Chapter

Chapter 2.1 Introduction to basic crystallography

Crystallography of biological macromolecules

Second Online Edition (2012)

Part 2. Basic crystallography

  1. J. Drenth

Published Online: 14 APR 2012

DOI: 10.1107/97809553602060000808

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Drenth, J. 2012. Introduction to basic crystallography. International Tables for Crystallography. F:2:2.1:45–63.

Author Information

  1. Laboratory of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

Publication History

  1. Published Online: 14 APR 2012

Abstract

Crystals are the indispensable objects for the structure determination of globular proteins by X-ray diffraction. They consist of building blocks (unit cells) arranged in a three-dimensional array. According to their internal symmetry, they belong to one of the 230 possible space groups. Owing to the asymmetric structure of biological macromolecules, their crystals are restricted to the 65 enantiomorphic (not superimposable on its mirror image) space groups. The diffraction of X-rays by a crystal is explained in steps, from diffraction by one electron and two electrons via an atom and a unit cell to the diffraction by a crystal. This results in the Laue conditions for diffraction and the famous law introduced by Bragg: equation image. Reciprocal space is introduced as a most useful concept in constructing the directions of diffraction. The X-ray beams diffracted by a crystal are characterized by their structure factor equation image, where equation image is the amplitude of the beam and equation image is its phase angle with respect to a chosen origin. equation image, where equation image is the intensity of the diffracted beam. This is true if some correction factors (Lorentz, polarization and absorption) are neglected. For the determination of equation image various indirect and direct methods are available. Because the structure factor equation image is the result of the scattering by all electrons in the unit cell, it can be written as equation image, where V is the volume of the unit cell. The electron density equation image is obtained by Fourier inversion: equation image. The final result of a structure determination by X-ray diffraction is a molecular model based on the calculated electron density equation image.

Keywords:

  • Ewald sphere;
  • Patterson functions;
  • anomalous scattering;
  • crystal systems;
  • diffraction-pattern symmetry;
  • diffraction physics;
  • calculation of electron density;
  • mosaicity;
  • point groups;
  • reciprocal space;
  • integrated reflection intensity;
  • structure factors;
  • symmetry