Agreed, and this is even more true if you consider R-merge is calculated
on I's and Rfree on F's, Rmerge of 5% should contribute 2.5% to Rfree;
and furthermore errors add vectorially so it would be
more like ,025/sqrt(2).
I guess I have to take all those other errors that have to do with
the inability of a simple atomic model to account for the diffraction
of a crystal, lump them together and assume they have nothing to do
with NCS and are not affected by the simple modification under
consideration.
I am thinking about the CHANGE in |Fo-Fc| at two sym-related reflections
when the refinement program moves a single atom from position 1 to
position 2. If we do not apply NCS, this is the only atom that
will move, and for Fc we can definitely say there is no reason
to expect the two Fc's to move in the same direction, therefore
there is no coupling in the case we do not apply NCS.
If we apply strict NCS then granted the sym related Fc's are equal
before and after the change, so they move in the same direction.
As I said, the argument is weaker now. If there are systematic
errors contributing to the gap between Rfree and 0.5*Rmerge/sqrt(2),
and if these systematic errors follow the NCS, then initial Fo-Fc
is likely to be of the same sign at the related reflections and
larger than the change in Fc, so |Fo-Fc| would go in the same
direction. But to justify this you would have to explin why
the systematic errors follow ncs. Crystal morphology related
to ncs resulting in similar absorption errors? But how large
are absorbtion errors, and is there any reason for morphology
to follow NCS?
After reading Dean Madden's latest-
We might need some assumption here that we are reasonably close
to the refined structure. If we start with random atoms then
shoving the atoms around in a way that fits the density better
might be seen as "improving the structure" from the point of
modeling the density, but not from the point of approximating the
real structure. But in this case the change in sign of Fc is
completely decoupled between sym-related reflections, and if you
enforce symmetry you will be enforcing the wrong symmetry and
worsening both the structure and the fit to the density.
I think Gerard Kleywegt has an example of enforcing NCS on a
an erroneous structure, and it was not very effective
at reducing Rfree? And in that case the structure may have had some
resemblence to the density at low resolution,the NCS may have been
somewhat correct.
I guess there are two questions depending whether you are at the
beginning at the beginning of a refinement and may have a completely
wrong structure, or whether refinement isnearly complete and you
want to know whether the further improvement you get on applg NCS
is real.
Jon Wright wrote:
Dear Ed,
I don't see how you "decouple" symmetry mates in the case of a wrong
space group. Symmetry mates should agree with each other typically
within "R_sym" or "R_merge" percent, eg; about 2-5% . Observed and
calculated reflections agree within "R_Factor" of each other, so about
20-30%. The experimental errors are pretty much negligible and
overfitting is not a question about error bars; it is about how hard to
push a round peg into a square hole?
Cheers,
Jon
Edward Berry wrote:
Actually the bottom lines below were my argument in the case
that you DO apply strict NCS (although the argument runs into
some questionable points if you follow it out).
In the case that you DO NOT apply NCS, there is a second
decoupling mechanism:
Not only the error in Fo may be opposite for the two reflections,
but also the change in Fc upon applying a non-symmetrical
modification to the structure is likely to be opposite. So there
is no way of predicting whether |Fo-Fc| will move in the same
direction for the two reflections. I completely agree with Dirk
(although I am willing to listen to anyone explain why I am wrong).
Ed
Edward Berry wrote:
Dean Madden wrote:
Hi Dirk,
I disagree with your final sentence. Even if you don't apply NCS
restraints/constraints during refinement, there is a serious risk of
NCS "contaminating" your Rfree. Consider the limiting case in which
the "NCS" is produced simply by working in an artificially low
symmetry space-group (e.g. P1, when the true symmetry is P2): in
this case, putting one symmetry mate in the Rfree set, and one in
the Rwork set will guarantee that Rfree tracks Rwork.
I don't think this is right- remember Rfree is not just based on Fc
but Fo-Fc. Working in your lower symmetry space group you will have
separate values for the Fo at the two "ncs-related" reflections.
Each observation will have its own random error, and like as not
the error will be in the opposite direction for the two reflections.
Hence a structural modification that improves Fo-Fc at one reflection
is equally likely to improve or worsen the fit at the related
reflection.
The only way they are coupled is through the basic tenet of R-free:
If it makes the structure better, it is likely to improve the fit
at all reflections.
For sure R-free will go down when you apply NCS- but this is because
you drastically improve your data/parameters ratio.
Best,
Ed
