Francis,
I think in the cases you describe the region in question is disordered.
Time and time again I have users coming to my beamline wanting to clean
up a "questionable region" by getting experimental phases. Ahh! If
only I had a nickle for each one. Oh wait, I suppose I kind of do? I
take that back! Go MAD everyone!
Much as I hate to discourage people from using my favorite technique,
Tim is right: phases are not region-specific in electron density maps.
Dale does make a good point that there is such a thing as "model bias"
and one can argue that experimental phases don't have it. But, this is
only true if you have not yet applied solvent flattening. How long has
it been since you looked at a "raw" experimentally-phased map (before
solvent flattening)? I'm willing to bet a while. With very few
exceptions, raw experimental phases are lousy. We have actually become
quite dependent on density modification to clean them up. In fact,
solvent flattening is the only reason why SAD works at all.
However, you CAN use anomalous differences to clear up disordered
regions in a different way. Something I started calling "SeMet
scanning" a number of years ago. A few of my users have done this, and
a good example of it is Figure 3 of Huang et al. 2004
(doi:10.1038/nsmb826). Basically, you mutate residues in the disordered
region one at a time to SeMet, and look at phased anomalous difference
Fourier (PADF) maps. These maps are surprisingly clear, even when the
anomalous difference signal is so weak as to make experimental phasing
hopeless. Yes, the best phases to use for PADF maps are model phases,
but, as always, it is prudent to refine the model after omitting the
thing you are looking for before calculating such phases.
Another way to get residue-specific labeling for low-resolution chain
tracing is radiation damage. If you expose for the right amount of
time, Asp and Glu side chains will be specifically "burnt off", but not
Asn and Gln. You will also see Met loosing its head, etc. So, as long
as you have read Burmeister (2000), an Fo-Fo map of damaged vs undamaged
can be used to guide sequence assignment, even at 4.5 A and worse.
Anyway, when it comes to the question of "is it disordered or is it
model bias?", I think it is usually the former. It is very difficult to
make "model bias" suppress a region that is actually well-ordered. Try
it! After all, this is the whole reason why we bother looking at fo-fc
maps. Then again, it is always possible to have a model so bad that the
phase error is enough to squash anything. An excellent example of this
can be found in the Book of Fourier. Taking amplitudes from the image
of a cat, you can see what happens when you use the phases of a duck:
http://www.ysbl.york.ac.uk/~cowtan/fourier/picduckcatfft.gif
as opposed to what happens if you use the phases of a manx:
http://www.ysbl.york.ac.uk/~cowtan/fourier/piccatmanx2.gif
A manx is a species of cat that doesn't have a tail, so no animals were
harmed in obtaining these phases. My point here is that the cat's tail
can be seen quite readily in the 2fo-fc map if most of the structure is
already "right", but if your model is completely unrelated to the true
structure (fitting a duck into a cat-shaped hole), then everything is
"in the noise".
Real structures are usually somewhere between these two extremes, and I
think an important shortcoming in modern crystallography is that we
don't have a good quantitative description of this middle-ground. We
all like to think we know what "model bias" is, but we don't exactly
have "units" for it. Should we be using a scale of 0 to 1? Or perhaps
"duck" to "cat"? Yes, I know we have "figure of merit", but FOM is not
region-specific.
In my experience, as long as you have ~50% of the electrons in the
"right" place (and none of them in the "wrong" place), then you can
generally trust that the biggest difference feature in the fo-fc map is
"real", and build from there. As the model becomes more complete, the
phases should continue to get better, not worse. Eventually, this does
break down, although I'm not really sure why. With small molecules, the
maximum fo-fc peak keeps getting bigger (on a sigma scale) as you add
more and more atoms, and the biggest one you will ever see is the last
one. For macromolecules, the difference features keep getting smaller
and smaller as you build. Perhaps small errors (like non-Gaussian
atomic displacement distributions being modeled as Gaussians) slowly
accumulate? Perhaps there are other sources of systematic error that we
don't yet fully understand? Eventually, for whatever reason, you stop
building. Having electrons in the wrong place is about twice as bad as
not having them at all, which I think is why we trim models so
aggressively for molecular replacement, and also why we are so reticent
to model in things that we are not "sure" about. Disordered regions, of
course, will always lie at a lower level of electrons/A^3 than ordered
regions, and therefore will be the last things to show up as the "top
peak" in the fo-fc map. They will also be the last things to poke their
heads above the 1-sigma contour in a 2fo-fc map, but that does not mean
they are "not there". You can lower the map contour and see them easily
enough (even in 3bcl). The trick is having some kind of
statistically-sound rule for "being sure". Otherwise, we might start
seeing "map contour creep", just as we currently see "R factor creep" in
high-profile journals.
-James Holton
MAD Scientist
On 4/10/2012 1:04 PM, Francis E Reyes wrote:
Dale
Thank you for the case study. I will certainly remember it when I next see:
"I don't see density for these atoms therefore they must be
disordered."
You do mention though, that when you were able to assign the sequence to the
beta sheets, that the loop regions became clear.
I consider the case (which a majority of cases seem to be), where the author
has built and sequence assigned 95% of the ASU, but is unable to model a loop
region. One possibility is that the loop is truly disordered (95% of the ASU is
built and is presumably right), the other possibility is that there's an
inherent error in the existing structure that is affecting the interpretation
of the loop region. The errors are probably extremely subtle and distributed
throughout the model (think of the improvements DEN refinement gave for the
rerefinement of p97).
I guess in either case, because of the dependency of the map on the existing
set of phases it's difficult to determine whether it's truly disordered or not.
P.S.: The author should not look at an 2fofc-map but a
sigma-A-weighted map to reduce model bias.
Tim,
I assume a sigmaA weighted 2Fo-Fc map (which I believe is the default for most
crystallographic refinement packages).
F
---------------------------------------------
Francis E. Reyes M.Sc.
215 UCB
University of Colorado at Boulder
