Hi,

   I have to take issue with one of Ian's points.  His statement that
the integral of the electron density does not change with the change
in a B factor but does change with a change in occupancy is the equivalent
to stating that the integral of an occupancy difference map feature is
nonzero while the integral of a B factor difference map feature is zero.
These conditions only occur when all of the Fourier coefficients are used
to calculate the difference map, which only truly occurs with a very
high resolution map, and one that includes the F000 reflection.  Refinements
that occur in practice only approximate these conditions and this approximation
results in the oft observed difficulty in identifying a difference map feature
as either due to an error in occupancy or B factor.

   The problem gets worst as the resolution of the map decreases and the
series termination effects become larger.

   To overcome this difficulty of interpreting the difference map feature one
needs some other source of information, as others in this thread have suggested.
The classics are assuming that the B factors of the mystery group are similar
to the surrounding atoms that are presumed to be at full occupancy, or assuming
that the occupancy of a significantly large group of atoms are equal to each other.
Each of these assumptions have been used in real refinements to help solve this
problem.  Each are made more difficult if atoms in question are sitting atop
atoms of the alternative structure.  When your compound is not present something
else probably is (water most likely) and if you don't have a model for the
alternative structure you will end up overestimating the occupancy of your
compound.

   In your particular case, your molecule superimposes upon its symmetry image.
This situation introduces additional correlations due to the apparently
superimposed atoms of the two images, including correlations with the positional
parameters.  You will have to be very careful to enforce strict stereochemical
restraints, more strict than you would for the rest of the model. In addition
you will likely have to run more cycles of refinement to achieve convergence
than you normally expect.

   With your resolution, an assumption of a group occupancy, strict geometry
restraints, and selecting the occupancy that gives the B factors you want, you
will come up with a number for the occupancy of your compound.  Verifying the
accuracy of that number will be difficult.  I predict that the R value and R free
will not change by a significant amount.  (That is the definition of a correlation
between two parameters, that you can change them in compensating ways and not
affect the fit to your data.)  Your best hope would be that the new difference
map will show you the water molecules that occupy this site when your compound
does not.  Failing that you will have an occupancy for your group but no error
bars for that value.

Dale Tronrud


Ian Tickle wrote:
> Hi Pat
> 
> I concur with George, we routinely refine together the group B factor
> and occupancy of our ligands and frequently see significant deviations
> of the group occupancy from the starting value even if it is highly
> correlated with the group B factor (the significance test takes account
> of the correlation), sometimes at 2.8 Ang, but rather easily detectable
> at 2 Ang.  This often eliminates negative difference density,
> particularly at the heavier atoms such as S, Cl, Br (of course this
> could also be explicable by inducement of disorder by radiation damage
> as opposed to the ligand binding with partial occupancy on soaking or
> co-crystallisation).  Whenever I see a significant difference (say > 10
> Ang.^2) between the average B factor of the ligand and the average B
> factor of the protein atoms in the binding site I suspect that partial
> occupancy of the ligand is the true explanation.
> 
> There is in fact no reason why the occupancy and B factor should be
> completely correlated, unless of course the data errors are large and/or
> the resolution is very low and/or the group only makes a small
> contribution to the total scattering, in which the errors will dominate
> and the results will not be significant.  This is because increasing the
> B factor of an atom or group of course makes the density broader and
> lower but does not change the integral of the density (i.e. the number
> of electrons scattering), whereas changing the occupancy clearly does
> change the number of electrons (in fact proportionally).  Hence the
> effects of changing the B factor and occupancy are quite different.
> 
> Cheers
> 
> -- Ian
> 
> PS I wasn't your referee either!
> 
>> -----Original Message-----
>> From: [log in to unmask] [mailto:[log in to unmask]]
> On
>> Behalf Of George M. Sheldrick
>> Sent: 31 May 2009 17:20
>> To: Patrick Loll
>> Cc: [log in to unmask]
>> Subject: Re: [ccp4bb] coupling between occupancy and b-values in
>> refinement
>>
>> Dear Pat,
>>
>> You don't say how large your ligand is, but if the occupancy is
>> refined as a single parameter so that all the atoms in the ligand
>> are constrained to have the same occupancy, it should be rather
>> well-defined and not highly correlated with the B-values. By
>> the way, I was not your referee!
>>
>> Best wishes, George
>>
>> Prof. George M. Sheldrick FRS
>> Dept. Structural Chemistry,
>> University of Goettingen,
>> Tammannstr. 4,
>> D37077 Goettingen, Germany
>> Tel. +49-551-39-3021 or -3068
>> Fax. +49-551-39-22582
>>
>>
>> On Sun, 31 May 2009, Patrick Loll wrote:
>>
>>> Hi all,
>>>
>>> I'm looking for a reference to bolster my response to a referee, in
>> which I
>>> defend my decision not to refine the occupancy of a ligand in
> structure
>>> refined at around 2 A resolution (note the ligand binding slte lies
> on a
>>> two-fold crystallographic axis, so the maximum occupancy is 0.5)
>>>
>>> I recall reading a paper a LONG time ago (decades) in which someone
>> described
>>> some careful refinement experiments, and concluded that  the
> correlation
>>> between occupancy and B-value is so strong that it simply makes no
> sense
>> to
>>> "independently" refine both parameters (at least for light atoms,
> and in
>> the
>>> absence of super high resolution data).
>>>
>>> Alas, all that I recall is this take-home message. I have no idea of
>> where the
>>> paper appeared, or the names of the authors (or indeed, if I'm even
>>> remembering the paper's message correctly). I've tried trolling
> through
>> Acta,
>>> without success.  Does anyone have a better idea of where I might
> find
>> this
>>> paper, or one espousing a similar message?
>>>
>>> Thanks,
>>>
>>> Pat
>>>
>>>
>>>
> ------------------------------------------------------------------------
>> -------------
>>> Patrick J. Loll, Ph. D.                 		Professor of
>>> Biochemistry & Molecular Biology
>>> Director, Biochemistry Graduate Program
>>> Drexel University College of Medicine
>>> Room 10-102 New College Building
>>> 245 N. 15th St., Mailstop 497
>>> Philadelphia, PA  19102-1192  USA
>>>
>>> (215) 762-7706
>>> [log in to unmask]
>>>
>>>
>>>
>>>
> 
> 
> 
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