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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