Twinning (another verbose reply)
Randy Read
rndy at wimsey.mmid.ualberta.ca
Wed Feb 15 16:31:44 EST 1995
In article <PHIL.95Feb14103055 at xtreme1.mskcc.org> phil at xtreme1.mskcc.org (Phil
Jeffrey) writes:
>
> (most of the post deleted)
>
> We were, however, assisted by the fact that the non-xtallographic symmetry
> and the twinning operation were similar operators in reciprocal space (they
> might act in different ways mathematically, but they both work to increase
> the correlation between I(hkl) and I(h'k'l'), so I actually ignored the
> twinning in the case where alpha=0.11 for most of the refinement). The
> twinning-ignored maps were often better than the twin-corrected maps,
> presumably because the data was more complete in the former case.
>
This brings up a point that has to be considered in dealing with data from
twinned crystals. Most often exact twinning seems to arise *as a result* of
parallel non-crystallographic symmetry. So most of the time, there would be
some correlation between "twin-related" reflections even in data from a
completely untwinned crystal. Almost all of the methods that have been
proposed for estimating the twinning fraction assume that the reflections
superimposed by the twinning operation are uncorrelated, or independent. If
the intrinsic correlation is not too high (because the interplay between
crystallographic and non-crystallographic symmetry causes the contributions of
the NCS related molecules to add up with different relative phases in the
twin-related reflections), these methods probably work reasonably well. But
you can't count on it, and you should be certain of what is going on.
The particular case I'm thinking of is human GAPDH, the high resolution
refinement of which we took over from Herman Watson while I was working with
Wim Hol. Herman's group published a nice paper about the twinning (JMB
104:277-283, 1976), which you can read to get the background. It turns out
that, in this case, NCS-related contributions have more-or-less the same
relative phase in the twin-related reflections, so reflections related by the
twinning operation would have very similar intensities in an untwinned crystal.
(It's close enough to exact that the methods to estimate twinning fraction by
assuming independence are completely invalidated, but far enough from exact
that you can't get away with ignoring the twinning.) We used an idea we got
from Herman to work out the twinning fraction. It turns out that only half of
the reflections are twinned, while the other half interleave in the diffraction
pattern. If you assume that the average intensities should be the same in both
halves of the untwinned data (and there's no translational pseudosymmetry to
invalidate this), you can work out the twinning fraction simply by comparing
the average intensities in the observed data. The twinned reflections have a
higher average intensity because they are the sum of diffraction from both twin
components. This seems to work quite well, but of course, it is a special
solution to a very special case.
Randy Read
rndy at mycroft.mmid.ualberta.ca
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