[phenixbb] How should we estimate the "uncertainty" of the occupancy of an atom?

Dale Tronrud detBB at daletronrud.com
Wed Feb 11 11:57:42 PST 2015

   Pavel's test does not even come close to estimating the uncertainty
in occupancy.  Imagine you are optimizing a parameter with a broad
minimum. (Which is true when you are refining both the occupancy and B
factor of an atom.)  A number of refinements with differing starting
positions (within the radius of convergence) will always result in a
cluster of answers near the minimum.  The breadth, or uncertainty, of
the parameter is unimportant in Pavel's test because the purpose of
refinement is to find the minimum.

   The breadth of the minimum is described by the second derivative of
the target function.  You can't calculate the uncertainty without
calculating it.  In the absence of the program doing the calculus for
you (As Shelxl will do at high resolution) I suppose you could create a
number of models when the occupancy and B factor of the atom are varied
jointly (There is no use wandering off the line.) and calculating the
value of the target function for each.  Fitting a parabola to these
results will give you the curvature.

   The differences in the target function for such coordinated
alterations to one atom will be very small so one hopes the program uses
high precision mathematics.

   I hope you are now beginning to understand why people don't routinely
quote uncertainties for occupancies and therefore don't take their exact
values very seriously.  If your interpretation of your model depends on
whether the occupancy of this atom is 0.65 or 0.75 crystallography is
the tool you need.


On 2/11/2015 10:21 AM, Pavel Afonine wrote:
> Hello Masaki,
>> We determined the structure of an enzyme-substrate complex. The
>> substrate of the enzyme contains some partially occupied atoms. We
>> were able to calculate the occupancies of these atoms using PHENIX_refine.
>> By the way, I would like to know the uncertainties of the occupancies
>> of these atoms. How can I estimate the uncertainties? For example, the
>> occupancy of an atom was calculated as 0.65; can we write it as 0.65
>> (+/- 0.05) or 0.65 (+/- 0.1)?  I know that it is related to B-factor
>> and depends on the resolution (number of diffraction data per
>> parameters), but I would like to know how to estimate (calculate?) the
>> uncertainty.  Could someone tell me about this issue?
> an approximation to what you want can be easily achieved as following:
> 1) create 10-100 structures where occupancies in question are perturbed
> and vary from say 0.1-0.9. Also slightly perturb B-factors of atoms that
> surround these atoms.
> 2) Refine all these perturbed structures using refinement protocols that
> you usually use (the one used to obtain your final structure). Make sure
> to use sufficient amount of refinement macro-cycles so that refinement
> achieves near-convergence.
> 3) Extract occupancies in question. They will make some distribution and
> the spread of that distribution will tell you hint you the uncertainty.
> Pavel 
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