Dean Madden wrote:
Hi Ed,
This is an intriguing argument, but I know (having caught such a case as
a reviewer) that even in cases of low NCS symmetry, Rfree can be
significantly biased. I think the reason is that the discrepancy between
pairs of NCS-related reflections (i.e. Fo-Fo') is generally
significantly smaller than |Fo-Fc|. (In general, Rsym (on F) is lower
than Rfree.) Thus, moving Fc closer to Fo will also move its NCS partner
Fc' closer to Fo' *on average*, if they are coupled.
OK, I see that now, the systematic errors must be related to "NCS"
in this case because we know if we reduced the data in the higher
space group, our Rsyms would be OK. I stand educated. But it is
difficult to go from there to real ncs where the large unaccounted
errors may not be related to ncs. Furthermore if you don't enforce
NCS the structural changes are asymmetric and there is no reason to
believe Fc will move in the same direction, even in this artificial
case. So Dirk's assertion still stands, I believe.
Dean
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
