Position of a noncrystallographic symmetry element in a poorly defined electron-density map

Rossmann, M. G.; Arnold, E.

doi:10.1107/97809553602060000556

International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

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International Tables for Crystallography (2006). Vol. B. ch. 2.3, p. 260 | 1 | 2 |

Section 2.3.7.4. Position of a noncrystallographic symmetry element in a poorly defined electron-density map

M. G. Rossmann^a ^* and E. Arnold^b

^aDepartment of Biological Sciences, Purdue University, West Lafayette, Indiana 47907, USA, and ^bCABM & Rutgers University, 679 Hoes Lane, Piscataway, New Jersey 08854-5638, USA
Correspondence e-mail: mgr@indiana.bio.purdue.edu

2.3.7.4. Position of a noncrystallographic symmetry element in a poorly defined electron-density map

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If an initial set of poor phases, for example from an SIR derivative, are available and the rotation function has given the orientation of a noncrystallographic rotation axis, it is possible to search the electron-density map systematically to determine the translation axis position. The translation function must, therefore, measure the quality of superposition of the poor electron-density map on itself. Hence $[{\bf S}_{x} = {\bf S}_{x'} = {\bf S}]$ and the function (2.3.7.1) now becomes $[T({\bf S}) = {2 \over V_{{\bf h}}^{2}} {\sum\limits_{{\bf h}}} {\sum\limits_{{\bf p}}} |{\bf F}_{{\bf h}}| |{\bf F}_{{\bf p}}| G_{{\bf hp}} \cos [\alpha_{{\bf h}} + \alpha_{{\bf p}} - 2 \pi ({\bf h} + {\bf p}) \cdot {\bf S}].]$ This real-space translation function has been used successfully to determine the intermolecular dyad axis for α-chymotrypsin (Blow et al., 1964) and to verify the position of immunoglobulin domains (Colman & Fehlhammer, 1976).

References

Blow, D. M., Rossmann, M. G. & Jeffery, B. A. (1964). The arrangement of α-chymotrypsin molecules in the monoclinic crystal form. J. Mol. Biol. 8, 65–78.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

International Tables for Crystallography (2006). Vol. B. ch. 2.3, p. 260