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*To*: stefano@if.sc.usp.br*Subject*: Re: [ccp4bb]: 3Fo-2Fc maps*From*: Randy J Read <rjr27@cam.ac.uk>*Date*: Wed, 29 Nov 2000 09:45:35 +0000*Cc*: ccp4bb@dl.ac.uk*Reply-To*: rjr27@cam.ac.uk*Sender*: owner-ccp4bb@dl.ac.uk

*** For details on how to be removed from this list visit the *** *** CCP4 home page http://www.dl.ac.uk/CCP/CCP4/main.html *** On Tue, 28 Nov 2000 17:00:14 -0200 (EDT), Stefano Trapani <stefano@if.sc.usp.br> wrote: > > *** For details on how to be removed from this list visit the *** > *** CCP4 home page http://www.dl.ac.uk/CCP/CCP4/main.html *** > > > A question about electron density maps. > > Does it make any sense to use a weighted (3mFo-2DFc) difference map > (with phases from a MR solution) during model building and refinement, > where m and D are the Sigma-A-style weights of Read (Acta Cryst > A42,1986)? Fred Vellieux first suggested combining my SIGMAA map coefficients with different relative weights. I'm afraid I can't track down a reference at the moment. The unweighted case (nFo-(n-1)Fc) was considered systematically by Vijayan, who showed that, as the amount of missing structure increases, the relative height of peaks for missing atoms drops, so a higher n is needed to equalise peaks from modeled and missing atoms. In principle, this shouldn't apply to the m and D weighted coefficients, where the weighting should put the two kinds of peaks on the same relative scale. Nonetheless, Fred found by examining maps that he had a better indication of what was wrong when looking at maps with higher n, such as 3mFo-2DFc. I think the reason is that the derivation of the SIGMAA map coefficients assumes a certain probability distribution relating Fo and Fc, where the expected value of Fo is given by DFc and the components of the error parallel and perpendicular to Fc are equally large, on average. But if you think about what is happening when we overfit the data (which is inevitable given typical observation to parameter ratios), the overfitting must cause the error in the parallel direction (amplitude) to be reduced systematically compared to the error in the perpendicular direction (essentially the phase component of the error). Overweighting the difference component of the map will correct to some extent for such overfitting. Another way to look at this is that our model is represented by DFc, which corresponds to model density smeared out by overall coordinate uncertainty. The difference map coefficient, mFo-DFc, turns out to be proportional to the gradient of the likelihood function with respect to Fc, the Fourier transform of which tells us where the likelihood function would like to see changes in the density. Varying the value of n in Fred's map coefficients corresponds to adding different amounts of this gradient map to the DFc map. I've been planning for some time to look into this more systematically, by devising a measure of overfitting (e.g. by comparing the relationship between Fo and Fc in the working data with that seen in the cross-validation data) and using that to choose an appropriate map coefficient. The more overfitting (generally corresponding to lower resolution), the bigger the value of n would have to be. But there's always too much to do. In the meantime, it's doesn't hurt to look at 2mFo-DFc and 3mFo-2DFc maps to see which shows regions of error more clearly. The other thing to note is that the difference map (mFo-DFc) is much less affected by considerations of relative heights of peaks for included and missing atoms. Randy J. Read Department of Haematology, University of Cambridge Wellcome Trust Centre for Molecular Mechanisms in Disease Cambridge Institute for Medical Research Wellcome Trust/MRC Building Tel: + 44 1223 336500 Hills Road Fax: + 44 1223 336827 Cambridge CB2 2XY, U.K. E-mail: rjr27@cam.ac.uk

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