Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 13.3, p. 349   | 1 | 2 |

Section 13.3.5. Packing check in translation functions

L. Tonga*

aDepartment of Biological Sciences, Columbia University, New York, NY 10027, USA
Correspondence e-mail:

13.3.5. Packing check in translation functions

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A correct molecular-replacement solution should lead to the placement of the search model at the correct orientation and position in the crystal unit cell. For this solution, there should be no or minimal steric clashes among the crystallographically related and noncrystallographically related molecules in the unit cell (unless there are large conformational changes for the model in the crystal unit cell). Therefore, proper packing of the search model in the crystal unit cell is an important component of the molecular-replacement structure solution.

The packing of the search model in the unit cell can be estimated by determining the electron-density overlap among the molecules. This overlap can be calculated numerically, given the molecular envelope (Hendrickson & Ward, 1976[link]). It can also be estimated by an analytical function (Harada et al., 1981[link]), [O\left(v_{0}\right) = {\textstyle\sum\limits_{h}}\left|\bar{F}_{h}^{c} \left(v_{0}\right)\right|^{2}\Big/N{\textstyle\sum\limits_{h}}\left|\,\bar{f}_{h,  1}\right|^{2}, \eqno (]where N is the number of crystallographic symmetry operators. This overlap function assumes a value of 1 when there is no overlap among the molecules, and higher values when there is overlap. This function has been used to replace the [({\textstyle\sum_{h}}|\bar{F}_{h}^{c}|^{4})^{1/2}] term in the denominator of equation ([link]) (Harada et al., 1981[link]). Consequently, those positions that lead to steric clashes among the molecules will be down-weighted, thereby increasing the signal for the correct solution.

The overlap functions provide an overall estimate for the packing of the search model in the unit cell. A more detailed packing analysis can be based on the checking of atomic contacts (Tong, 1993[link]). For example, the number of [\hbox{C}_{\alpha} \cdots \hbox{C}_{\alpha}] contacts below a pre-specified distance cutoff (normally between 2 to 3 Å) in a protein crystal can be determined. Too many such contacts would indicate significant overlap of the molecules. For nucleic acid structures, a set of representative atoms (for example, P, [{\rm C}'_{1}]) can be selected from each nucleotide for this packing analysis.


Harada, Y., Lifchitz, A., Berthou, J. & Jolles, P. (1981). A translation function combining packing and diffraction information: an application to lysozyme (high-temperature form). Acta Cryst. A37, 398–406.Google Scholar
Hendrickson, W. A. & Ward, K. B. (1976). A packing function for delimiting the allowable locations of crystallized macromolecules. Acta Cryst. A32, 778–780.Google Scholar
Tong, L. (1993). Replace, a suite of computer programs for molecular-replacement calculations. J. Appl. Cryst. 26, 748–751.Google Scholar

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