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Dear Randy and CCP4ers,
why isn't there (to my knowledge) a full rotational symmetry orientation
search in molecular replacement, that, for instance in Patterson space,
generates for all trial orientations _all_ the Patterson vectors
according to the rotational symmetry of the space group? Wouldn't that
enhance the signal-to-noise for the orientation search in a similar way
as the full-symmetry approach in the translation search does?
Best regards,
Dirk.
Randy J. Read wrote:
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On Jan 5 2007, Jenny wrote:
I heard that it's quite tricky for R32 and I wondered what's that.
I've lost the post that talked about the impact of high symmetry on
molecular replacement, but it might be worth clarifying what was said.
For those who were at the recent CCP4 study weekend, Phil Evans
discussed this point. When you are carrying out a translation search
with the full symmetry methods in modern programs (fast CC search in
AMoRe or Molrep, LLG search in Phaser), the model is complete for every
translation, so symmetry doesn't have an effect on signal-to-noise. The
difficulty with high crystallographic symmetry comes at the point of the
rotation search, and it is the number of *primitive* symmetry operations
that matters, not the lattice translations. Phil mentioned two ways of
looking at this. One is in terms of the traditional Patterson overlap
rotation function, which compares the observed and calculated Pattersons
in a sphere around the origin. As the number of primitive symmetry
operations increases, the number of intramolecular vector sets
superimposed on each other around the origin also increases. Another way
to look at it is in terms of the rotation likelihood target used in
Phaser. This target considers what structure factors could be built up
by adding the contributions of the symmetry-related molecules, with
unknown relative phase. As the number of contributions increases, the
uncertainty in their sum increases, reducing the signal-to-noise. The
relative phases of contributions from molecules related by lattice
translations are known, because their relative positions are known. So
lattice translations don't affect the difficulty.
Actually, there's a third way to look at it, which might be the most
intuitive. The rotation search can also be carried out by computing the
correlation between the observed and calculated Patterson maps in P1.
This could be done in our old program BRUTE, but is most familiar as the
direct rotation function in XPLOR or CNS. The observed Patterson map has
contributions from the vectors between all pairs of molecules. If there
are N primitive symmetry operations, there are N^2 unique sets of
vectors between molecules. Of these, N are intramolecular vector sets
and can be predicted just knowing the orientation of the molecule. The
rest (N^2-N) are intermolecular vector sets, which cannot be predicted
until the translation is known and thus add noise to the rotation
search. So the rotation search can in principle explain the fraction
N/N^2 or 1/N of the vectors in the Patterson, which accounts nicely for
the increasing difficulty with higher primitive symmetry.
Non-crystallographic symmetry has a similar effect, and what matters is
the product of the number of NCS operations with the number of
crystallographic symmetry operations. But NCS also makes the translation
search more difficult, because you're only explaining a fraction of the
data in all but the last translation search.
Getting back to R32, it shouldn't be intrinsically difficult. There are
only 6 primitive symmetry operations, coming from the combination of the
3-fold and 2-fold operators, and the rest of the symmetry comes from
lattice translations. So R32 shouldn't be any more difficult than, say,
P32 or P6. We haven't noticed any differences in test cases.
I hope that helps!
Randy Read
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Dirk Kostrewa
Paul Scherrer Institut
Biomolecular Research, OFLC/110
CH-5232 Villigen PSI, Switzerland
Phone: +41-56-310-4722
Fax: +41-56-310-5288
E-mail: [EMAIL PROTECTED]
http://sb.web.psi.ch
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