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

International Tables for Crystallography (2006). Vol. F, ch. 13.3, pp. 276-277   | 1 | 2 |

Section 13.3.4. Phased translation function

L. Tonga*

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

13.3.4. Phased translation function

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If an atomic model needs to be placed in an electron-density map that has been obtained through other methods (e.g. the multiple-isomorphous-replacement method or partial model phases), the phased translation function can be used (Bentley & Houdusse, 1992[link]; Colman et al., 1976[link]; Read & Schierbeek, 1988[link]; Tong, 1993[link]). It is essentially based on the correlation between observed and calculated electron-density values throughout the unit cell: [PTF\left(v_{0}\right) = {\textstyle\sum\limits_{h}} {\textstyle\sum\limits_{n}}\ \overline{F}_{h}^{o}\ \overline{f}_{h, \, n}^{*} \exp(- 2\pi ih\left[T_{n}\right]v_{0}). \eqno (] Therefore, the phased translation function can also be evaluated by the FFT technique. As with the Patterson-correlation translation function, the phased translation function can be placed on an `absolute' scale by introducing appropriate normalizing factors or by converting the results to R factors or correlation coefficients. It should be noted that the prior phase could be in the wrong hand, so both [\overline{F}_{h}^{o}] and [(\overline{F}_{h}^{o})^{*}] may need to be tried in the phased translation function.

The stationary molecules contribute a constant to the phased translation function and are not shown in equation ([link]). However, the phase information from the stationary molecules can be applied to the observed structure-factor amplitudes, and the phased translation function, rather than the Patterson-correlation translation function, can be used in the search for additional molecules (Bentley & Houdusse, 1992[link]; Driessen et al., 1991[link]; Read & Schierbeek, 1988[link]). This could prove especially useful in locating the last few molecules in cases where there are several molecules in the asymmetric unit.


Bentley, G. A. & Houdusse, A. (1992). Some applications of the phased translation function in macromolecular structure determination. Acta Cryst. A48, 312–322.Google Scholar
Colman, P. M., Fehlhammer, H. & Bartels, K. (1976). Patterson search methods in protein structure determination: β-trypsin and immunoglobulin fragments. In Crystallographic computing techniques, edited by F. R. Ahmed, K. Huml & B. Sedlacek, pp. 248–258. Copenhagen: Munksgaard.Google Scholar
Driessen, H. P. C., Bax, B., Slingsby, C., Lindley, P. F., Mahadevan, D., Moss, D. S. & Tickle, I. J. (1991). Structure of oligomeric βB2-crystallin: an application of the T2 translation function to an asymmetric unit containing two dimers. Acta Cryst. B47, 987–997.Google Scholar
Read, R. J. & Schierbeek, A. J. (1988). A phased translation function. J. Appl. Cryst. 21, 490–495.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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