John R Helliwell wrote:
>
> Dear James,
> I enjoyed your simulations.
Thank you!
>
> Re your conclusion:-
> "However, if the disorder is correlated across the entire mosaic
> domain, then the "diffuse scatter" intensity pattern migrates from in
> between the spots to influencing the spots themselves! ......Could
> this "correlated disorder" be responsible for why almost no protein
> crystal R factors can be refined to below ~20%? Possibly, but the
> nature of the correlations will need to be figured out before we can
> model it."
I made sure I used the word "possibly" in that sentence for a reason!
After all, the "R-factor Gap" could be anything. No one has solved it.
Many ideas have been tried (such as multi-copy refinement), but so far
the best improvements in R factors are no more than a few percent, and
in a large-dimensional parameter space this generally means you are
still missing something big.
However, the idea of "correlated disorder" (such as a side chain in the
same conformation for many unit cells in a row) I don't think has been
tried, but it is supported I think by Colin Nave's observations from
1998 that protein crystals have a spectrum of unit cell sizes. His
evidence was the resolution-dependence of of spot shape. In order to
broaden spots in the way he saw, a given unit cell size must persist for
a micron or so of crystal mass. So, that means that whatever is making
the unit cells bigger or smaller must have a "persistence length" very
much larger than one unit cell. Randomly-placed large and small unit
cells will not shift or broaden the Bragg peaks (because the average
unit cell is the same for every "domain" in the crystal), but if you
move all the "big ones" into their own crystal, and all the "small ones"
into another crystal, then you get diffraction that is really just the
overlap of two patterns with two different unit cell sizes, and that
broadens the spots.
Not exactly proof of correlated disorder, but suggestive of it.
>
> Thus the Bragg spot size versus the shoulder-under-the-Bragg-peak-size
> can get in the way of one another unless efforts are made to reduce
> Bragg spot size as much as possible. An example of removing the
> correlated diffuse scatter and improving R factors (slightly) is the
> Grigorieff and Henderson paper example I listed recently.
I'm still not really sure what the difference is between a Bragg spot
and a feature "under" it. Why not define a "Bragg intensity"
operationally? Subtracting local background with a least-squares plane
is pretty much universally done, and as long as the disorder is
uncorrelated, the intensities obtained this way really are those of the
partial-occupancy models we currently build. It is when this assumption
breaks down that we need a "correction factor".
I'll have to have a closer look at what Grigorieff and Henderson did.
My thought was that maybe X-ray crystallographic refinement programs
should "add back" some of the cross-term associated with explicitly
"disordered" side chains (two headed beasts). A single scale factor
would relate this cross-term to the "domain size" or "correlation
length" or what have you. Easier said than done I suppose. Especially
if you are considering what to do with bulk solvent.
>
> As for the non-correlated diffuse scattering between the Bragg peaks
> some crystals offer rich information and makes the use of whole images
> approach interesting. The hard part is then how we link into it ie
> since we don't have a neat Fourier synthesis of Bragg peaks to work
> with. This is then the meat of the various protein crystal
> diffuse scattering projects in the USA and UK that have occurred over
> the years.
I agree that this will be difficult, particularly deconvoluting the
diffuse scatter from the lattice from all the other background
contributions. The signal is very weak, but perhaps the sheer number of
pixels involved could make it a decent restraint. I wonder, however,
how much information will we get that we can't already see in the
electron density? Two-headed side chains or TLS will cause potentially
interpretable DS features, but something more universal like the
disorder we currently model with B factors just gives a flat, uniform
haze. At least, as far as I can tell.
> There are the two chem cryst diffuse scattering books to help us ie
> Welberry 'Diffuse X-ray Scattering and Models of Disorder and Diffuse
> Scattering and Defect Structure Simulations: a Cookbook using the
> program DISCUS' by Neder and Proffen
Yes, Welberry is a good book! The opening chapter was the first time I
understood what DS was all about. I keep a copy at the beamline, as it
often serves as comfort to poor protein crystallographers who have
horrible diffraction patterns to see that something as simple as urea
can do the same thing.
-James Holton
MAD Scientist
>
>
>
>
> On Tue, Jan 26, 2010 at 7:27 AM, James Holton <[log in to unmask]
> <mailto:[log in to unmask]>> 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:[log in to unmask]
> <mailto:[log in to unmask]>] On Behalf Of Ian Tickle
> Sent: 22 January 2010 10:54
> To: [log in to unmask] <mailto:[log in to unmask]>
> Subject: Re: [ccp4bb] Refining against images instead of
> only reflections
>
>
> > -----Original Message-----
>
>
> From: [log in to unmask]
> <mailto:[log in to unmask]>
> [mailto:[log in to unmask]
> <mailto:[log in to unmask]>] On Behalf Of
> James Holton
> Sent: 21 January 2010 08:39
> To: [log in to unmask] <mailto:[log in to unmask]>
> 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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