Free R factor - Revision history

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-13T13:39:59Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-15T11:31:28Z

Style edits to align with printed edition

MassimoNespolo: languages

2016-04-14T11:56:09Z

languages

BrianMcMahon at 13:05, 7 April 2008

2008-04-07T13:05:20Z

BrianMcMahon at 12:49, 7 April 2008

2008-04-07T12:49:01Z

New page

== Definition ==

A residual function calculated during structure [[refinement]] in the same way as the conventional [[R factor|''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 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.

A weighted free ''R'' factor may also be calculated over the set of reflections not used in the refinement:

<math>wR = ({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|})^{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). [http://dx.doi.org/10.1016/S0076-6879%2897%2977021-6 ''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 [http://dx.doi.org/10.1107/97809553602060000707 doi:10.1107/97809553602060000707]

[[Category:Structure determination]]

← Older revision		Revision as of 13:39, 13 November 2017
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−	<font color='blue'>Facteur R libre</font> (''Fr''). <font color='black'>Fattore R libero</font> (''It''). <font color='purple'>自由Ｒ因子</font> (''Ja'').	+	<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'').

@@ Line 1: / Line 1: @@
-<font color='blue'>Facteur R libre</font> (''Fr''); <font color='black'>Fattore R libero</font> (''It''); <font color='purple'>自由Ｒ因子</font> (''Ja'').
+<font color='blue'>Facteur R libre</font> (''Fr''). <font color='black'>Fattore R libero</font> (''It''). <font color='purple'>自由Ｒ因子</font> (''Ja'').
@@ Line 16: / Line 16: @@
 A weighted free ''R'' factor may also be calculated over the set of reflections not used in the refinement:
-<math>wR = ({{\sum |w |Y_o - Y_c|^2|}\over{\sum |wY^2_o}|})^{1/2}</math>,
+<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''.
@@ Line 28: / Line 28: @@
 == 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]
 [[Category:Structure determination]]

← Older revision		Revision as of 11:56, 14 April 2016
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		+	<font color='blue'>Facteur R libre</font> (''Fr''); <font color='black'>Fattore R libero</font> (''It''); <font color='purple'>自由Ｒ因子</font> (''Ja'').
		+
		+
	== Definition ==		== Definition ==

@@ Line 9: / Line 9: @@
 <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: