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

Dale Tronrud detBB at daletronrud.com
Thu Feb 12 13:23:51 PST 2015

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On 2/11/2015 8:08 PM, Peter Zwart wrote:
> Dear All,
>
> How meaningful are the second derivative based estimates obtained
> via full matrix inversion when the gradient is not 0 (i.e. when not
> in the minimum)? I can understand that when you are working with
> high-resolution data and your R-value is close to 0, things could
> work, but what happens when around a more challenging 2A?

The problem at 2 A resolution isn't that the analysis breaks down.
Its that the second derivative matrix has a singular subspace which
causes failure of the implementations we have.  A
single-value-decomposition would do the trick, but with the cost of
much more CPU time.  The singular subspace would tell you which
aspects of your model are not defined by your data (or your
restraints) and where you could use additional restraints.  The
non-singular part would tell you the SU's of those parts that are
determined, at least to some extent.

>
> If you are interested in the uncertainty of the occupancy, I
> recommend not doing any refinement, but just generate a list of
> occupancies and B-values for the atom of interest and compute the
> (free) likelihood for each model. Subsequent normalisation of the
> neg-exponent of these values, should provide you with an answer
> that could be just as believable as any other method around.  A
> little bit of python scripting should do the trick quite easily.

This is pretty much what I recommended.  If I recall the variance
of the parameter is equal to -(1/2)/(2nd derivative of log likelihood)
evaluated near the optimal parameter.  This will be an underestimate
because it ignores the correlation of this parameter will all the
others, but the correlation between B factor and occupancy of a
particular atom will be dominate.

Dale Tronrud
>
> Both the full matrix inversion and the suggestion above probe the
> steepness of the data-agreement hole the structure is sitting in.
> Pavels suggestion explores the spread of local minima around the
> starting configuration. I am not sure what method is more
> appropriate, perhaps it is instructive to know what problem you are
> trying to solve.
>
> HTH P
>
>
>
>
>
> On 11 February 2015 at 16:13, Masaki UNNO <unno19 at mx.ibaraki.ac.jp
> <mailto:unno19 at mx.ibaraki.ac.jp>> wrote:
>
> Dear all
>
> Thank you very much for your suggestions. I will try making a
> number of models in which the atom has different occupancies (e.g.
> 0.1-1.0). Then, I will refine them by restraining the B-factors.
> Actually, our structure contains some reaction intermediates not
> only the substrate. So I would like to estimate the ratio.
>
> Best regards
>
> Masaki -----Original Message----- From:
> phenixbb-bounces at phenix-online.org
> <mailto:phenixbb-bounces at phenix-online.org>
> [mailto:phenixbb-bounces at phenix-online.org
> <mailto:phenixbb-bounces at phenix-online.org>] On Behalf Of Pavel
> Afonine Sent: Thursday, February 12, 2015 6:36 AM To: Dale Tronrud;
> phenixbb at phenix-online.org <mailto:phenixbb at phenix-online.org>
> Subject: Re: [phenixbb] How should we estimate the "uncertainty" of
> the occupancy of an atom?
>
> Hi Dale,
>
>> 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.
>
> it is open access:
>
> http://phenix-online.org/papers/wd5073_reprint.pdf
>
> All the best, Pavel
>
>
>
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>
>
> --
> -----------------------------------------------------------------
> P.H. Zwart Staff Scientist Berkeley Center for Structural Biology,
> Science lead Lawrence Berkeley National Laboratories 1 Cyclotron
> Road, Berkeley, CA-94703, USA Cell: 510 289 9246 SASTBX:
> http://sastbx.als.lbl.gov BCSB:      http://bcsb.als.lbl.gov
> PHENIX:   http://www.phenix-online.org
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