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/
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:ccp...@jiscmail.ac.uk] On
Behalf Of Ian Tickle
Sent: 22 January 2010 10:54
To: 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] On Behalf Of James Holton
Sent: 21 January 2010 08:39
To: 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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