Difference between revisions of "Free R factor"
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| + | <font color="blue">Facteur R libre</font> (''Fr''). <font color="red">Freier R-Faktor</font> (''Ge''). <font color="black">Fattore R libero</font> (''It''). <font color="purple">自由Ｒ因子</font> (''Ja''). <font color="green">Factor R libre</font> (''Sp''). | ||
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== Definition == | == Definition == | ||
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<math>R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}</math>, | <math>R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}</math>, | ||
| − | but uses a small subset of reflections that are ''not'' used in the refinement of the structural model. Thus <math>R_\textrm{free}</math> tests how well the model predicts experimental observations that are not themselves used to fit the model. A fixed percentage of the total number of reflections is usually assigned to the free group. | + | but uses a small subset of randomly selected reflections that are set aside from the beginning and ''not'' used in the refinement of the structural model. Thus <math>R_\textrm{free}</math> tests how well the model predicts experimental observations that are not themselves used to fit the model. A fixed percentage of the total number of reflections is usually assigned to the free group. |
A weighted free ''R'' factor may also be calculated over the set of reflections not used in the refinement: | A weighted free ''R'' factor may also be calculated over the set of reflections not used in the refinement: | ||
| − | <math>wR = ( | + | <math>wR = \left( {\sum | w | Y_o - Y_c |^2{| }\over{\sum |wY^2_o}| }\right)^{1/2}</math>, |
where ''Y'' represents ''F'', <math>F^2</math> or ''I''. | where ''Y'' represents ''F'', <math>F^2</math> or ''I''. | ||
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== See also == | == See also == | ||
| − | Validation of protein crystal structures. | + | *Validation of protein crystal structures. G. J. Kleywegt. ''International Tables for Crystallography'' (2006). ''Vol. F'', [https://doi.org/10.1107/97809553602060000707 ch. 21.1, pp. 497-506 doi:10.1107/97809553602060000707] |
| − | G. J. Kleywegt. ''International Tables for Crystallography'' (2006). Vol. F, | ||
[[Category:Structure determination]] | [[Category:Structure determination]] | ||
Latest revision as of 13:39, 13 November 2017
Facteur R libre (Fr). Freier R-Faktor (Ge). Fattore R libero (It). 自由Ｒ因子 (Ja). Factor R libre (Sp).
Contents
Definition
A residual function calculated during structure refinement in the same way as the conventional R factor, but applied to a small subset of reflections that are not used in the refinement of the structural model. The purpose is to monitor the progress of refinement and to check that the R factor is not being artificially reduced by the introduction of too many parameters.
Discussion
Many macromolecular structure refinements now use the statistical cross-validation technique of monitoring a `free' R factor [math]R_\textrm{free}[/math]. It is calculated in the same way as the conventional least-squares R factor
[math]R = {{\sum | F_{obs} - F_{calc} | } \over {\sum |F_{obs} |}}[/math],
but uses a small subset of randomly selected reflections that are set aside from the beginning and not used in the refinement of the structural model. Thus [math]R_\textrm{free}[/math] tests how well the model predicts experimental observations that are not themselves used to fit the model. A fixed percentage of the total number of reflections is usually assigned to the free group.
A weighted free R factor may also be calculated over the set of reflections not used in the refinement:
[math]wR = \left( {\sum | w | Y_o - Y_c |^2{| }\over{\sum |wY^2_o}| }\right)^{1/2}[/math],
where Y represents F, [math]F^2[/math] or I.
After each cycle of refinement, the free R factor and the R factor for the working set of reflections are both calculated. However, as the refinement converges, the working and free R factors both approach stable values. It is common practice, particularly in structures at high resolution, to stop monitoring [math]R_\textrm{free}[/math] at this point and to include all the reflections in the final rounds of refinement.
History
The idea of the free R factor was introduced by Brünger, A. T. [(1997). Methods Enzymol. 277, 366–396. Free R value: cross-validation in crystallography.]
See also
- Validation of protein crystal structures. G. J. Kleywegt. International Tables for Crystallography (2006). Vol. F, ch. 21.1, pp. 497-506 doi:10.1107/97809553602060000707