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

-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 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 mailto:[email protected]> 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: [email protected] mailto:[email protected] [mailto:[email protected] mailto:[email protected]] On Behalf Of Pavel Afonine Sent: Thursday, February 12, 2015 6:36 AM To: Dale Tronrud; [email protected] mailto:[email protected] 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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