Chapter 2.3 Patterson and molecular replacement techniques, and the use of noncrystallographic symmetry in phasing

Reciprocal space

Second Online Edition (2010)

Part 2. Reciprocal space in crystal-structure determination

  1. L. Tong3,
  2. M. G. Rossmann1,
  3. E. Arnold2

Published Online: 1 JUN 2010

DOI: 10.1107/97809553602060000765

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Tong, L., Rossmann, M. G. and Arnold, E. 2010. Patterson and molecular replacement techniques, and the use of noncrystallographic symmetry in phasing. International Tables for Crystallography. B:2:2.3:244–281.

Author Information

  1. 1

    Department of Biological Sciences, Columbia University, New York 10027, USA

  2. 2

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

  3. 3

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

Publication History

  1. Published Online: 1 JUN 2010


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 dramatically increasing number of macromolecular structures is expected to broaden the applicability of the molecular replacement method, since suitable search models can be found for more and more unknown structures. 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;
  • locked rotation functions;
  • fast rotation function;
  • translation functions;
  • locked translation functions;
  • phase improvement