrystallographic symmetry (pp. 263-265) | html | pdf |
    - 13.1.3.1. Rotation operations (pp. 263-264) | html | pdf |
    - 13.1.3.2. Translation operations (pp. 264-265) | html | pdf |
  - 13.1.4. Interpretation of generalized noncrystallographic symmetry where the molecular structure is partially known (pp. 265-266) | html | pdf |
    - 13.1.4.1. The cross-rotation function (p. 265) | html | pdf |
    - 13.1.4.2. The cross-translation function (p. 265) | html | pdf |
    - 13.1.4.3. Structure determination (pp. 265-266) | html | pdf |
  - 13.1.5. The power of noncrystallographic symmetry in structure analysis (pp. 266-268) | html | pdf |
    - 13.1.5.1. Relevant parameters: standard case (p. 266) | html | pdf |
    - 13.1.5.2. Information gain from ideal noncrystallographic symmetry (pp. 266-267) | html | pdf |
    - 13.1.5.3. Information gain in the non-ideal case (p. 267) | html | pdf |
    - 13.1.5.4. Relevant parameters: generalized case (p. 267) | html | pdf |
    - 13.1.5.5. Noncrystallographic symmetry in atomic coordinate refinement (pp. 267-268) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 13.1.3.1. ( a ) A dimer in which the two subunits are related by arbitrary rotation and translation (p. 264) | html | pdf |
  - Tables
    - Table 13.1.2.1. Noncrystallographic symmetry in crystals (p. 263) | html | pdf |
    - Table 13.1.4.1. Structure determination using noncrystallographic symmetry (p. 265) | html | pdf |
- 13.2. Rotation functions (pp. 269-274) | html | pdf | chapter contents |
  J. Navaza
  - 13.2.1. Overview (p. 269) | html | pdf |
  - 13.2.2. Rotations in three-dimensional Euclidean space (pp. 269-270) | html | pdf |
    - 13.2.2.1. The metric of the rotation group (pp. 269-270) | html | pdf |
  - 13.2.3. The rotation function (pp. 270-272) | html | pdf |
    - 13.2.3.1. Computing the rotation function (p. 271) | html | pdf |
    - 13.2.3.2. Plotting and sampling the rotation function (p. 271) | html | pdf |
    - 13.2.3.3. Strategies (p. 272) | html | pdf |
    - 13.2.3.4. Symmetry properties of the rotation function (p. 272) | html | pdf |
  - 13.2.4. The locked rotation function (pp. 272-273) | html | pdf |
  - 13.2.5. Other rotation functions (p. 273) | html | pdf |
  - 13.2.6. Concluding remarks (p. 273) | html | pdf |
  - Appendix 13.2.1. Formulae for the derivation and computation of the fast rotation function (pp. 273-274) | html | pdf |
    - A13.2.1.1. Euler parameterization (p. 273) | html | pdf |
    - A13.2.1.2. The $[D^{\ell}_{m, \, m'}]$ matrices (pp. 273-274) | html | pdf |
    - A13.2.1.3. Spherical harmonics (p. 274) | html | pdf |
    - A13.2.1.4. Spherical Bessel functions (p. 274) | html | pdf |
    - A13.2.1.5. Expansion of $[\exp (2\pi i{\bf sr})]$ (p. 274) | html | pdf |
    - A13.2.1.6. Expansion of the interference function (p. 274) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 13.2.2.1. Illustration of rotations defined by ( a ) the spherical polar angles (χ, ω, ϕ); ( b ) the Euler angles (α, β, γ) (p. 269) | html | pdf |
- 13.3. Translation functions (pp. 275-278) | html | pdf | chapter contents |
  L. Tong
  - 13.3.1. Introduction (p. 275) | html | pdf |
  - 13.3.2. R -factor and correlation-coefficient translation functions (pp. 275-276) | html | pdf |
  - 13.3.3. Patterson-correlation translation function (p. 276) | html | pdf |
  - 13.3.4. Phased translation function (pp. 276-277) | html | pdf |
  - 13.3.5. Packing check in translation functions (p. 277) | html | pdf |
  - 13.3.6. The unique region of a translation function (the Cheshire group) (p. 277) | html | pdf |
  - 13.3.7. Combined molecular replacement (p. 277) | html | pdf |
  - 13.3.8. The locked translation function (pp. 277-278) | html | pdf |
  - 13.3.9. Miscellaneous translation functions (p. 278) | html | pdf |
  - References | html | pdf |
- 13.4. Noncrystallographic symmetry averaging of electron density for molecular-replacement phase refinement and extension (pp. 279-292) | html | pdf | chapter contents |
  M. G. Rossmann and E. Arnold
  - 13.4.1. Introduction (p. 279) | html | pdf |
  - 13.4.2. Noncrystallographic symmetry (NCS) (pp. 279-280) | html | pdf |
  - 13.4.3. Phase determination using NCS (pp. 280-281) | html | pdf |
  - 13.4.4. The p - and h -cells (pp. 281-282) | html | pdf |
  - 13.4.5. Combining crystallographic and noncrystallographic symmetry (pp. 282-283) | html | pdf |
    - 13.4.5.1. General considerations (p. 282) | html | pdf |
    - 13.4.5.2. Averaging with the p -cell (pp. 282-283) | html | pdf |
    - 13.4.5.3. Averaging the p -cell and placing the results into the h -cell (p. 283) | html | pdf |
  - 13.4.6. Determining the molecular envelope (pp. 283-284) | html | pdf |
  - 13.4.7. Finding the averaged density (pp. 284-285) | html | pdf |
  - 13.4.8. Interpolation (p. 285) | html | pdf |
  - 13.4.9. Combining different crystal forms (p. 285) | html | pdf |
  - 13.4.10. Phase extension and refinement of the NCS parameters (pp. 285-286) | html | pdf |
  - 13.4.11. Convergence (p. 286) | html | pdf |
  - 13.4.12. Ab initio phasing starts (pp. 286-287) | html | pdf |
  - 13.4.13. Recent salient examples in low-symmetry cases: multidomain averaging and systematic applications of multiple-crystal-form averaging (pp. 287-288) | html | pdf |
  - 13.4.14. Programs (p. 288) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 13.4.2.1. The two-dimensional periodic design shows crystallographic twofold axes perpendicular to the page and local noncrystallographic rotation axes in the plane of the paper (design by Audrey Rossmann) (p. 279) | html | pdf |
    - Fig. 13.4.2.2. ( a ) NCS in a triclinic cell (p. 280) | html | pdf |
    - Fig. 13.4.2.3. The position of the twofold rotation axis which relates the two piglets is completely arbitrary (p. 280) | html | pdf |
    - Fig. 13.4.4.1. Stereographic projections showing alternative definitions of the `standard orientation' of an icosahedron in the h -cell (p. 281) | html | pdf |
    - Fig. 13.4.6.1. The volume of the molecular mask expressed as a percentage of the volume of the p -cell asymmetric unit, as determined by the density cutoff in the h -cell (p. 284) | html | pdf |
    - Fig. 13.4.8.1. Interpolation box for finding the approximate electron density at G (Δ x , Δ y , Δ z ), given the eight densities at the corners of the box (p. 285) | html | pdf |
    - Fig. 13.4.11.1. Plot of a correlation coefficient as the phases were extended from 8 to 3 Å resolution in the structure determination of Mengo virus (p. 286) | html | pdf |
    - Fig. 13.4.12.1. Structure amplitudes of the type II crystals of southern bean mosaic virus, averaged within shells of reciprocal space, shown in relation to the Fourier transform of a 284 Å diameter sphere (p. 287) | html | pdf |
  - Tables
    - Table 13.4.7.1. Mean root-mean-square scatter between noncrystallographically related points (p. 284) | html | pdf |

Part 14. Anomalous dispersion
- 14.1. Heavy-atom location and phase determination with single-wavelength diffraction data (pp. 293-298) | html | pdf | chapter contents |
  B. W. Matthews
  - 14.1.1. Introduction (p. 293) | html | pdf |
  - 14.1.2. The isomorphous-replacement method (pp. 293-294) | html | pdf |
  - 14.1.3. The method of multiple isomorphous replacement (p. 294) | html | pdf |
  - 14.1.4. The method of Blow & Crick (pp. 294-295) | html | pdf |
  - 14.1.5. The best Fourier (p. 295) | html | pdf |
  - 14.1.6. Anomalous scattering (p. 295) | html | pdf |
  - 14.1.7. Theory of anomalous scattering (pp. 295-296) | html | pdf |
  - 14.1.8. The phase probability distribution for anomalous scattering (p. 296) | html | pdf |
  - 14.1.9. Anomalous scattering without isomorphous replacement (p. 297) | html | pdf |
  - 14.1.10. Location of heavy-atom sites (p. 297) | html | pdf |
  - 14.1.11. Use of anomalous-scattering data in heavy-atom location (p. 297) | html | pdf |
  - 14.1.12. Use of difference Fourier syntheses (p. 297) | html | pdf |
  - 14.1.13. Single isomorphous replacement (pp. 297-298) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 14.1.2.1. ( a ) Harker construction for a single isomorphous replacement (p. 293) | html | pdf |
    - Fig. 14.1.3.1. ( a ) Harker construction for a double isomorphous replacement (p. 294) | html | pdf |
    - Fig. 14.1.4.1. Vector diagram illustrating the lack of closure, , of an isomorphous-replacement phase triangle (p. 294) | html | pdf |
    - Fig. 14.1.7.1. ( a ) Vector diagrams illustrating anomalous scattering for the reflections hkl and $[\overline{hkl}]$ (p. 295) | html | pdf |
    - Fig. 14.1.7.2. Harker construction for a single isomorphous replacement with anomalous scattering, in the absence of errors (p. 296) | html | pdf |
    - Fig. 14.1.8.1. Vector diagrams illustrating lack of closure in the anomalous-scattering method (p. 296) | html | pdf |
    - Fig. 14.1.8.2. Combination of isomorphous replacement and anomalous-scattering phase probabilities for a single isomorphous replacement (p. 296) | html | pdf |
    - Fig. 14.1.13.1. The consequences of using the incorrect hand for the heavy-atom arrangement in phase determination (p. 297) | html | pdf |
- 14.2. MAD and MIR (pp. 299-309) | html | pdf | chapter contents |
  J. L. Smith, W. A. Hendrickson, T. C. Terwilliger and J. Berendzen
  - 14.2.1. Multiwavelength anomalous diffraction (pp. 299-303) | html | pdf |
    J. L. Smith and W. A. Hendrickson
    - 14.2.1.1. Anomalous scattering factors (pp. 299-300) | html | pdf |
    - 14.2.1.2. A phase equation for MAD (p. 300) | html | pdf |
    - 14.2.1.3. Diffraction ratios for estimating the MAD phasing signal (p. 301) | html | pdf |
    - 14.2.1.4. Experimental considerations (pp. 301-302) | html | pdf |
    - 14.2.1.5. Data handling (p. 302) | html | pdf |
    - 14.2.1.6. Approaches to MAD phasing (pp. 302-303) | html | pdf |
    - 14.2.1.7. Determination of the anomalous-scatterer partial structure (p. 303) | html | pdf |
    - 14.2.1.8. General anomalous-scatterer labels for biological macromolecules (p. 303) | html | pdf |
  - 14.2.2. Automated MAD and MIR structure solution (pp. 303-307) | html | pdf |
    T. C. Terwilliger and J. Berendzen
    - 14.2.2.1. Introduction (p. 303) | html | pdf |
    - 14.2.2.2. MAD and MIR structure solution (pp. 303-304) | html | pdf |
    - 14.2.2.3. Decision making and structure solution (p. 304) | html | pdf |
    - 14.2.2.4. The need for rapid refinement and phasing during automated structure solution (p. 304) | html | pdf |
    - 14.2.2.5. Conversion of MAD data to a pseudo-SIRAS form (pp. 304-305) | html | pdf |
    - 14.2.2.6. Scoring of trial heavy-atom solutions (pp. 305-306) | html | pdf |
    - 14.2.2.7. Automated MIR and MAD structure determination (p. 306) | html | pdf |
    - 14.2.2.8. Generation of model X-ray data sets (pp. 306-307) | html | pdf |
    - 14.2.2.9. Conclusions (p. 307) | html | pdf |
    - 14.2.2.10. Software availability (p. 307) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 14.2.1.1. Anomalous scattering factors for Se in a protein labelled with selenomethionine (p. 300) | html | pdf |

Part 15. Density modification and phase combination
- 15.1. Phase improvement by iterative density modification (pp. 311-324) | html | pdf | chapter contents |
  K. Y. J. Zhang, K. D. Cowtan and P. Main
  - 15.1.1. Introduction (p. 311) | html | pdf |
  - 15.1.2. Density-modification methods (pp. 311-318) | html | pdf |
    - 15.1.2.1. Solvent flattening (pp. 311-314) | html | pdf |
      - 15.1.2.1.1. Introduction (pp. 311-313) | html | pdf |
      - 15.1.2.1.2. The automated convolution method for molecular-boundary identification (p. 313) | html | pdf |
      - 15.1.2.1.3. The solvent-flattening procedure (p. 314) | html | pdf |
    - 15.1.2.2. Histogram matching (pp. 314-316) | html | pdf |
      - 15.1.2.2.1. Introduction (p. 314) | html | pdf |
      - 15.1.2.2.2. The prediction of the ideal histogram (pp. 314-315) | html | pdf |
      - 15.1.2.2.3. The process of histogram matching (pp. 315-316) | html | pdf |
      - 15.1.2.2.4. Scaling the observed structure-factor amplitudes according to the ideal density histogram (p. 316) | html | pdf |
    - 15.1.2.3. Averaging (pp. 316-317) | html | pdf |
      - 15.1.2.3.1. Introduction (p. 316) | html | pdf |
      - 15.1.2.3.2. The determination of noncrystallographic symmetry (pp. 316-317) | html | pdf |
      - 15.1.2.3.3. The refinement of noncrystallographic symmetry (p. 317) | html | pdf |
      - 15.1.2.3.4. The averaging of NCS-related molecules (p. 317) | html | pdf |
    - 15.1.2.4. Skeletonization (pp. 317-318) | html | pdf |
    - 15.1.2.5. Sayre's equation (p. 318) | html | pdf |
      - 15.1.2.5.1. Sayre's equation in real and reciprocal space (p. 318) | html | pdf |
      - 15.1.2.5.2. The application of Sayre's equation to macromolecules at non-atomic resolution – the θ( $[{\bf h}]$ ) curve (p. 318) | html | pdf |
    - 15.1.2.6. Atomization (p. 318) | html | pdf |
  - 15.1.3. Reciprocal-space interpretation of density modification (p. 319) | html | pdf |
  - 15.1.4. Phase combination (pp. 319-321) | html | pdf |
    - 15.1.4.1. Sim and $[\sigma_{a}]$ weighting (p. 320) | html | pdf |
    - 15.1.4.2. Reflection omit (p. 320) | html | pdf |
    - 15.1.4.3. The γ correction and solvent flipping (pp. 320-321) | html | pdf |
  - 15.1.5. Combining constraints for phase improvement (pp. 321-323) | html | pdf |
    - 15.1.5.1. The system of nonlinear constraint equations (p. 321) | html | pdf |
    - 15.1.5.2. Least-squares solution to the system of nonlinear constraint equations (pp. 321-323) | html | pdf |
      - 15.1.5.2.1. The conjugate-gradient method (p. 322) | html | pdf |
      - 15.1.5.2.2. The full-matrix solution (pp. 322-323) | html | pdf |
      - 15.1.5.2.3. The diagonal approximation (p. 323) | html | pdf |
  - 15.1.6. Example (pp. 323-324) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 15.1.2.1. Density-modification calculation showing iterative application of real-space and reciprocal-space constraints (p. 311) | html | pdf |
    - Fig. 15.1.2.2. Solvent mask determined from a map by Wang's method (p. 313) | html | pdf |
    - Fig. 15.1.2.3. Transformation of density ρ to $[\rho'_{\rm mod}]$ by histogram matching (p. 315) | html | pdf |
    - Fig. 15.1.2.4. Types of noncrystallographic symmetry and averaging calculation (p. 316) | html | pdf |
    - Fig. 15.1.3.1. The functions $[g({\bf x})]$ and $[G({\bf h})]$ for solvent flattening, histogram matching and averaging (p. 319) | html | pdf |
    - Fig. 15.1.6.1. Phase correlations after different combinations of density modifications (p. 323) | html | pdf |
  - Tables
    - Table 15.1.2.1. Constraints used in density modification (p. 312) | html | pdf |
- 15.2. Model phases: probabilities, bias and maps (pp. 325-331) | html | pdf | chapter contents |
  R. J. Read
  - 15.2.1. Introduction (p. 325) | html | pdf |
  - 15.2.2. Model bias: importance of phase (p. 325) | html | pdf |
    - 15.2.2.1. Parseval's theorem (p. 325) | html | pdf |
  - 15.2.3. Structure-factor probability relationships (pp. 325-327) | html | pdf |
    - 15.2.3.1. Wilson and Sim structure-factor distributions in P 1 (pp. 325-326) | html | pdf |
    - 15.2.3.2. Probability distributions for variable coordinate errors (p. 326) | html | pdf |
    - 15.2.3.3. General treatment of the structure-factor distribution (pp. 326-327) | html | pdf |
    - 15.2.3.4. Estimating $[\sigma_{A}]$ (p. 327) | html | pdf |
  - 15.2.4. Figure-of-merit weighting for model phases (p. 327) | html | pdf |
  - 15.2.5. Map coefficients to reduce model bias (pp. 327-328) | html | pdf |
    - 15.2.5.1. Model bias in figure-of-merit weighted maps (pp. 327-328) | html | pdf |
    - 15.2.5.2. Model bias in combined phase maps (p. 328) | html | pdf |
  - 15.2.6. Estimation of overall coordinate error (p. 328) | html | pdf |
  - 15.2.7. Difference-map coefficients (p. 328) | html | pdf |
  - 15.2.8. Refinement bias (pp. 328-329) | html | pdf |
  - 15.2.9. Maximum-likelihood structure refinement (p. 329) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 15.2.2.1. Schematic illustration of the relative errors introduced by a random choice of phase or a random choice of amplitude (p. 325) | html | pdf |
    - Fig. 15.2.3.1. Centroid of the structure-factor contribution from a single atom (p. 326) | html | pdf |
    - Fig. 15.2.3.2. Schematic illustration of the general structure-factor distribution, relevant in the case of any set of independent random errors in the atomic model (p. 327) | html | pdf |
    - Fig. 15.2.4.1. Figure-of-merit weighted model-phased structure factor, obtained as the probability-weighted average over all possible phases (p. 327) | html | pdf |

Part 16. Direct methods
- 16.1. Ab initio phasing (pp. 333-345) | html | pdf | chapter contents |
  G. M. Sheldrick, H. A. Hauptman, C. M. Weeks, R. Miller and I. Usón
  - 16.1.1. Introduction (p. 333) | html | pdf |
  - 16.1.2. Normalized structure-factor magnitudes (pp. 333-334) | html | pdf |
    - 16.1.2.1. SIR differences (p. 334) | html | pdf |
    - 16.1.2.2. SAS differences (p. 334) | html | pdf |
  - 16.1.3. Starting the phasing process (pp. 334-335) | html | pdf |
    - 16.1.3.1. Structure invariants (p. 334) | html | pdf |
    - 16.1.3.2. `Multisolution' methods and trial structures (pp. 334-335) | html | pdf |
  - 16.1.4. Reciprocal-space phase refinement or expansion ( shaking ) (pp. 335-336) | html | pdf |
    - 16.1.4.1. The tangent formula (p. 335) | html | pdf |
    - 16.1.4.2. The minimal function (p. 335) | html | pdf |
    - 16.1.4.3. Parameter shift (pp. 335-336) | html | pdf |
  - 16.1.5. Real-space constraints ( baking ) (p. 336) | html | pdf |
    - 16.1.5.1. Simple peak picking (p. 336) | html | pdf |
    - 16.1.5.2. Iterative peaklist optimization (p. 336) | html | pdf |
    - 16.1.5.3. Random omit maps (p. 336) | html | pdf |
  - 16.1.6. Fourier refinement ( twice baking ) (pp. 336-337) | html | pdf |
  - 16.1.7. Computer programs for dual-space phasing (pp. 337-339) | html | pdf |
    - 16.1.7.1. Flowchart and program comparison (p. 337) | html | pdf |
    - 16.1.7.2. Parameters and procedures (pp. 337-338) | html | pdf |
    - 16.1.7.3. Recognizing solutions (pp. 338-339) | html | pdf |
  - 16.1.8. Applying dual-space programs successfully (pp. 339-344) | html | pdf |
    - 16.1.8.1. Utilizing Pattersons for better starts (p. 340) | html | pdf |
    - 16.1.8.2. Avoiding false minima (pp. 340-341) | html | pdf |
    - 16.1.8.3. Data resolution and completeness (p. 341) | html | pdf |
    - 16.1.8.4. Choosing a refinement strategy (pp. 342-343) | html | pdf |
    - 16.1.8.5. Expansion to P 1 (p. 343) | html | pdf |
    - 16.1.8.6. Substructure applications (pp. 343-344) | html | pdf |
  - 16.1.9. Extending the power of direct methods (pp. 344-345) | html | pdf |
    - 16.1.9.1. Integration with isomorphous replacement (p. 344) | html | pdf |
    - 16.1.9.2. Integration with anomalous dispersion (pp. 344-345) | html | pdf |
    - 16.1.9.3. Integration with multiple-beam diffraction (p. 345) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 16.1.3.1. The conditional probability distribution of the three-phase structure invariants (p. 334) | html | pdf |
    - Fig. 16.1.7.1. A flowchart for the Shake-and-Bake procedure, which is implemented in both SnB and SHELXD (p. 337) | html | pdf |
    - Fig. 16.1.7.2. A histogram of figure-of-merit values (minimal function) for 378 scorpion toxin II trials (p. 338) | html | pdf |
    - Fig. 16.1.7.3. Tracing the history of a solution and a nonsolution trial for scorpion toxin II as a function of Shake-and-Bake cycle (p. 338) | html | pdf |
    - Fig. 16.1.8.1. Success rates for triclinic lysozyme are strongly influenced by the size of the parameter-shift angle (p. 341) | html | pdf |
    - Fig. 16.1.8.2. ( a ) Mean phase error as a function of resolution for the two independent ab initio SHELXD solutions of the previously unsolved protein hirustasin (p. 341) | html | pdf |
    - Fig. 16.1.8.3. ( a ) Success rates and ( b ) cost effectiveness for several dual-space strategies as applied to a 148-atom P 1 structure (p. 342) | html | pdf |
    - Fig. 16.1.8.4. Success rates for the 317-atom $[P2_{1}2_{1}2_{1}]$ structure of gramicidin A (p. 343) | html | pdf |
  - Tables
    - Table 16.1.2.1. Theoretical values pertaining to 's (p. 334) | html | pdf |
    - Table 16.1.7.1. Recommended parameter values for the SnB program (p. 338) | html | pdf |
    - Table 16.1.8.1. Some large structures solved by the Shake-and-Bake method (p. 339) | html | pdf |
    - Table 16.1.8.2. Overall success rates for full structure solution for hirustasin using different two-atom search vectors chosen from the Patterson peak list (p. 340) | html | pdf |
    - Table 16.1.8.3. Success rates for three P 1 structures illustrate the importance of using complete data to the highest possible resolution (p. 342) | html | pdf |
    - Table 16.1.8.4. Improving success rates by `completing' the vancomycin data (p. 342) | html | pdf |
- 16.2. The maximum-entropy method (pp. 346-351) | html | pdf | chapter contents |
  G. Bricogne
  - 16.2.1. Introduction (p. 346) | html | pdf |
  - 16.2.2. The maximum-entropy principle in a general context (pp. 346-348) | html | pdf |
    - 16.2.2.1. Sources of random symbols and the notion of source entropy (p. 346) | html | pdf |
    - 16.2.2.2. The meaning of entropy: Shannon's theorems (p. 346) | html | pdf |
    - 16.2.2.3. Jaynes' maximum-entropy principle (pp. 346-347) | html | pdf |
    - 16.2.2.4. Jaynes' maximum-entropy formalism (pp. 347-348) | html | pdf |
  - 16.2.3. Adaptation to crystallography (p. 348) | html | pdf |
    - 16.2.3.1. The random-atom model (p. 348) | html | pdf |
    - 16.2.3.2. Conventional direct methods and their limitations (p. 348) | html | pdf |
    - 16.2.3.3. The notion of recentring and the maximum-entropy criterion (p. 348) | html | pdf |
    - 16.2.3.4. The crystallographic maximum-entropy formalism (p. 348) | html | pdf |
    - 16.2.3.5. Connection with the saddlepoint method (p. 348) | html | pdf |
  - References | html | pdf |

Part 17. Model building and computer graphics
- 17.1. Around O (pp. 353-356) | html | pdf | chapter contents |
  G. J. Kleywegt, J.-Y. Zou, M. Kjeldgaard and T. A. Jones
  - 17.1.1. Introduction (p. 353) | html | pdf |
  - 17.1.2. O (pp. 353-354) | html | pdf |
  - 17.1.3. RAVE (pp. 354-355) | html | pdf |
  - 17.1.4. Structure analysis (p. 355) | html | pdf |
  - 17.1.5. Utilities (pp. 355-356) | html | pdf |
  - 17.1.6. Other services (p. 356) | html | pdf |
  - References | html | pdf |
- 17.2. Molecular graphics and animation (pp. 357-368) | html | pdf | chapter contents |
  A. J. Olson
  - 17.2.1. Introduction (p. 357) | html | pdf |
  - 17.2.2. Background – the evolution of molecular graphics hardware and software (pp. 357-358) | html | pdf |
  - 17.2.3. Representation and visualization of molecular data and models (pp. 358-363) | html | pdf |
    - 17.2.3.1. Geometric representation (pp. 359-360) | html | pdf |
    - 17.2.3.2. Volumetric representation (pp. 360-362) | html | pdf |
    - 17.2.3.3. Information visualization (pp. 362-363) | html | pdf |
  - 17.2.4. Presentation graphics (pp. 363-365) | html | pdf |
    - 17.2.4.1. Illustration (pp. 363-364) | html | pdf |
    - 17.2.4.2. Animation (pp. 364-365) | html | pdf |
    - 17.2.4.3. The return of physical models (p. 365) | html | pdf |
  - 17.2.5. Looking ahead (pp. 365-366) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 17.2.1.1. Model of a crystal structure proposed by René Häuy (p. 357) | html | pdf |
    - Fig. 17.2.2.1. One bay of X-RAC showing coefficient panels and the display oscilloscope (p. 357) | html | pdf |
    - Fig. 17.2.3.1. ORTEP plot of phenylhydroxynorbornanone showing atomic thermal ellipsoids (p. 358) | html | pdf |
    - Fig. 17.2.3.2. Ribbon diagram of actin monomer (PDB code: 1atn) (Kabsch et al (p. 359) | html | pdf |
    - Fig. 17.2.3.3. Simple bonding diagram of a DNA structure (PDB code: 140D) (Mujeeb et al (p. 359) | html | pdf |
    - Fig. 17.2.3.4. CPK representation of the same DNA structure as in Fig. 17.2.3.3 (p. 360) | html | pdf |
    - Fig. 17.2.3.5. Solvent-excluded surface of the DNA structure using a water probe radius of 1.5 Å (p. 360) | html | pdf |
    - Fig. 17.2.3.6. Hydrophobicity mapped onto a molecular surface (p. 361) | html | pdf |
    - Fig. 17.2.3.7. Crystallographic electron-density isosurfaces, showing details of a protein iron–sulfur cluster (p. 362) | html | pdf |
    - Fig. 17.2.3.8. A difference-electron-density map of a minor-groove drug binding in DNA (p. 362) | html | pdf |
    - Fig. 17.2.3.9. A difference distance matrix plot of the α ₁ –β ₂ interface of haemoglobin in the T to R transformation (p. 363) | html | pdf |
    - Fig. 17.2.4.1. Line-art molecular illustration (p. 364) | html | pdf |
    - Fig. 17.2.4.2. A stereolithographic model of betalactamase inhibitory protein (BLIP) (p. 364) | html | pdf |
    - Fig. 17.2.5.1. This image represents a volume of blood plasma 750 Å on a side (p. 365) | html | pdf |

Part 18. Refinement
- 18.1. Introduction to refinement (pp. 369-374) | html | pdf | chapter contents |
  L. F. Ten Eyck and K. D. Watenpaugh
  - 18.1.1. Overview (p. 369) | html | pdf |
  - 18.1.2. Background (p. 369) | html | pdf |
  - 18.1.3. Objectives (p. 369) | html | pdf |
  - 18.1.4. Least squares and maximum likelihood (pp. 369-370) | html | pdf |
  - 18.1.5. Optimization (p. 370) | html | pdf |
  - 18.1.6. Data (p. 370) | html | pdf |
  - 18.1.7. Models (pp. 370-372) | html | pdf |
  - 18.1.8. Optimization methods (pp. 372-373) | html | pdf |
    - 18.1.8.1. Solving the refinement equations (p. 372) | html | pdf |
    - 18.1.8.2. Normal equations (p. 372) | html | pdf |
    - 18.1.8.3. Choice of optimization method (p. 373) | html | pdf |
    - 18.1.8.4. Singularity in refinement (p. 373) | html | pdf |
  - 18.1.9. Evaluation of the model (pp. 373-374) | html | pdf |
    - 18.1.9.1. Examination of outliers in the model (p. 373) | html | pdf |
    - 18.1.9.2. Examination of model electron density (pp. 373-374) | html | pdf |
    - 18.1.9.3. R and R _free (p. 374) | html | pdf |
  - 18.1.10. Conclusion (p. 374) | html | pdf |
  - References | html | pdf |
- 18.2. Enhanced macromolecular refinement by simulated annealing (pp. 375-381) | html | pdf | chapter contents |
  A. T. Brunger, P. D. Adams and L. M. Rice
  - 18.2.1. Introduction (p. 375) | html | pdf |
  - 18.2.2. Cross validation (p. 375) | html | pdf |
  - 18.2.3. The target function (pp. 375-377) | html | pdf |
    - 18.2.3.1. X-ray diffraction data versus model (pp. 376-377) | html | pdf |
    - 18.2.3.2. A priori chemical information (p. 377) | html | pdf |
  - 18.2.4. Searching conformational space (pp. 377-379) | html | pdf |
    - 18.2.4.1. Molecular dynamics (p. 378) | html | pdf |
    - 18.2.4.2. Temperature control (p. 378) | html | pdf |
    - 18.2.4.3. Annealing schedules (pp. 378-379) | html | pdf |
    - 18.2.4.4. An intuitive explanation of simulated annealing (p. 379) | html | pdf |
  - 18.2.5. Examples (pp. 379-380) | html | pdf |
  - 18.2.6. Multi-start refinement and structure-factor averaging (p. 380) | html | pdf |
  - 18.2.7. Ensemble models (p. 380) | html | pdf |
  - 18.2.8. Conclusions (p. 381) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 18.2.2.1. Effect of resolution on coordinate-error estimates (p. 376) | html | pdf |
    - Fig. 18.2.3.1. The Gaussian probability distribution forms the basis of maximum-likelihood targets in crystallographic refinement (p. 376) | html | pdf |
    - Fig. 18.2.4.1. Illustration of simulated annealing for minimization of a one-dimensional function (p. 378) | html | pdf |
    - Fig. 18.2.5.1. Simulated annealing produces better models than extensive conjugate-gradient minimization (p. 379) | html | pdf |
    - Fig. 18.2.5.2. Maximum-likelihood targets significantly decrease model bias in simulated-annealing refinement (p. 380) | html | pdf |
- 18.3. Structure quality and target parameters (pp. 382-392) | html | pdf | chapter contents |
  R. A. Engh and R. Huber
  - 18.3.1. Purpose of restraints (p. 382) | html | pdf |
    - 18.3.1.1. Utility of restraints: protein/special geometries (p. 382) | html | pdf |
    - 18.3.1.2. Risk of restraints: bias, lack of cross validation (p. 382) | html | pdf |
  - 18.3.2. Formulation of refinement restraints (pp. 382-392) | html | pdf |
    - 18.3.2.1. Choice of properties for restraint (p. 383) | html | pdf |
    - 18.3.2.2. Simple derivation of force constants from parameter distributions (pp. 383-384) | html | pdf |
      - 18.3.2.2.1. Clustering (p. 383) | html | pdf |
      - 18.3.2.2.2. Treatment of outliers (pp. 383-384) | html | pdf |
    - 18.3.2.3. Bonds and angles (pp. 384-390) | html | pdf |
      - 18.3.2.3.1. Peptide parameters: proline, glycine, alanine and CB substitution (p. 384) | html | pdf |
      - 18.3.2.3.2. Aromatic residues: tryptophan, phenylalanine, tyrosine, histidine (p. 384) | html | pdf |
      - 18.3.2.3.3. Aliphatic residues: leucine, isoleucine, valine (p. 384) | html | pdf |
      - 18.3.2.3.4. Neutral polar residues: serine, threonine, glutamine, asparagine (p. 384) | html | pdf |
      - 18.3.2.3.5. Acidic residues: glutamate, aspartate (pp. 384-387) | html | pdf |
      - 18.3.2.3.6. Basic residues: arginine, lysine (p. 387) | html | pdf |
      - 18.3.2.3.7. Sulfur-containing residues: methionine, cysteine, disulfides (pp. 387-390) | html | pdf |
    - 18.3.2.4. Planarity restraints (p. 390) | html | pdf |
    - 18.3.2.5. Torsion angles (pp. 390-391) | html | pdf |
    - 18.3.2.6. Non-bonded interactions (p. 391) | html | pdf |
    - 18.3.2.7. Effects of hydrogen atoms in parameterization (p. 391) | html | pdf |
    - 18.3.2.8. Special geometries: cofactors, ligands, metals etc. (p. 391) | html | pdf |
    - 18.3.2.9. Addition of tailored information sources (p. 392) | html | pdf |
  - 18.3.3. Strategy of application during building/refinement (p. 392) | html | pdf |
    - 18.3.3.1. Confidence in restraints versus information from diffraction (p. 392) | html | pdf |
  - 18.3.4. Future perspectives (p. 392) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 18.3.2.1. Torsion dependence of proline angle geometry (p. 387) | html | pdf |
    - Fig. 18.3.2.2. Bimodal distributions for tyrosine (p. 387) | html | pdf |
    - Fig. 18.3.2.3. Tryptophan $[\chi_{2}]$ dihedral angle distribution (p. 390) | html | pdf |
  - Tables
    - Table 18.3.2.1. Bond lengths of standard amino-acid side chains (pp. 385-386) | html | pdf |
    - Table 18.3.2.2. Bond angles of standard amino-acid side chains (pp. 388-390) | html | pdf |
    - Table 18.3.2.3. Bond lengths (Å) and angles (°) of peptide backbone fragments (p. 391) | html | pdf |
- 18.4. Refinement at atomic resolution (pp. 393-402) | html | pdf | chapter contents |
  Z. Dauter, G. N. Murshudov and K. S. Wilson
  - 18.4.1. Definition of atomic resolution (pp. 393-395) | html | pdf |
    - 18.4.1.1. Ab initio phasing and atomic resolution (p. 395) | html | pdf |
  - 18.4.2. Data (p. 395) | html | pdf |
    - 18.4.2.1. Data quality (p. 395) | html | pdf |
    - 18.4.2.2. Anisotropic scaling (p. 395) | html | pdf |
  - 18.4.3. Computational algorithms and strategies (p. 396) | html | pdf |
    - 18.4.3.1. Classical least-squares refinement of small molecules (p. 396) | html | pdf |
    - 18.4.3.2. Least-squares refinement of large structures (p. 396) | html | pdf |
    - 18.4.3.3. Fast Fourier transform (p. 396) | html | pdf |
    - 18.4.3.4. Maximum likelihood (p. 396) | html | pdf |
    - 18.4.3.5. Computer power (p. 396) | html | pdf |
  - 18.4.4. Computational options and tactics (pp. 396-398) | html | pdf |
    - 18.4.4.1. Use of F or F ² (pp. 396-397) | html | pdf |
    - 18.4.4.2. Restraints and/or constraints on coordinates and ADPs (p. 397) | html | pdf |
    - 18.4.4.3. Partial occupancy (p. 397) | html | pdf |
    - 18.4.4.4. Validation of extra parameters during the refinement process (pp. 397-398) | html | pdf |
    - 18.4.4.5. Practical strategies (p. 398) | html | pdf |
  - 18.4.5. Features in the refined model (pp. 398-401) | html | pdf |
    - 18.4.5.1. Hydrogen atoms (pp. 398-399) | html | pdf |
    - 18.4.5.2. Anisotropic atomic displacement parameters (p. 399) | html | pdf |
    - 18.4.5.3. Alternative conformations (p. 399) | html | pdf |
    - 18.4.5.4. Ordered solvent water (pp. 399-400) | html | pdf |
    - 18.4.5.5. Automatic location of water sites (p. 400) | html | pdf |
    - 18.4.5.6. Bulk solvent and the low-resolution reflections (pp. 400-401) | html | pdf |
    - 18.4.5.7. Metal ions and other ligands in the solvent (p. 401) | html | pdf |
    - 18.4.5.8. Deformation density (p. 401) | html | pdf |
  - 18.4.6. Quality assessment of the model (p. 401) | html | pdf |
  - 18.4.7. Relation to biological chemistry (pp. 401-402) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 18.4.1.1. The thermal-ellipsoid model used to represent anisotropic atomic displacement, with major axes indicated (p. 393) | html | pdf |
    - Fig. 18.4.1.2. Histograms of B values for a protein structure, Micrococcus lysodecticus catalase (Murshudov et al (p. 394) | html | pdf |
    - Fig. 18.4.5.1. ( a ), ( b ) Representative electron-density maps for the refinement of Clostridium acidurici ferredoxin at 0.94 Å resolution (Dauter, Wilson et al (p. 398) | html | pdf |
    - Fig. 18.4.5.2. Schematic representation of the bulk-solvent models described in the text (p. 400) | html | pdf |
  - Tables
    - Table 18.4.1.1. The parameters of an atomic model (p. 393) | html | pdf |
    - Table 18.4.1.2. Features which can be seen in the electron density at different resolutions (p. 394) | html | pdf |
- 18.5. Coordinate uncertainty (pp. 403-418) | html | pdf | chapter contents |
  D. W. J. Cruickshank
  - 18.5.1. Introduction (p. 403) | html | pdf |
    - 18.5.1.1. Background (p. 403) | html | pdf |
    - 18.5.1.2. Accuracy and precision (p. 403) | html | pdf |
    - 18.5.1.3. Effect of atomic displacement parameters (or `temperature factors') (p. 403) | html | pdf |
  - 18.5.2. The least-squares method (pp. 404-405) | html | pdf |
    - 18.5.2.1. The normal equations (p. 404) | html | pdf |
    - 18.5.2.2. Weights (p. 404) | html | pdf |
    - 18.5.2.3. Statistical descriptors and goodness of fit (pp. 404-405) | html | pdf |
  - 18.5.3. Restrained refinement (pp. 405-406) | html | pdf |
    - 18.5.3.1. Residual function (p. 405) | html | pdf |
    - 18.5.3.2. A very simple protein model (pp. 405-406) | html | pdf |
    - 18.5.3.3. Relative weighting of diffraction and restraint terms (p. 406) | html | pdf |
  - 18.5.4. Two examples of full-matrix inversion (pp. 406-409) | html | pdf |
    - 18.5.4.1. Unrestrained and restrained inversions for concanavalin A (pp. 406-408) | html | pdf |
    - 18.5.4.2. Unrestrained inversion for an immunoglobulin (p. 408) | html | pdf |
    - 18.5.4.3. Comments on restrained refinement (p. 408) | html | pdf |
    - 18.5.4.4. Full-matrix estimates of precision (pp. 408-409) | html | pdf |
  - 18.5.5. Approximate methods (p. 409) | html | pdf |
    - 18.5.5.1. Block calculations (p. 409) | html | pdf |
    - 18.5.5.2. The modified Fourier method (p. 409) | html | pdf |
    - 18.5.5.3. Application of the modified Fourier method (p. 409) | html | pdf |
  - 18.5.6. The diffraction-component precision index (p. 410) | html | pdf |
    - 18.5.6.1. Statistical expectation of error dependence (p. 410) | html | pdf |
    - 18.5.6.2. A simple error formula (p. 410) | html | pdf |
    - 18.5.6.3. Extension for low-resolution structures and use of R _free (p. 410) | html | pdf |
    - 18.5.6.4. Position error (p. 410) | html | pdf |
  - 18.5.7. Examples of the diffraction-component precision index (pp. 411-412) | html | pdf |
    - 18.5.7.1. Full-matrix comparison with the diffraction-component precision index (p. 411) | html | pdf |
    - 18.5.7.2. Further examples of the DPI using R (p. 411) | html | pdf |
    - 18.5.7.3. Examples of the DPI using R _free (pp. 411-412) | html | pdf |
    - 18.5.7.4. Comments on the diffraction-component precision index (p. 412) | html | pdf |
  - 18.5.8. Luzzati plots (pp. 412-414) | html | pdf |
    - 18.5.8.1. Luzzati's theory (pp. 412-413) | html | pdf |
    - 18.5.8.2. Statistical reinterpretation of Luzzati plots (pp. 413-414) | html | pdf |
    - 18.5.8.3. Comments on Luzzati plots (p. 414) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 18.5.4.1. Plots of $[\sigma (r)]$ versus $[B_{\rm eq}]$ for concanavalin A with 0.94 Å data, ( a ) restrained full-matrix $[\sigma_{\rm res}(r)]$ , ( b ) unrestrained full-matrix $[\sigma_{\rm diff}(r)]$ (p. 407) | html | pdf |
    - Fig. 18.5.4.2. Plots of $[\sigma (l)]$ versus average $[B_{\rm eq}]$ for concanavalin A with 0.94 Å data, ( a ) restrained full-matrix $[\sigma_{\rm res}(l)]$ , ( b ) unrestrained full-matrix $[\sigma_{\rm diff}(l)]$ (p. 407) | html | pdf |
    - Fig. 18.5.4.3. Plot of $[\sigma_{\rm diff}(r)]$ versus $[B_{\rm eq}]$ from an unrestrained full matrix for immunoglobulin mutant (T39K) with 1.70 Å data (p. 408) | html | pdf |
    - Fig. 18.5.4.4. Plot of $[\sigma_{\rm diff}(l)]$ versus average $[B_{\rm eq}]$ from an unrestrained full matrix for immunoglobulin mutant (T39K) with 1.70 Å data (p. 408) | html | pdf |
    - Fig. 18.5.8.1. Luzzati plots showing the refined R factor as a function of resolution for 1TGI (solid squares) and 1TGF (open squares) (Daopin et al ., 1994) (p. 413) |

International Tables for CrystallographyVolume F: Crystallography of biological macromolecules

Edited by M. G. Rossmann and E. Arnold

Contents

International Tables for Crystallography
Volume F: Crystallography of biological macromolecules