Ian Tickle wrote:
Sorry I don't have instant access to Acta A here so can't comment in the
light of the Flack & Shmueli paper. But it seems to me that Kevin's
point is still valid,
I think that I stated that I agree with him ?
regardless of whether or not the anomalously
scattering atoms have different ADPs from the average or not. I agree
that this would have the complicating effects described, but I don't see
that it's necessary to invoke it as an explanation.
I don't invoke it as an explanation. I simply commented on the
(first-order) independence of Bijvoet or Friedel (anomalous) intensity
ratios with respect to atomic displacement parameters. Such Bijvoet
ratios (e.g. RMS(Delta_ano)/mean(I) or the same variant with F's) are
widely advocated in the methodological SAD/MAD literature as estimates
for gauging the theoretical signal strength of anomalous scattering. Of
course we can debate over the relevance of such theoretical estimates
for practical purposes, but I really just wanted to point out that these
ratios are (to first order) independent of atomic displacements.
The reason is that
the anomalous phasing power doesn't depend on Rano = <|delta-ano|>/<I>,
I agree. R_{ano} was brought up earlier in this thread, so I just
commented on this. Personally, I also have found over the years that
R_{ano} is not a particularly useful indicator for assessing the
feasibility of SAD or MAD phasing.
I trust that the discussion of what is a good indicator would offer
enough material for another thread.
Cheers
Marc
it depends on the anomalous signal/noise ratio =
<|delta-ano|/s.u.(delta-ano)>, or something related to it, and the
standard uncertainty of course depends largely on the background). So
if the fall-off due to overall thermal motion etc as described by Kevin
causes the S/N ratio to dip much below 1 then the anomalous signal won't
help you.
Cheers
-- Ian
-----Original Message-----
From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk]
On
Behalf Of Marc SCHILTZ
Sent: 13 May 2009 11:26
To: Kevin Cowtan; CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] phasing with se-met at low resolution
Kevin Cowtan wrote:
This is absolutely correct - in the analysis you present, the
non-anomalous scattering drops with resolution, but the anomalous
part
does not. And since counting noise varies with intensity, we should
actually be better off at high resolution, since there is less
non-anomalous scattering to contribute to the noise! (This is
somewhat
masked by the background, however).
So why don't we see this in practice?
The reason is that you've missed out one important term: the atomic
displacement parameters (B-factors), which describe a combination of
thermal motion and positional disorder between unit cells. This
motion
and disorder applies equally to the core and outer electrons, and so
causes a drop-off in both the anomalous and non-anomalous
scattering,
over and above that caused by the atomic scattering factors.
I agree with everything but would like to add the following: if we
assume an overall atomic displacement parameter, the drop-off in both
the anomalous and non-anomalous scattering is the same. Therefore, the
ratio of anomalous differences over mean intensity (which is what
comes
closest to R_{ano} - in whichever way this is defined) is essentially
unaffected by atomic displacements and should still go up at high
resolution, irrespective of the values of the atomic displacement
parameter !
Things are more complicated if individual isotropic atomic
displacements
are considered, because the anomalously scattering atoms (e.g. the Se
atoms) may have significantly larger or smaller displacement
parameters
than the average.
All this is discussed in section 4.4. of Flack & Shmueli (2007) Acta
Cryst. A63, 257--265.
Marc
But your reasoning was sound as far as it went, and it is a point
which
many people haven't recognised!
Kevin
Raja Dey wrote:
Dear James,
I don't understand why measuring anomalous differences has nothing
to
do
with resolution.
Heavy atoms
scatter anomalously because the inner shell electrons
of the heavy atom cannot be considered to be free anymore
as was assumed for normal Thomson scattering. As a result
the atomic scattering factor of the heavy atom becomes
complex and this compex contribution to the structure
factor leads to non-equality of Friedel pairs in non-centro
symmetric systems(excluding centric zone). This feature is taken
advantage in
phase determination. Since the inner shell electrons
being relatively more strongly bound in heavy atoms
contribute to anomalous scattering and its effect
is more discernable for high angle reflections . Here
the anomalous component of the scattering do not
decrease much because of the effectively small atomic
radii (only inner shell being effective). FOR HIGH
ANGLE REFLECTIONS ANOMALOUS DATA
BECOMES IMPORTANT.
Raja
--
Marc SCHILTZ http://lcr.epfl.ch
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