[log in to unmask] wrote:
> Rotational near-crystallographic ncs is easy to handle this way, but
> what about translational pseudo-symmetry (or should that be
> pseudo-translational symmetry)? In such cases one whole set of spots is
> systematically weaker than the other set. Then what is the
> "theoretically correct" way to calculate Rfree? Write one's own code to
> sort the spots into two piles?
> Phoebe
>
Dear Phoebe,
I've always been a fan of splitting the test set in these situations.
The weak set of reflections provide information about the differences
between the ncs mates (and the deviation of the ncs operator from a
true crystallography operator) while the strong reflections provide
information about the average of the ncs mates. If you mix the two
sets in your Rfree calculation the strong set will tend to dominate
and will obscure the consequences of allowing you ncs mates too much
freedom to differ.
Let's say you have a pseudo C2 crystal with the dimer as the ncs
pair and you are starting with a perfect C2 symmetry model. The
initial rigid body refinement will cause the Rfree(weak) to drop
because the initial model had Fc's equal to zero for all these
reflections and the deviation from crystal symmetry allows nonzero
values to arise.
Now you want to test if there are real differences between the
two copies. If you allow variation between the two copies but
monitor the Rfree(strong) you are actually monitoring the quality
of the average of the two copies, and you basically have a two-fold
multimodel. It is the same as putting two molecules at each site
in the crystal and forcing both models to have perfect ncs.
Axel Brunger's "Methods in Enzymology" chapter indicates that a
two-fold multimodel is expected to have a lower Rfree than a single
model and we would expect in our imaginary crystal that the
Rfree(strong) will drop even if there is no real difference between
the ncs mates. When you allow differences between the ncs mates
the Rfree(strong) will tend to drop even if those differences are
not real.
The Rfree(weak) is a different story, however. It is controlled
specifically by the differences between the two ncs mates and will
drop only if the refinement creates differences that are significant.
This is the statistic that can be used to determine the ncs weight.
(Or probably the log likelihood gain (weak))
If you insist on mixing the strong and weak reflections in your
test set you have to design your null hypothesis test differently.
First you should do a refinement where you have two models at
each site, with exact ncs imposed. The you do a refinement with one
copy at each site but allow differences between the ncs mates.
Compare the Rfree of each model to decide which is the better model.
There are exactly the same number of parameters in each model but
one allows the ncs to be violated and the other does not.
Even so, the signal in the Rfree is mixed unless you split the
systematically weak from the systematically strong.
If you have a general ncs and don't have weak and strong subsets
of reflections you still have to worry about the multimodel affect.
If a refinement that allows ncs violations does not drop the Rfree
by more that a two-fold multimodel with perfect ncs you cannot
justify breaking your ncs. A drop in Rfree when you break ncs does
not necessarily mean that breaking ncs is a good idea. You always
have to perform the proper null hypothesis test.
Dale Tronrud
> At 01:05 PM 2/8/2008, Axel Brunger wrote:
>> In such cases, we always define the test set first in the high-symmetry
>> space group choice. Then, if it is warranted to lower the
>> crystallographic
>> symmetry and replace with NCS symmetry, we expand the test set
>> to the lower symmetry space group. In other words, the test set itself
>> will be invariant upon applying any of the crystallographic or NCS
>> operators,
>> so will be maximally "free" in these cases. It is then also possible to
>> directly compare the free R between the high and low crystallographic
>> space group choices.
>>
>> Our recent Neuroligin structure is such an example (Arac et al.,
>> Neuron 56, 992-, 2007).
>>
>>
>> Axel
>>
>>
>>
>>
>> On Feb 8, 2008, at 10:48 AM, Ronald E Stenkamp wrote:
>>
>>> I've looked at about 10 cases where structures have been refined in
>>> lower
>>> symmetry space groups. When you make the NCS operators into
>>> crystallographic
>>> operators, you don't change the refinement much, at least in terms of
>>> structural changes. That's the case whether NCS restraints have been
>>> applied
>>> or not. In the cases I've re-done, changing the refinement program
>>> and dealing
>>> with test set choices makes some difference in the R and Rfree
>>> values. One
>>> effect of changing the space group is whether you realize the copies
>>> of the
>>> molecule in the lower symmetry asymmetric unit are "identical" or
>>> not. (Where
>>> "identical" means crystallographically identical, i.e., in the same
>>> packing
>>> environments, subject to all the caveats about accuracy, precision,
>>> thermal
>>> motion, etc). Another effect of going to higher symmetry space
>>> groups of
>>> course has to do with explaining the experimental data with simpler
>>> and smaller
>>> mathematical models (Occam's razor or the Principle of Parsimony).
>>>
>>> Ron
>>
>> Axel T. Brunger
>> Investigator, Howard Hughes Medical Institute
>> Professor of Molecular and Cellular Physiology
>> Stanford University
>>
>> Web: http://atb.slac.stanford.edu
>> Email: [log in to unmask] <mailto:[log in to unmask]>
>> Phone: +1 650-736-1031
>> Fax: +1 650-745-1463
>>
>>
> ---------------------------------------------------------------------------------------------------------------------------
> Phoebe A. Rice
> Assoc. Prof., Dept. of Biochemistry & Molecular Biology
> The University of Chicago
> phone 773 834 1723
> fax 773 702 0439
> http://bmb.bsd.uchicago.edu/Faculty_and_Research/01_Faculty/01_Faculty_Alphabetically.php?faculty_id=123
> http://www.nasa.gov/mission_pages/cassini/multimedia/pia06064.html
>
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