[sharp-discuss] Rcullis(anomalous) for SAD data?

[Marc SCHILTZ]

Dear Ed,

In SHARP, anomalous lack-of-closure variance (LOCV) for a
reflection is defined as:

LOCV_ano(hkl) = <(DANO_obs - DANO_calc)**2>

where: 
DANO_obs = |Fph+|_obs - |Fph-|_obs
DANO_calc = Scale*(|Fp* + Fh+_calc| - |Fp* + Fh-_calc|)

Fp* = 'trial' point for protein structure-factor
Fh+_calc / Fh-_calc = structure factors computed from
                      heavy-atom model

(in the case of SAD, 'heavy atom' means anomalous scatterer)

The average < ... > in the above formula is a weighted average
over all possible Fp* on the complex plane. Remember Fp* is
unknown and the philosophy of SHARP is to integrate over all
possible values of Fp* (a process termed 'marginalization').

More intuitively, LOCV_ano represents the (squared) part of
observed anomalous differences that can not be explained by
the heavy atom model (i.e. which may be termed non-isomorphism).


Now, anomalous R-Cullis is defined as:

               SQRT[Sum_{hkl} LOCV_ano(hkl)]
RCullis_ano = --------------------------------
              SQRT[Sum_{hkl} DANO_obs(hkl)**2]


And anomalous Phasing Power is:
              
              SQRT[Sum_{hkl} <DANO_calc(hkl)**2>]
PhasPow_ano = -----------------------------------
                 SQRT[Sum_{hkl} LOCV_ano(hkl)]

where again, the average < ... > is a weighted average
over all possible Fp* on the complex plane.


EXCEPT for the integration over Fp*, these relations are
equivalent to:


               rms(DANO_calc - DANO_obs)
RCullis_ano = ---------------------------
                     rms(DANO_obs)


                     rms(DANO_calc)
PhasPow_ano = ---------------------------
               rms(DANO_calc - DANO_obs)




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* Marc SCHILTZ                                                 *
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