On Tue, Jan 26, 2010 at 7:27 AM, James Holton <jmhol...@lbl.gov
<mailto:jmhol...@lbl.gov>> wrote:
At the risk of creating another runaway thread, I have spent some
time trying to reconcile what Ian was talking about and what I was
talking about. The discussion actually is still relevant to the
original posted question about refining against images, so I am
continuing it here.
Ian made a good criticism of one of my statements, which I should
take back: diffuse scatter does contain information about the
disorder in the structure, and this can be measured under
favorable conditions. The point I was trying to make, however, is
that one is still at the mercy of the lattice transform when
looking at diffuse scatter, and the total scattering is the
product of the molecular transform and the lattice transform.
There is generally no a-priori way to deconvolute the two! And
this will make refinement against images difficult.
However, Colin makes a good point that the differences are largely
semantic. Unlike crystallographers, crystals, atoms, electrons
and photons don't really care what names we call them. They just
do whatever it is they do, and the photons make little pops when
they hit the detector. That's all we really know.
So, in an effort to clear things up (both in my head and on this
thread), I have assembled some simulated diffraction patterns from
my nearBragg program here:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/
<http://bl831.als.lbl.gov/%7Ejamesh/diffuse_scatter/>
I have included some limited discussion about how the images were
made, but the point here is that all these images are generated by
simply computing the general scattering equation for a
constellation of atoms. I found in an instructive exercise and
perhaps other interested parties will as well.
-James Holton
MAD Scientist
Colin Nave wrote:
Nice overview from Ian - though I think James did make some
good points
too.
I thought it might be helpful to categorise the various
contributions to
an imperfect diffraction pattern. Categorising things seems to
be one of
the English (as distinct from Scottish, Irish or Welsh!)
diseases.
1. Those that contribute to the structure of a Bragg reflection
i) Mosaic structure - limited size and mosaic spread
ii) Dislocations, shift and stacking disorders
iii) More macroscopic defects giving "split" spots
iv) Unit cell variations (e.g. due to strain on cooling)
v) Twinning (?)
2. Diffuse scatter
i) Uncorrelated disorder - broad diffuse scatter distributed
over image
ii) Disorder correlated between cells - sharper diffuse
scatter centred
on Bragg peaks iii) Related to above inelastic scattering -
Brillouin scattering,
acoustic scattering, scattering from phonons
iv) Compton scattering (essentially elastic but incoherent)
v) Fluorescence
vi) Disordered material between crystalline "blocks" but
within whole
crystal
vii) Scatter from mother liquor
viii) Scatter from sample mount
3. Instrument effects
i) Air scatter
ii)Scatter from apertures, poorly mounted beamstop
iii) Smearing of spot shapes due to badly matched incident
beams, poor
detector resolution, too large a rotation range, iv) Detector
noise
The trouble with categorisation is that one can (Oh no) i)
Have multiple categories for the same thing
ii) Miss out something important
iii) Give impression that categories are distinct when they
might merge
in to each other. Categorising seagulls (or any species) is an
example,
perhaps categorising protein folds is too. Not sure about
categorising
in to English, Scottish etc.
All of these flaws will be in the categories above. Despite
this, I
believe it would help structure determination to have an
accurate as
possible model of the crystal. This should be coupled with the
ability
to determine the parameters of the model from the best possible
recording instrument. Such a set up would enable better
estimates of the
intensity of weak Bragg spots in the presence of a high
"background".
There may be an additional gain by exploiting information from the
diffuse scatter of the protein.
At present, the normal procedure is to treat the background
components
as the same, have some parameter called "mosaicity" and use
learned
profiles derived from nearby stronger spots (ignoring the fact
that the
intrinsic profiles of a hkl and a 6h 6k 6l reflection will be
closely
related). The normal procedure is obviously very good but we
don't know
what we are missing!
Any corrections additions to the categories plus other
comments welcome
Regards
Colin
-----Original Message-----
From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK
<mailto:CCP4BB@JISCMAIL.AC.UK>] On Behalf Of Ian Tickle
Sent: 22 January 2010 10:54
To: CCP4BB@JISCMAIL.AC.UK <mailto:CCP4BB@JISCMAIL.AC.UK>
Subject: Re: [ccp4bb] Refining against images instead of
only reflections
> -----Original Message-----
From: owner-ccp...@jiscmail.ac.uk
<mailto:owner-ccp...@jiscmail.ac.uk>
[mailto:owner-ccp...@jiscmail.ac.uk
<mailto:owner-ccp...@jiscmail.ac.uk>] On Behalf Of
James Holton
Sent: 21 January 2010 08:39
To: CCP4BB@jiscmail.ac.uk <mailto:CCP4BB@jiscmail.ac.uk>
Subject: Re: [ccp4bb] Refining against images instead
of only reflections
It is interesting and relevant here I think that if
you measure background-subtracted spot intensities you
actually are
measuring the
AVERAGE electron density. Yes, the arithmetic average
of
all the unit
cells in the crystal. It does not matter how any of
the vibrations are "correlated", it is still just the
average (as long as you subtract the background). The
diffuse scatter does NOT
tell you about
the deviations from this average; it tells you how the
deviations are
correlated from unit cell to unit cell.
James, as I've pointed out before this is completely
inconsistent with both established DS theory and many
experiments performed over the years. If you're
simulation is producing this result, then the obvious
conclusion is that you're not simulating what you claim to
be. I don't know of a single experimental result that
supports your claim. In order for it to be true the total
background (i.e. the sum of the detector noise, air
scatter, scattering from the cryobuffer, Compton
scattering from the crystal and of course the diffuse
scattering itself) would have to be a linear function (or
more precisely planar since the detector co-ords are
obviously 2-D) of the detector co-ordinates in the region
of the Bragg spots, since that is the background model
that is used for background subtraction. Whilst it may be
true that detector noise and non-crystalline scattering
can be accurately modeled by a linear background model (at
least in the local region of each Bragg spot), this cannot
possibly be generally true of the DS component, and since
getting at the DS component is the whole purpose of the
experiment, it is crucial that this be modeled accurately.
Of course your claim may well be true if there's no DS,
but we're talking specifically about cases where there is
observable DS (otherwise what's the point of your
simulation?). The reason it can't be true that the DS is
a linear function is that there's a wealth of simulation
work and experimental data that demonstrate that it's not
true (not to mention simple manual observation of the
images!). The simulations cannot easily be dismissed as
unrealistic because in many cases they give an accurate
fit to the experimental data.
As an example see here:
http://journals.iucr.org/a/issues/2008/01/00/sc5007/sc5007.pdf
.
Looking at the various simulations here (Figs 3 & 5) it's
obvious that the DS is very non-linear at the Bragg
positions (and more importantly it's also non-linear
between the Bragg positions). Note that the simulated
calculated patterns here contain no Bragg peaks since as
noted in the Figure legends, the average structure (or the
average density) has been subtracted in the calculation,
i.e. the simulations are showing only the DS component. I
fail to see how any kind of background subtraction model
could cope with the DS and give the right answer for the
Bragg intensity in these kind of cases. Even from the
observed patterns it's plain that the DS is non-linear,
and therefore a linear background correction couldn't
possibly correct the raw integrated intensity for the DS
component.
Well-established theory says that the total coherent
scattered intensity is proportional to (~=) the
time-average of the squared modulus of the structure
factor of the crystal:
I(coherent) ~= <|Fc|^2>
If we make the assumption that the deviations of the
contributions to the structure factor from different unit
cells are uncorrelated, we can show that the Bragg
intensity is the squared modulus of the time and
lattice-averaged SF sampled at the reciprocal lattice points:
I(Bragg) ~= |<F>|^2
The time/lattice-averaged SF is the FT of the average
density, and therefore I(Bragg) indeed corresponds to the
average density.
The diffuse intensity is the difference between these:
I(diffuse) = I(coherent) - I(Bragg)
~= <|F|^2> - |<F>|^2
The assumption above implies that we're assuming that
there's no 'acoustic' component of the DS, since this
arises from correlations between different unit cells.
However this doesn't mean that there *is* no acoustic
component, it simply means that we are ignoring it: for
one thing we have no alternative since the acoustic and
Bragg scattering are practically inseparable; for another,
correlations between different unit cells are purely an
artifact of the crystallisation process, so have no
biological significance, hence we're usually not
interested in them anyway.
The diffuse scatter does NOT tell you about the
deviations
from this
average; it tells you how the deviations are
correlated
from unit cell
to unit cell.
This is completely wrong, the previous equation can be
rewritten as:
I(diffuse) = <|F - <F>|^2>
clearly demonstrating that the DS does indeed tell you
about the mean-squared deviation of the SF from the
average (i.e. the variance of the SF), and therefore the
density from its time/lattice average. Note that
I(diffuse) must necessarily be positive implying that the
measured intensity always overestimates the Bragg
intensity; it cannot average out to zero.
If we further assume the usual harmonic model for the
atomic displacements, we can show that the DS intensity is
related to the covariance (or less correctly the
correlation) of the displacements: I suspect this is what
you meant. This is all nicely explained in Michael Wall's
doctorate thesis which is available online:
http://lunus.sourceforge.net/Wall-Princeton-1996.pdf .
This also has a nice historical survey of all PX DS
results obtained up until 1996.
Cheers
-- Ian
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