I agree that simple truncation is not a great way to "create" a
lower-resolution dataset. However, neither is simply applying a B
factor. It is harder than that to "fool" the downstream phasing
programs you will probably be running.
That said, the combination of a B factor with a resolution cutoff does
effectively suppress "Fourier ripples", which are always there, but the
rms error they contribute to the map is just the rms value of all
structure factors "beyond" the resolution limit, divided by the cell
volume. So, if you apply a big enough B factor everything beyond the
resolution limit will be essentially "zero". I recommend as a rule of
thumb combining a resolution cutoff of "d" with the B factor taken from
the general trend of the PDB:
B = 4*d^2+12
where "B" is the average atomic B factor from structures claiming
resolution "d". That is, if you download every PDB entry with a
"resolution" of 2 A, and then take the average value of the B factor of
all the atoms in all those files, you'll get ~28. So, if you start with
a 1.8 A data set, chances are it will have an average atomic (aka
"Wilson") B factor of 25. If you apply a B-factor of 45 to the observed
data with CAD, then the Wilson B will become 70, and the structure
factors at 3.8 A will now be about the same average magnitude as the 1.8
A data were in the original set. So, you can now cut of the data at
3.8 A and not change the maps in any serious way. The maps will "look"
like 3.8A data. This is actually how I made my "resolution" example movie:
http://bl831.als.lbl.gov/~jamesh/movies/index.html#reso
This treatment is fine for map calculation, but if you are trying to
test the effect of "resolution" on something more complicated, like
phasing or refinement, you will run into problems. For example, if you
calculate the "isomorphism" of the old 1.8 A dataset to the "new" 3.8 A
dataset with SCALEIT, you will find the R-factor between them is zero.
This is because the standard procedure for calculating an R factor is to
"scale" the two datasets together first, and "scaling" generally implies
fitting a B factor as well as an overall scale. In this case the
relative B factor (aka "scaling B factor") will be 45, the number you
gave to CAD above. So, if you take a coordinate file refined against
the 1.8A data and refine it against your "new" 3.8A data, all the atomic
B factors will simply increase by 45, the atoms will hardly move, and
the R and Rfree will be a little better than they were with the 1.8A
data (because the "noisy" high-angle stuff is now cut off). You will
also find that the quality of the anomalous differences are largely
unaffected by applying a B factor. This is because if you scale all the
Fs and sigFs on a Harker diagram by a constant, it doesn't change the
phase. Yes, the refined B factor of the heavy atom sites will increase
by 45, but the phasing power, etc will be the same. I imagine this is
not what you had in mind?
Clearly, you have to add some noise in addition to applying the B factor
and cutting off the resolution. But what sort of noise? You have the
"sigmas" from the original dataset, but those are not noise, they are an
estimate of the noise that is already there, hidden in the value of "F"
itself. Nevertheless, it's all you've got, so it is helpful to consider
where "SIGF" comes from.
SIGF begins its life as the estimate of the number of photons that were
counted in a given spot area on the detector. The error in the
background-subtracted spot intensity is (at least) the square root of
the _total_ number of photons that hit in the "spot" region. That is,
background plus spot. You might have a hope of reconstructing the spot
intensity using F^2 and some sort of overall "scale factor" (related to
the illuminated crystal volume, beam intensity, etc), but the background
level is lost in the scaling and mergeing process. After all, different
observations of the same or symmetry-equivalent hkls will generally have
different background levels. They also have different intensities, due
to the Lorentz and polarization factors. This latter fact is often
neglected, but if you take the average value of the Lp factor (Holton &
Frankel, 2010) vs resolution for a typical data collection situation
(wavelength = 1A, resolution up to ~1.5A), you will find that it is a
fairly straight line:
<L*p*frac_obs> ~ 1.55*d
where "d" is the d spacing of the spot. So, yes, high-angle spot
intensities are weaker than low-angle spot intensities not just because
F is smaller, but because d is smaller as well, and the actual spot
intensities on the detector are not proportional to F^2, but rather
d*F^2. On average. Most data sets have a few hkls that by chance are
very close to the rotation axis and stay in contact with the Ewald
sphere for the entire rotation range. These will accumulate a VERY
large number of counts. On the other hand, a spot that appears on the
"equator" won't register very many photons at all because it spends such
a brief amount of time on the Ewald sphere (relatively speaking). The
sad part is that the high-count spots near the blind region get thrown
out before scaling because their Lorentz factors are "too high".
Interestingly, if you don't rotate the crystal at all, then there is no
Lorentz factor, and you get F^2 again, or much brighter high-angle spots
that you would get if the crystal were rotating. You just don't get as
many spots.
Anyway, the unfortunate problem here is that to get a "realistic" SIGF
you actually do need to know a lot about the detector geometry. This is
why I resorted to writing a diffraction image simulator which I
flippantly called "MLFSOM" because it is "MOSFLM" in reverse: takes an
*.mtz file and gives you diffraction images (with noise). You can then
process those diffraction patterns with your favorite software and get
your "realistic" sigmas out of it. You can download MLFSOM from here:
http://bl831.als.lbl.gov/~jamesh/mlfsom/development_snapshot.tar.gz
I'm afraid its not too well documented yet, so feel free to ask if you
can't get it to run.
But remember! If you feed "Fobs" values to MLFSOM, then the errors in
the original dataset do not go away. Yes, you can drop "SIGF", but you
can't subtract the noise from "F" itself. This is not so worrisome for
if all you want to do is degrade the resolution limit, but for anomalous
data, the fractional errors of the original experiment will almost
always dominate (detector calibration, shutter jitter, beam flicker,
absorption effects, etc). These also cannot be "subtracted" from
observed data.
So, what I usually do is refine a model against the relevant Fobs and
then use my ano_sfall.com script to generate the calculated structure
factors (with anomalous) and then feed F+ and F- to MLFSOM. You can
also make calculated anomalous Fs with phenix.fmodel. The only trick
with calculated structure factors is that you will often find your
R/Rfree dropping to ~3%, even when every conceivable source of
experimental noise has been included. That's a problem I'm still
working on.
-James Holton
MAD Scientist
On 2/13/2014 6:54 AM, Mooers, Blaine H.M. (HSC) wrote:
For some simulated phasing experiments, I want to create a lower resolution
diffraction data set by truncating a high resolution data set. I would like to avoid
Fourier ripples due to the truncation of the high resolution data by downscaling the
data such that <I/sigma>=2.0 in the highest resolution shell of the truncated
data. What is the best way to do this?
Blaine Mooers
Assistant Professor
Department of Biochemistry and Molecular Biology
University of Oklahoma Health Sciences Center
S.L. Young Biomedical Research Center Rm. 466
Shipping address:
975 NE 10th Street, BRC 466
Oklahoma City, OK 73104-5419
Letter address:
P.O. Box 26901, BRC 466
Oklahoma City, OK 73190
office: (405) 271-8300 lab: (405) 271-8313 fax: (405) 271-3910
e-mail:[email protected] <mailto:[email protected]>
Faculty
webpage:http://www.oumedicine.com/department-of-biochemistry-and-molecular-biology/faculty/blaine-mooers-ph-d-
X-ray lab
webpage:http://www.oumedicine.com/department-of-biochemistry-and-molecular-biology/department-facilities/macromolecular-crystallography-laboratory
Small Angle Scattering
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