Re: [ccp4bb]: Non-merohedral twinning

["Peter Mueller" <peterm@mbi.ucla.edu>]

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Hi Roeland,

As far as I know there is no program that does the job for all possible cases.
However, the procedure is relatively simple:

The observed diffraction pattern is the overlay of two twin-related true
diffraction patterns. Each observed reflection has a twin-related reflection,
which can be calculated by the reciprocal twin-operator (in order to get the
reciprocal twin-operator you need to transpose AND invert the real
twin-matrix). If Ia and Ib are two OBSERVED twin-related reflections and I1
and I2 are their TRUE intensities, then is:

     Ia = (1-k) * I1 + k * I2
and
     Ib = k * I1 + (1-k) * I2

with the twin ratio k between 0 and 1.

Some easy arithmetics leads to the TRUE intenities:

     I1 = [(1-k)Ia - k*Ib]/(1-2k)
and
     I2 = [(1-k)Ib - k*Ia]/(1-2k)

Using these equations you can calculate the true intensities for each
twin-pair of obeserved reflections. 

A problem is that normally, you do not know the twin ratio k. Unfortunately, k
is a rather critical value for the untwinning. The best thing is to untwin the
data with different values for k, and to calculate the |E^2-1|-statistics for
each untwinned data-set. The best value for k gives you a value close to 0.736
in the |E^2-1|-statistics. 

Another problem is that while one reduces or removes the systematical errors
from the twinning, one artifically creates some new systematical errors. These
new errors are the larger the closer your twin ratio is to 0.5 (I think k<0.4,
or k>0.6, respectively, is required). For k = 0.5 (i.e. a perfect twin) the
wohle thing does not work at all (division by zero).

Because of the serious systematical errors created by the untwinning, you
should never REFINE against untwinned data.

See as well T.R. Schneider et al., Acta Cryst. 2000 D56, 705-713. In this
publication the authors report a case where untwinning of the data made a
solution by direct methods possible.

I hope this may help you

Cheers,
Peter





Roeland Boer <boer@dq.fct.unl.pt> said:

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> 
> Hi there,
> 
> I'm working on a dataset from a sample that is non-merohedrally twinned.
> I got the twinning operation and can process the reflections of the
> major component of the twin, but got a rather high Rint (11%). I thought
> that the two lattices would not overlap too much, but apparently they
> do. I'd like to detwin the data, and was wondering if somebody can point
> out programs that can handle NON-merohedral twinned data.
> 
> Thanks a lot,
> Roeland.
> 
> 



-- 
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Dr. Peter Mueller                                   fon: +1-310-825-142
UCLA-DOE Laboratory of Structural Biology           fax: +1-310-206-3914
and Molecular Medicine
201 MBI
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