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CCP4BB  May 2012

CCP4BB May 2012

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Subject:

Re: Calculating ED Maps from structure factor files with no sigma

From:

George Sheldrick <[log in to unmask]>

Reply-To:

George Sheldrick <[log in to unmask]>

Date:

Wed, 23 May 2012 18:57:09 +0200

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In SHELXL. a refinement program sometimes used by small molecule 
crystallographers, all Fourier map for at least the last 20 years were 
weighted by Ic^2/(Ic^2+sigma^2(I)), where Ic is the calculated squared 
structure factor and sigma(I) is the square root of 1/w. w is the weight 
assigned to a reflection in the refinement (e.g. w=1/(sig(I)^2+(gI)^2), 
where sig(I) is the esd of the measured intensity I and g is a small 
constant. This purely empirical scheme appears to result in a 
significant reduction in the noise level of the map, at least for 
typical small molecule structures. Such schemes have been called 
'maximum likelihood by intuition', a proper maximum likelihood treatment 
taking the esds of the intensities into account would of course do much 
better.

George

On 05/23/2012 06:59 PM, Dale Tronrud wrote:
> On 05/23/12 08:06, Nicholas M Glykos wrote:
>> Hi Ed,
>>
>>
>>> I may be wrong here (and please by all means correct me), but I think
>>> it's not entirely true that experimental errors are not used in modern
>>> map calculation algorithm.  At the very least, the 2mFo-DFc maps are
>>> calibrated to the model error (which can be ideologically seen as the
>>> "error of experiment" if you include model inaccuracies into that).
>> This is an amplitude modification. It does not change the fact that the
>> sigmas are not being used in the inversion procedure [and also does not
>> change the (non) treatment of missing data]. A more direct and relevant
>> example to discuss (with respect to Francisco's question) would be the
>> calculation of a Patterson synthesis (where the phases are known and
>> fixed).
>>
>>
>>> I have not done extensive (or any for that matter) testing, but my
>>> evidence-devoid gut feeling is that maps not using experimental errors
>>> (which in REFAMC can be done either via gui button or by excluding SIGFP
>>> from LABIN in a script) will for a practicing crystallographer be
>>> essentially indistinguishable.
>> It seems that although you are not doubting the importance of maximum
>> likelihood for refinement, you do seem to doubt the importance of closely
>> related probabilistic methods (such as maximum entropy methods) for map
>> calculation. I think you can't have it both ways ... :-)
>>
>>
>>
>>> The reason for this is that "model errors" as estimated by various
>>> maximum likelihood algorithms tend to exceed experimental errors.  It
>>> may be that these estimates are inflated (heretical thought but when you
>>> think about it uniform inflation of the SIGMA_wc may have only
>>> proportional impact on the log-likelihood or even less so when they
>>> correlate with experimental errors).  Or it may be that the experimental
>>> errors are underestimated (another heretical thought).
>> My experience from comparing conventional (FFT-based) and maximum-entropy-
>> related maps is that the main source of differences between the two maps
>> has more to do with missing data (especially low resolution overloaded
>> reflections) and putative outliers (for difference Patterson maps), but in
>> certain cases (with very accurate or inaccurate data) standard deviations
>> do matter.
>     In a continuation of this torturous diversion from the original question...
>
>     Since your concern is not how the sigma(Fo) plays out in refinement but
> how uncertainties are dealt with in the map calculation itself (where an
> FFT calculates the most probable density values and maximum entropy would
> calculate the "best", or centroid, density values) I believe the most
> relevant measure of the uncertainty of the Fourier coefficients would be
> sigma(2mFo-DFc).  This would be estimated from a complex calculation of
> sigma(sigmaA), sigma(Fo), sigma(Fc) and sigma(Phic).  I expect that the
> contribution of sigma(Fo) would be one of the smallest contributors to this
> calculation, as long as Fo is "observed".  I wouldn't expect the loss of
> sigma(Fo) to be catastrophic.
>
>     Wouldn't sigma(sigmaA) be the largest component since sigmaA is a function
> of resolution and based only on the test set?
>
> Dale Tronrud
>
>
>>
>> All the best,
>> Nicholas
>>
>>


-- 
Prof. George M. Sheldrick FRS
Dept. Structural Chemistry,
University of Goettingen,
Tammannstr. 4,
D37077 Goettingen, Germany
Tel. +49-551-39-3021 or -3068
Fax. +49-551-39-22582

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