Since it is suggested to run SHARP in order to obtain the phasing
statistics, I take the liberty to provide a link where the expressions
for relevant quantities are specified :
http://www.globalphasing.com/pipermail/sharp-discuss/2003-March/001490.html
As a general problem, all these statistical indicators were defined in
the early days of protein crystallography, in the context of the Blow &
Crick (1959) framework (i.e. assuming error-free native measurements)
using MIR data (i.e. essentially yielding unimodal phase probability
distributions). The R-Cullis was initially defined for centric
reflections only.
Modern maximum-likelihood phasing methods have abandoned the Blow &
Crick concept of error-free native measurements and use a full
2-dimensional probability distribution for acentric structure factors on
the complex plane. The methods are therefore capable of adequately
dealing with highly bimodal probability distributions (e.g. SIR, SAD)
and with data where there is no native (or otherwise "special") data set
(e.g. MAD).
It is not entirely evident how the "Blow & Crick" Phasing-Power,
R-Cullis and FOM can be extended and generalized. The approach adopted
in SHARP is described in the page whose link is given above.
Concerning the FOM, it is not strictly true that the FOM, evaluated on a
2-dimensional probability distribution is equal to the cosine of the
phase error., This is only the case if one assumes the "native"
amplitude to be error-free. However, the cases discussed by Ian (bimodal
distributions in SIR or SAD) will be correctly dealt with by SHARP.
Things become also more tricky when computing and using
Hendrickson-Lattman (1970) coefficients since, in the general case,
these can not be calculated in a meaningful way for the "native" phase
probability distribution (see the discussion in section 8 of Bricogne et
al. (2003) [Acta Cryst D.59, 2023-2030]. This is a very important issue
in connection with the subsequent use of density-modification
techniques, but it is often overlooked.
Marc
Harmer, Nicholas wrote:
> Dear Colleagues,
>
> I am very grateful to everyone who contributed to the discussion regarding phasing statistics that I initiated. I certainly found it very informative. Below is a summary of the technical responses that I regarding this problem.
>
> 1) Use some of the statistics that SHELXD and SHELXE do provide (e.g. CC/CCfree for SHELXD, CCfree and connectivity for SHELXE). These could be compared to statistics produced for well determined structures (e.g. see Debreczeni et al. 2003 Acta Cryst. D., D59, 688-696).
>
> 2) Take the results from SHELX and put them into SHARP to generate the statistics.
>
> 3) Take the results from SHELX and put them into phaser_er, CRANK, or MLPHARE (perhaps with more difficulty) to generate the statistics.
>
> Thanks to Rick Lewis, Boaz Shaanan, Ed Lowe and Eleanor Dodson for suggestions.
>
> Cheers,
>
> Nic Harmer
>
> [For anyone interested, I took approaches 1 and 2. I got a good figures for phasing power from SHARP (somehow I failed to find the Rcullis, never mind), quoted the FOM at the end of SHELX, and the values for CC/CCfree from SHELXD, and the map contrast in the original and inverted hands from SHELXE. These all looked quite convincing, so hopefully my referees will be happy.]
--
Marc SCHILTZ http://lcr.epfl.ch
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