Dear Jacob,
The resolution in reciprocal and real space was addressed by R. W. James
in his paper 'False Detail in Three-Dimensional Fourier Representations
of Crystal Structures' piblished in Acta Cryst. (1948). 1, 132-134.
James showed that atomic density shape in the presence of series
terminations is described by the Bessel function of zero order:
3*[sin(m) - m*cos(m)]/m^3
where m=2*Pi*r/dmin
This function is equal to 1 at the atomic centre (r=0) and decreases as
r increases, then it oscillates. The function reduces to 0.5 for
r/dmin=0.4. Therefore, the two equal atoms to be separated (in a sense
of having a density in between lower than at their centres) the distance
between them should be equal (or higher) than 2*dmin*0.4
Main chain C and O atoms separated by 1.23 A should be resolved if dmin
is better than 1.55 A.
Two carbon sp3 atoms (distance 1.53 A) should be resolved if dmin is
better than 1.9 A.
Indeed, as Thomas wrote, 1.5 A is about right.
The above is correct in the absence of atomic displacement parameters
(Bfactor=0), for example for the normalised (sharpened) structure factor
amplitudes. And, of course, for the complete and error-free diffraction
data.
Victor
On 11/01/2018 21:07, Keller, Jacob wrote:
The reason behind this query is that I want to illustrate the power of
prior knowledge in data analysis. I want to say something like “even
though atoms cannot be directly observed at worse than X resolution,
which represents Y% of the PDB, all of these data sets have been fit
correctly with atomic models. This is due entirely to the power of the
excellent priors which exist in crystallography.”
JPK
+++++++++++++++++++++++++++++++++++++++++++++++++
Jacob Pearson Keller
Research Scientist / Looger Lab
HHMI Janelia Research Campus
19700 Helix Dr, Ashburn, VA 20147
(571)209-4000 x3159
+++++++++++++++++++++++++++++++++++++++++++++++++
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*From:* Thomas Edwards [mailto:t.a.edwa...@leeds.ac.uk]
*Sent:* Thursday, January 11, 2018 2:59 PM
*To:* Keller, Jacob <kell...@janelia.hhmi.org>
*Cc:* CCP4BB@JISCMAIL.AC.UK
*Subject:* Re: [ccp4bb] "Atomic resolution"
Dear Jacob,
Ah... this old chestnut!
Current EM people say that they are at atomic resolution because they
are building atomic models (naive??).
I have been criticised in the past for using the term with say 2.2A
diffraction data. By co-authors and reviewers alike. When I was young
and naive.
My (current) definition would be yours - visible with data.
I think 1.5A is about right for X-ray. Maybe higher res?
I’m sure there are lots of rigorous ways to think. I probably haven’t
taken that route. However, I think it is a semantic problem that might
benefit from some disambiguation rather than rigour.
It depends why you are asking the question...
Sorry..!
*/Ed is: Out and about.../*
*/Sent from iPhone6sPlus./*
On 11 Jan 2018, at 19:31, Keller, Jacob <kell...@janelia.hhmi.org
<mailto:kell...@janelia.hhmi.org>> wrote:
Dear Crystallographers,
Has there been a consensus as to what is meant by “atomic
resolution?” Seems like the term is taken by various practitioners
to mean different things.
A related question: at what resolution are atoms “visible” using
only the data? I have an empirical feeling that this would be
around 1.5 Ang Bragg spacings, but on the other hand, one can
contour up most maps and see individual atom peaks. I would be
interested to hear a more rigorous way to think about this.
All the best,
Jacob Keller
+++++++++++++++++++++++++++++++++++++++++++++++++
Jacob Pearson Keller
Research Scientist / Looger Lab
HHMI Janelia Research Campus
19700 Helix Dr, Ashburn, VA 20147
(571)209-4000 x3159
+++++++++++++++++++++++++++++++++++++++++++++++++
The content of this email is confidential and intended for the
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share any part of this message with any third party, without a
written consent of the sender. If you received this message by
mistake, please reply to this message and follow with its
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the future.
