Chapter 2.3 Patterson and molecular-replacement techniques

Reciprocal space

First Online Edition (2006)

Part 2. Reciprocal space in crystal-structure determination

  1. M. G. Rossmann1,
  2. E. Arnold2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000556

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Rossmann, M. G. and Arnold, E. 2006. Patterson and molecular-replacement techniques. International Tables for Crystallography. B:2:2.3:235–263.

Author Information

  1. 1

    Department of Biological Sciences, Purdue University, West Lafayette, Indiana 47907, USA

  2. 2

    CABM & Rutgers University, 679 Hoes Lane, Piscataway, New Jersey 08854-5638, USA

Publication History

  1. Published Online: 1 JAN 2006


The Patterson function is a phaseless Fourier synthesis of diffraction intensities that corresponds to an autocorrelation of electron densities in a crystal cell. Prominent non-origin peaks in a Patterson function represent interatomic vectors; deconvolution of this information can be used to locate heavy atoms, known structures or structural fragments. Interpretation of Patterson maps lies at the foundation of most macromolecular structure elucidation processes, both in determining the position of heavy atoms and/or anomalous scatterers for the isomorphous replacement and anomalous scattering methods, and in determining the orientation and position of a homologous protein model for the molecular-replacement method. The molecular-replacement method also encompasses the use of noncrystallographic redundancy within a crystal or between crystal forms to phase and refine crystal structures. Applications of Patterson and molecular-replacement techniques to structure determination including Patterson interpretation methods, rotation functions, translation functions, symmetry averaging, density modification and phase extension are discussed.


  • Patterson functions;
  • molecular replacement;
  • origin removal;
  • sharpened Patterson functions;
  • enantiomorphic solutions;
  • Harker sections;
  • heavy-atom location;
  • superposition methods;
  • vector-search procedures;
  • isomorphous replacement;
  • difference Patterson functions;
  • correlation functions;
  • centrosymmetric projections;
  • heavy-atom substitution;
  • anomalous dispersion;
  • anomalous scattering;
  • noncrystallographic symmetry;
  • rotation functions;
  • fast rotation function;
  • translation functions;
  • phase improvement