detwin HKLIN foo_in.mtz HKLOUT foo_out.mtz
[Keyworded input]
Twinned data is measured when two or more copies of the reciprocal lattice overlap. Hence we need to deconvolute the two twinned components to obtain useable data. The equations for two overlapping reflections, Itrue(h1) and Itrue(h2), are:
ITw(h1) = (1-tf)*Itrue(h1) + tf*Itrue(h2)
ITw(h2) = tf*Itrue(h1) + (1-tf)*Itrue(h2)
where tf is the twin fraction, often denoted as 'alpha'
thus Itrue(h1) = ((1-tf)*iTw(h1) -tf*iTw(h2)) / (1-2tf)
thus Itrue(h2) = ((1-tf)*iTw(h2) -tf*iTw(h1)) / (1-2tf)
also
var(h1) = ((1-tf)/(1-2tf))**2 * sdTw(h1)**2 + (tf/(1-2tf))**2 * sdTw(h2)**2
var(h2) = ((1-tf)/(1-2tf))**2 * sdTw(h2)**2 + (tf/(1-2tf))**2 * sdTw(h1)**2
This deconvolution is only possible if tf is not exactly 0.5. As it approaches this value the variances become extremely large.
The occurrence of twinning can often be recognised from the intensity statistics of the data set. It is important to first check whether the crystal has a pseudo translation relating two or more molecules in the asymmetric unit. Such a translation will result in some reflection classes being very weak. This program carries out several tests for twinning as a function of both twinning fraction, and resolution. It reads either intensities or amplitudes from an MTZ file, It can also detwin merohedrally twinned data for a given twinning fraction and write either corrected intensities or amplitudes for a given twinning fraction.
The twin operator is required (see TABLE OF POSSIBILITIES), and for MTZ output, the chosen twin fraction. The CCP4 GUI suggests possible twinning operators derived from the space group, or it can be entered by the user.
The twinning tests performed are:
The partial twin test (see reference [4]) <H> = <|Itw1 -Itw2|/(Itw1 +Itw2)> plotted against theoretical expectations.
The estimate of the twinning factor as (0.5 -<H>), plotted against resolution.
Those tabulated against the twinning factor, for values ranging from 0.00 to 0.48, are
(N.B. it is impossible to evaluate Itrue if the twinning-factor is exactly 0.5):
If the output MTZ file contains IMEAN, it can be run through TRUNCATE again, and the other moments and the N(z) test examined to see if the intensity statistics now follow the expected distribution for non-twinned data. twinned. See Cumulative distribution plot, which for twinned data becomes sigmoidal, and the moments of E (or Z) which are different for twinned data than for untwinned.
The general formulae for expected moments <Z^k> for untwinned acentric data are (Z defined above):
k-th moment of Z = Gamma(k+1) = k! if k is an integer k-th moment of Z = sqrt(PI) * k * (k-1) * ... * 0.5 if k equals integer+0.5 k-th moment of E = (k/2)-th moment of ZSee also the truncate documentation. Table of moments:
Acentric Centric
Untwinned data Perfect twin. Untwinned data Perfect twin.
<E> 0.886 0.94 0.798 0.886
<E^3> 1.329 1.175 1.596 1.329
<Z^2> 2.0 1.5 3.0 2.0
<Z^3> 6.0 3.0 15.0 6.0
<Z^4> 24.0 7.5 105.0 24.0
Input Files:
Output Files:
DEBUG, PLOT,LABIN, RESOLUTION, OPERATOR, SIGMACUT,TITLE, TWIN_FRACTION
Title to write to output reflection file.
Default is to keep the title on the input MTZ file. If there is no title on the input MTZ file, then the title is set to: "From Detwin on the <date>"
[OPTIONAL INPUT]
The various tests are carried out with all reflections, and repeated for those reflections which are greater than <Nsig>*I. Tests such as the Britton plot or those using <H> are unreliable for weak data.
[OPTIONAL INPUT]
Resolution limits - either 4(sin theta/lambda)**2 or d in Angstroms (either order). Reflections outside these limits will be excluded from all analysis and omitted on output. Defaults are taken from the range of data in the input file (i.e. all data included).
Twinning operator, given as the indices of the reflection that is related to the reflection (h,k,l) by the twin operator. See TABLE for likely operators for each space group. If there is only one possibility for a spacegroup this will be used, and there is no need to input an operator. Otherwise it is COMPULSORY.
For example for P31
either OPERATOR -h,-k, l
or OPERATOR k, h,-l
or OPERATOR -k,-h,-l
If string is set to MURR, a Murray-Rust plot of |Fo1|/|Fo2| is generated. There is no debug information possible. (See reference [5].)
If this is given, an output MTZ file will be written to HKLOUT with Is or Fs corrected assuming the twin fraction <alpha>. It is difficult to estimate the twinfrac accurately unless the data is of very good quality, but look at all the information plotted. To carry out the exhaustive TRUNCATE tests you will need to run the program several times and look at the resulting intensity statistics. The value which gives the best fit to the theoretical distribution for the acentric terms should be used. Alternatively, run the Uppsala program "dataman" (keyword GEminin) which will estimate the twin fraction.
Once a refined model has been obtained, it is possible to use the Fcalc values from this model to obtain a better estimate of the twin fraction (not yet implemented).
Specify input column labels. [OPTIONAL INPUT]
Truncate takes output from SCALA and SCALEPACK2MTZ which generate standard labels. This is the most common usage of the program, in which case LABIN records are not required.
The program labels defined are: F SIGF IMEAN SIGIMEAN F(+) SIGF(+) F(-) SIGF(-) I(+) SIGI(+) I(-) SIGI(-)
NB: Only F/SIGF or IMEAN/SIGIMEAN or F(+) F(-) SIGF(+) SIGF(-) or I(+) I(-) SIGI(+) SIGI(-) can be assigned. If F(+-) or I(+-) are assigned the anomalous pairs are detwinned.
- F
- A Structure Amplitude. The structure intensity used for detwinning is generated on input.
- SIGF
- Standard deviation of the above
- IMEAN
- Original average Structure Intensity
- SIGIMEAN
- Standard deviation of the above
- I(+)
- Structure Intensity of hkl
- SIGI(+)
- Standard deviation of the above
- I(-)
- Structure Intensity of -h -k -l
- SIGI(-)
- Standard deviation of the above
Debug output will be printed for <ndebug> reflections
#!/bin/csh -fv
detwin hklin /ss5/hotaylor/andrew/h1_scala.mtz \
hklout $scr0/detwin.mtz << eof-detwin
title DETWIN WITH TWIN FRAC 0.4
SYM -k,-h,-l
twin 0.4
LABI IMEAN=I SIGIMEAN=SIGI
eof-detwin
# Run TRUNCATE to check all moments and N(z) statistics
trunc:
truncate hklin $scr0/detwin.mtz hklout $scr0/trunc_detwin.mtz <
#!/bin/csh -f
#
detwin HKLIN s100_tetpt.mtz \
HKLOUT $SCRATCH/s100_tetpt-detw.mtz \
<< eof
TITLE Sp100 test R3
RESO 10 3.5
#SYMM k,h,-l # No need for detwinning operator this is the only possibility for R3
TWIN 0.19 # the output file will have Idetw1 and Idetw2
SIG 6 # only analyse data where Ih1 and Ih2 are greater than 6Sigma
LABI F=F SIGF=SIGF
END
eof