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

Dale Tronrud detBB at daletronrud.com
Wed Feb 11 13:33:47 PST 2015

```   If I draw an Gaussian curve on a piece of paper and then try to
estimate the location of the highest point, I will get a scatter of
points near the maximum.  The width of this distribution might be
related to the standard deviation of the curve but it will certainly not
be an estimate of it.  It will be much, much smaller.  If they are
linearly related, I could not guess what the multiplicative constant
would be, but it would be very large.

Dale Tronrud

P.S. I'll look up the paper you reference but my university does not
subscribe to acta Cryst and getting those papers takes time.

On 2/11/2015 12:21 PM, Pavel Afonine wrote:
> What I suggested is a quick and simple work-around that will provide an
> *estimate* of the uncertainty. How this estimate is going to be
> different from the uncertainty derived from 2nd derivatives is difficult
> to say (and whether the difference is going to be significant!). You
> need to try both and see the difference - that's the only way to get THE
> answer. Also, I'm not entirely sure how much uncertainties obtained from
> 2nd derivatives would account for uncertainties due to refinement result
> variations described in Acta Cryst. D63, 597-610 (2007) (I tend to think
> they won't at all, though again I would not bet on that until I try).
>
> Pavel
>
> On 2/11/15 11:57 AM, Dale Tronrud wrote:
>>     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.
>>
>> Dale
>>
>> 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
>>>>
>>> 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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