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 > > > > > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 ----- 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 ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/
