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

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. F. ch. 25.2, p. 712   | 1 | 2 |

Section 25.2.3.4. Statistical functions

A. T. Brunger,v* P. D. Adams,e W. L. DeLano,f P. Gros,g R. W. Grosse-Kunstleve,e J.-S. Jiang,h N. S. Pannu,i R. J. Read,j L. M. Ricek and T. Simonsonl

25.2.3.4. Statistical functions

| top | pdf |

The CNS language contains a number of statistical operations, such as binwise averages and summations. The resolution bins are defined by a central facility in CNS.

Fig. 25.2.3.3[link] shows how [\sigma_{A}], [\sigma_{\Delta}] and D (Read, 1986[link], 1990[link]) are computed from the observed structure factors (`fobs') and the calculated model structure factors (`fcalc') using the CNS statistical operations. The first five operations are performed for the reflections in the test set, while the last three operations expand the results to all reflections. The `norm' function computes normalized structure-factor amplitudes for the specified arguments. The `sigacv' function evaluates [\sigma_{A}] from the normalized structure factors. The `save' function computes the statistical average [\hbox{save}(\;f) = {\textstyle\sum_{hkl}\displaystyle f_{hkl} (w/\varepsilon) \over \textstyle\sum_{hkl}\displaystyle w}, \eqno(25.2.3.10)] where w is 1 and 2 for centric and acentric reflections, respectively, and ɛ is the statistical weight. The averages are computed binwise, and the result for a particular bin is stored in all selected reflections belonging to the bin.

[Figure 25.2.3.3]

Figure 25.2.3.3| top | pdf |

Example for statistical operations provided by the CNS language. `norm', `sigacv', `save' and `sum' are functions that are computed internally by the CNS program. Binwise operations are in italics (`sigacv', `save' and `sum'). The result for a particular bin is stored in all elements belonging to the bin. The [\sigma_{A}] (`sigmaA') parameters are computed in binwise resolution shells. The [\sigma_{\Delta}] (`sigmaD') and D parameters are then computed from [\sigma_{A}] and binwise averages involving [|{\bf F}_{o}|^{2}] and [|{\bf F}_{c}|^{2}]. The binwise results are expanded to all reflections by the last three statements. `test' is an array that is 1 for all reflections in the test set and 0 otherwise. `sum' is a binwise operation on all reflections with the same partitioning used for the test set.

References

First citation Read, R. J. (1986). Improved Fourier coefficients for maps using phases from partial structures with errors. Acta Cryst. A42, 140–149.Google Scholar
 First citation Read, R. J. (1990). Structure-factor probabilities for related structures. Acta Cryst. A46, 900–912.Google Scholar








































to end of page
to top of page