Re: [ccp4bb] Refining against images instead of only reflections

[James Holton]

I have re-visited these calculations over the weekend.  As far as I can 
tell, there is just no way to change background-subtracted spot 
intensities with "diffuse" scattering unless the motions are somehow 
"synchronized" across different unit cells.  Call it "optical" or 
"acoustic" or whatever you like.

 I have now repeated the previously-posted nearBragg simulations with 
10x more atoms, but still 10% of the scattering matter involved in a 
two-headed displacement.  I have also done a "disordered solvent" 
simulation where more than half of the unit cell volume is filled with 
completely random atoms.  In both cases the result was the same as 
before: subtracting the "average-electron-density" diffraction image 
from the "average diffraction over many configurations" image is a 
smooth and "locally uniform" image with no signs of spot intensities.  
This implies that subtracting a smooth "local background" from each spot 
will yield the Fourier coefficients of the average electron density (as 
long as the crystal has no "synchronized disorder").

Examples of "synchronized disorder" would be something like a sound wave 
moving through the crystal.  This would cause the motion of atoms in one 
unit cell to be related in some way to those in another.  Another way to 
do this is if the lattice is distorted by defects.  As this is a pet 
model of mine, I have now added an example of it on my little web page:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/index.html#dilatation

This effect does produce little "bumps" under Bragg peaks that can 
become quite significant.  Perhaps this is the "acoustic DS" that Ian is 
talking about?  Or perhaps it should be called "defect DS"?

The really interesting bit I think is that no matter what the 
lattice-distortion model, the fractional changes in spot intensities are 
the same.  If this is true in general, then such a "synchronized 
disorder correction" would be fairly easy to incorporate into a 
refinement program (very few new parameters).  The shape of the DS 
between spots could guide this correction, but might be unnecessary if 
the disorder is apparent in the average electron density.  So, I can 
still claim to be relevant to the original post!

-James Holton
MAD Scientist


Ian Tickle wrote:
James, I think the problem is that your simulation just doesn't contain
enough atoms in the unit cell with correlated displacements to exhibit
significant optic DS, i.e. with only 1 or 2 atoms it will be dominated
by Einstein-model DS which as I explained before is locally uniform and
therefore can be fitted by a planar background function.

Cheers

-- Ian

  
-----Original Message-----
From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk]
    
On
  
Behalf Of James Holton
Sent: 29 January 2010 09:43
To: CCP4BB@jiscmail.ac.uk
Subject: Re: [ccp4bb] Refining against images instead of only
    
reflections
  
All I'm saying is that when I calculate the average general scattering
from 8192 random configurations of one disordered atom per unit cell:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/xtal_diffuse.gif
and then subtract from that the general scattering from an
"occupancy-weighted model" with the two possible atom positions are at
half occupancy:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/xtalAB_Fsum.gif
I get an difference image that shows only the smooth diffuse-scatter
background, with no spots to speak of:

    
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/xtals_diffuse_minus_Fsu
m.
  
gif

But, if I calculate the average general scattering from an "all A" and
an "all B" crystal:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/xtalAB_Isum.gif
and subtract from it the same partial-occupancy model image as above:
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/xtalAB_Fsum.gif
I get an image where some of the spots have been subtracted out, but
others are still quite pronounced:

    
http://bl831.als.lbl.gov/~jamesh/diffuse_scatter/xtals_Isum_minus_Fsum.g
if
  
So, in the first case, the partial-occupancy model produced exactly
    
the
  
same background-subtracted spot intensities as the "unsynchronized
disorder" case, but this was not so when the disorder was
    
synchronized.
  
What did I do wrong?

As far as my "operational" definition of a "Bragg peak" (a term which
already has two definitions), I am merely suggesting that the
nearly-universal practice of subtracting the "local background" is a
very pragmatic definition of a "spot intensity".  Nearly all available
data were collected in this way, and it actually is a reasonable thing
to do if the disorder from cell to cell is uncorrelated (as evidenced
above).

However, I totally agree with you that the disorder in protein
    
crystals
  
may well be correlated across large patches of unit cells.  If that is
the case, then the "average occupancy model" that is all but
    
universally
  
implemented by refinement programs will never be able to explain the
background-subtracted spot intensities.

-James Holton
MAD Scientist


Ian Tickle wrote:
    
If all cells are completely unsynchronized, then the

        
occupancy-weighted

      
average electron density map of all the conformers will fully
        
explain
  
the background-subtracted spot intensities, but if there is
cell-to-cell synchronization: it won't!

        
This is not correct: as I tried to explain in a previous posting,
      
the
  
'optic' mode DS component which arises from what I would call 'short
      
to
  
medium range' correlated displacements (that is correlations due to
rigid side-chain motions, or of secondary-structure units,
      
individual
  
helices say, or of whole domains within the same molecule, or of
different molecules within the same unit cell), give rise to a
non-uniform DS distribution over the *whole* diffraction pattern.
      
You
  
can't assume that the contributions of the optic DS at the Bragg
positions are zero just because they can't be measured!  From the DS
equation there's absolutely no reason why the DS should be anything
other than non-uniform at the Bragg position as anywhere else.
      
Since
  
it's equally non-uniform over the whole pattern, including at and
      
around
  
the Bragg positions, a planar background correction can't possibly
remove it from the integrated Bragg intensities.  So it's simply not
correct to say that the mean electron density explains all the
      
intensity
  
at the Bragg positions.  There will be a residual I(diffuse) =
I(coherent) - I(Bragg) which is everywhere positive, as I
      
demonstrated.
  
I agree with you that what I would call 'long-range' correlations
between different unit cells contribute largely to the 'acoustic'
      
mode
  
DS which is centred largely *at* the Bragg peaks.  You say 'if' the
cells are completely unsynchronised, but that's a big 'if' -
      
certainly
  
you can't simply assume that it's true.

On another point you said you wanted an 'operational' definition of
I(Bragg).  I'm not entirely clear what you mean by that.  Are you
      
saying
  
that you want I(Bragg) to be the total background-subtracted
      
integrated
  
intensity under the peak at the Bragg position, i.e. what I'm
      
calling
  
I(coherent).  If so then it can't be the contribution from the mean
density at the same time! - seems to me that's what everyone means
      
by
  
I(Bragg) (including you I thought!) so changing the definition will
cause total confusion!

Cheers

-- Ian


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