All very true Randy,
But nevertheless every hkl has an FOM assigned to it, and that is used
to calculate the map. Statistical distribution or not, the trend is
that hkls with big amplitude differences get smaller FOMs, so that means
large model-to-data discrepancies are down-weighted. I wonder sometimes
at what point this becomes a self-fulfilling prophecy? If you look in
detail and the Fo-Fc differences in pretty much any refined structure in
the PDB you will find huge outliers. Some are hundreds of sigmas, and
they can go in either direction.
Take for example reflection -5,2,2 in the highest-resolution lysozyme
structure in the PDB: 2vb1. Iobs(-5,2,2) was recorded as 145.83 ± 3.62
(at 5.4 Ang) with Fcalc^2(-5,2,2) = 7264. A 2000-sigma outlier! What
are the odds? On the other hand, Iobs(4,-6,2) = 1611.21 ± 30.67 vs
Fcalc^2(4,-6,2) = 73, which is in the opposite direction. One can
always suppose "experimental errors", but ZD sent me these images and I
have looked at all the spots involved in these hkls. I don't see
anything wrong with any of them. The average multiplicity of this data
set was 7.1 and involved 3 different kappa angles, so I don't think
these are "zingers" or other weird measurement problems.
I'm not just picking on 2vb1 here. EVERY PDB entry has this problem.
Not sure where it comes from, but the FOM assigned to these huge
differences is always small, so whatever is causing them won't show up
in an FOM-weighted map.
Is there a way to "change up" the statistical distribution that assigns
FOMs to hkls? Or are we stuck with this systematic error?
-James Holton
MAD Scientist
On 10/4/2019 9:31 AM, Randy Read wrote:
Hi James,
I'm sure you realise this, but it's important for other readers to
remember that the FOM is a statistical quantity: we have a probability
distribution for the true phase, we pick one phase (the "centroid"
phase that should minimise the RMS error in the density map), and then
the FOM is the expected value of the phase error, obtained by taking
the cosines of all possible phase differences and weighting by the
probability of that phase difference. Because it's a statistical
quantity from a random distribution, you really can't expect this to
agree reflection by reflection! It's a good start to see that the
overall values are good, but if you want to look more closely you have
to look a groups of reflections, e.g. bins of resolution, bins of
observed amplitude, bins of calculated amplitude. However, each bin
has to have enough members that the average will generally be close to
the expected value.
Best wishes,
Randy Read
On 4 Oct 2019, at 16:38, James Holton <jmhol...@lbl.gov
<mailto:jmhol...@lbl.gov>> wrote:
I've done a few little experiments over the years using simulated
data where I know the "correct" phase, trying to see just how
accurate FOMs are. What I have found in general is that overall FOM
values are fairly well correlated to overall phase error, but if you
go reflection-by-reflection they are terrible. I suppose this is
because FOM estimates are rooted in amplitudes. Good agreement in
amplitude gives you more confidence in the model (and therefore the
phases), but if your R factor is 55% then your phases probably aren't
very good either. However, if you look at any given h,k,l those
assumptions become less and less applicable. Still, it's the only
thing we've got.
2qwAt the end of the day, the phase you get out of a refinement
program is the phase of the model. All those fancy "FWT"
coefficients with "m" and "D" or "FOM" weights are modifications to
the amplitudes, not the phases. The phases in your 2mFo-DFc map are
identical to those of just an Fc map. Seriously, have a look!
Sometimes you will get a 180 flip to keep the sign of the amplitude
positive, but that's it. Nevertheless, the electron density of a
2mFo-DFc map is closer to the "correct" electron density than any
other map. This is quite remarkable considering that the "phase
error" is the same.
This realization is what led my colleagues and I to forget about
"phase error" and start looking at the error in the electron density
itself (10.1073/pnas.1302823110). We did this rather pedagogically.
Basically, pretend you did the whole experiment again, but "change
up" the source of error of interest. For example if you want to see
the effect of sigma(F) then you add random noise with the same
magnitude as sigma(F) to the Fs, and then re-refine the structure.
This gives you your new phases, and a new map. Do this 50 or so times
and you get a pretty good idea of how any source of error of
interest propagates into your map. There is even a little feature in
coot for animating these maps, which gives a much more intuitive view
of the "noise". You can also look at variation of model parameters
like the refined occupancy of a ligand, which is a good way to put an
"error bar" on it. The trick is finding the right source of error to
propagate.
-James Holton
MAD Scientist
On 10/2/2019 2:47 PM, Andre LB Ambrosio wrote:
Dear all,
How is the phase error estimated for any given reflection,
specifically in the context of model refinement? In terms of math I
mean.
How useful is FOM in assessing the phase quality, when not for
initial experimental phases?
Many thank in advance,
Andre.
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------
Randy J. Read
Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research Tel: + 44 1223 336500
The Keith Peters Building Fax: + 44 1223 336827
Hills Road E-mail: rj...@cam.ac.uk <mailto:rj...@cam.ac.uk>
Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk
<http://www-structmed.cimr.cam.ac.uk>
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