Dear Marin,
In crystallography we do have the information gain measure (based on
Kullback-Leibler divergence) that my group put forward and implemented in our
Phaser program (https://doi.org/10.1107/s2059798320001588). Signal and noise
aren’t isotropic, so information gain isn’t isotropic either. However, we’ve
observed that the resolution at which the average information gain is about 1/2
bit per reflection corresponds roughly to the resolution limits suggested by
other techniques. Given the interpretation of information gain as the maximum
log-likelihood-gain that one could achieve from an observation with a perfect
model, it’s a very natural measure to use for the useful resolution. I don’t
think this measure has gained much traction in the crystallographic community
yet, but it’s becoming more widely available in some data analysis tools.
We’ve used the same KL-divergence approach to estimate the information gain
from a Fourier term in a cryo-EM reconstruction
(https://doi.org/10.1107/s2059798323001596). In the implementation of this in
our EM-placement docking software, we have anisotropic estimates of signal and
noise, so again the information gain is anisotropic. Somewhat to my surprise
(given the differences in the derivations), our information gain measure turns
out to be equivalent to yours (https://doi.org/10.48550/arXiv.2009.03223) if we
assume that the signal and noise are isotropic. As you point out there, for
cryo-EM reconstructions it’s essential to consider the effect of over-sampling
of the Fourier transform and the corresponding lack of independence of the
Fourier terms, so this has an over-sampling correction factor.
Best wishes,
Randy Read
On 8 Oct 2024, at 00:02, Marin van Heel<marin.vanh...@gmail.com> wrote:
Dear Marius Schmidt
In my (our) original FRC/FSC papers (1982; 1986 ; 2000; 2004; 2017; 2020; 2024) the
linearity of these correlation functions/metrics have been extensively discussed.
Historically, EM started at a low resolution "blobology" level whereas X-ray
crystallography (XRC) at that time, already had reached atomic resolution. This led to
the belief that the XRC resolution metrics ( like phase residuals and R-factors) were
also appropriate as resolution metrics for EM. However, in XRC the measurables are
diffraction patterns for which amplitudes corresponding phases had to be derived
iteratively. In EM and in imagining in general, the measurables are the images
themselves, that contain both the amplitude information and the phase information. To
revert to the then already established XRC resolution metrics like phase residuals or
R-factors, implied discarding the most important part of the available information (see
the Why-O-Why ).
(https://www.linkedin.com/posts/marin-van-heel-5845b422b_whyowhyarchive-activity-7149738255154946048-Oc93/?utm_source=share&utm_medium=member_desktop).
That problem was realized soon and the mentioned FRC and FSC metrics were thus
suggested which exploit all the available information. Thus, the XRC atomic
resolution technique of the 1980s came with a low-quality resolution metric
whereas the Cryo-EM low-resolution blobology approach of the 1980s came with a
high-quality resolution metric.
Thus, in summary, all resolution criteria in XRC are ad-hoc non-linear metrics
that have no general validity outside of XRC. Looking at only the amplitudes of
a diffraction pattern is like finding the highest resolution spot in a
diffraction pattern, where, even if the spot is clearly visible, that does not
mean one would be able to find its phase. We need a more comprehensive metric
that has a wide range of applicability. In other words, where a CC1-2 metric
cannot be applied to assess the 3D brain scan of a brain-tumor patient, the FRC
/ FSC, and the newest FRI / FSI metrics can be applied in all cases
where 2D and 3D data are dealt with!
Hope this helps,
Marin van Heel
On Mon, Oct 7, 2024 at 3:04 PM Marius Schmidt<smar...@uwm.edu> wrote:
I think this is taken care of:
The CC1/2 and the CC1/2* are appropriate metrics for the resolution limit.
They are all spit out by newer data processing software.
The CC1/2 is directly comparable to the FSC. Many people use CC1/2 = 1/e as
the resolution limit.
In many cases of data the CC1/2 = 1/e is equivalent to I/sigI of 1, which
is used sometimes as a metric for the resolution limit (some use I/sigI = 2),
and in more cases the CC1/2 corresponds to Rmerge in the range of 40%.
For serial crystallography, the R-split goes through the roof at CC1/2 = 1/e,
so the CC1/2 is the better metric.
Best
Marius
Marius Schmidt, Dr. rer. Nat. (habil.)
Professor
University of Wisconsin-Milwaukee
Kenwood Interdisciplinary Research Complex
Physics Department, Room 3087
3135 North Maryland Avenue
Milwaukee, Wi 53211
phone (office): 1-414-229-4338
phone (lab): 414-229-3946
email:smar...@uwm.edu
https://uwm.edu/physics/people/schmidt-marius/
https://sites.uwm.edu/smarius/
https://www.bioxfel.org/
Nature News and Views:https://www.nature.com/articles/d41586-023-00504-4
From: CCP4 bulletin board<CCP4BB@JISCMAIL.AC.UK> on behalf of Marin van
Heel<marin.vanh...@gmail.com>
Sent: Monday, October 7, 2024 11:24 AM
To:CCP4BB@JISCMAIL.AC.UK <CCP4BB@JISCMAIL.AC.UK>
Subject: [ccp4bb] Review: Linearity and Resolution in X-Ray Crystallography and
Electron Microscopy
Dear All,
Sayan Bhakta and I have recently posted the preprint of a review on resolution
and linearity which will appear in a book to be launched on the 16th of October
2024.
(https://doi.org/10.1201/9781003326106 ). It is the first Cryo-EM review that
I have been involved in for 25 years.
In our preparation, I was quite amazed about what other authors wrote (or did
not write) in their many reviews on these matters.
For example, I missed any serious discussion about resolution metrics in X-ray
crystallography, which technique is fundamentally non-linear.
Linearity is a prerequisite for defining the resolution of any instrument. The
iterative refinements applied in X-ray crystallography (and sometimes Cryo-EM)
makes that all Phase-residuals and R-factors or fixed threshold values cannot
be used to compare the results of independently conducted experiments. What is
an obvious consequence of the lack of universality of such metrics like
phase-residuals and R-factors, is that they cannot be used outside of the
immediate context in which they were defined, like X-ray crystallography or
structural biology. In contrast, the Fourier-Ring-Correlation (FRC);
Fourier-Shell-Correlation (FSC) and their recent successors: the
Fourier-Ring-Information (FRI) and the Fourier-Shell-Information (FSI), plus
their integrated versions, are universal metrics that are applicable to all
fields of science where 2D and 3D data are dealt with!
https://doi.org/10.31219/osf.io/5empt
Have fun reading it!
Marin
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-----
Randy J. Read
Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research Tel: +44 1223 336500
The Keith Peters Building
Hills Road
E-mail:rj...@cam.ac.uk
Cambridge CB2 0XY, U.K.
www-structmed.cimr.cam.ac.uk
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