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From Online Dictionary of Crystallography
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Facteur R libre (Fr). Freier R-Faktor (Ge). Fattore R libero (It). 自由Ｒ因子 (Ja). Factor R libre (Sp).
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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], Download all plugins for fl studio 10.
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
From Proteopedia
Free R (also called Rfree) 'is generally considered the most useful global measure of model-to-data agreement'[1]. It is a statistical quantity introduced in 1992 by Axel T. Brünger[2] to assess the quality of a model from X-ray crystallographic data. It is calculated in the same manner as the R value, but from a subset of the data set aside for the calculation of free R, and not used in the refinement of the model. It is a more reliable tool for assessing the model than the R value because it is not self-referential -- that is, as an estimation of errors, free R is free of any bias that may have been introduced during refinement. Free R is an example of the application of the more general method of cross validation.
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Good Values for Free R
As a rule of thumb, for models with resolution of 2.0 Å or better (Å values <2.0), free R should not exceed (resolution/10) by more than 0.05; that is, if the resolution is 2.0 Å, free R should not significantly exceed 0.25. For resolutions around 3.0 Å, the free R should not exceed (resolution/10). Free R values exceeding the worst 25% for the resolution of the model (see table below) raise doubts about the quality of the model.
Free R is positively correlated with resolution[1]:
| Resolution, Å | Median Free R[1] | Median Free R - (Resolution/10) | Free R Best 25% | Free R Worst 25% |
|---|---|---|---|---|
| 1.0 | 0.15 | 0.05 | <0.14 | >0.17 |
| 1.5 | 0.21 | 0.06 | <0.19 | >0.23 |
| 1.8 | 0.23 | 0.05 | <0.21 | >0.245 |
| 2.0 | 0.24 | 0.04 | <0.22 | >0.26 |
| 2.2 | 0.25 | 0.03 | <0.23 | >0.265 |
| 2.5 | 0.26 | 0.01 | <0.245 | >0.28 |
| 3.0 | 0.28 | - 0.02 | <0.26 | >0.30 |
| 3.5 | 0.30 | - 0.05 | <0.275 | >0.33 |
| ~4.0 | 0.31 | - 0.09 | <0.28 | >0.35 |
- Data in the above table for resolutions <= 3.5 Å are approximated from Figure 3C in [1], based on X-ray entries deposited in the PDB since 1990.
- Data for resolution ~4.0 Å are based on 199 X-ray entries, for which free R values are given, with resolutions of 3.9-4.1 Å (Feb 2013).
- The median resolution for X-ray entries in the PDB is 2.07 Å (Feb 2013).
Bad Values for Free R
In October, 2011, there are 182 X-ray crystallographic entries in the PDB with free R values of >= 0.37. 45 of these have a resolution <= 3.0 Å, and 5 have a resolution of <= 2.0 Å. It seems likely that there are serious errors in most of these 45 models.
In one amazing case, 1zff, the resolution is given as 0.94 Å, the R value as 0.428, and the free R as 0.444.
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No Value for Free R
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In October, 2011, there are 5,908 X-ray crystallographic entries in the PDB for which no free R value is given. These represent 8.8% of all 66,847 X-ray entries. Most of these were deposited before the free R methodology was described by Brünger in 1992[2].
| Deposition Date | X-ray entries | No Free R |
|---|---|---|
| Through 1990 | 666 | 666 (100%) |
| 1991-1995 | 3,209 | 2,852 (89%) |
| 1996-2000 | 8,832 | 1,858 (21%) |
| 2001-2005 | 18,522 | 342 (1.8%) |
| 2006- Oct 2011 | 35,618 | 190 (0.5%) |
See Also
Content Donors
The initial contents of this page were adapted from the Glossary of ProteinExplorer.Org, with the permission of the principal author, Eric Martz. The Free R entry there was written primarily by Diana Ditmore.
Literature Cited
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- ↑ 1.01.11.21.3 Read RJ, Adams PD, Arendall WB 3rd, Brunger AT, Emsley P, Joosten RP, Kleywegt GJ, Krissinel EB, Lutteke T, Otwinowski Z, Perrakis A, Richardson JS, Sheffler WH, Smith JL, Tickle IJ, Vriend G, Zwart PH. A new generation of crystallographic validation tools for the protein data bank. Structure. 2011 Oct 12;19(10):1395-412. PMID:22000512 doi:10.1016/j.str.2011.08.006
- ↑ 2.02.1 Brunger AT. Free R value: a novel statistical quantity for assessing the accuracy of crystal structures. Nature. 1992 Jan 30;355(6359):472-5. PMID:18481394
Proteopedia Page Contributors and Editors (what is this?)
Eric Martz, Eran Hodis