Even within the domain of crystallography 'resolution' is used (correctly) to mean exactly the same thing as it does in other fields where imaging finds application (such as astronomy and microscopy, as you mention). This is even true in certain applications of crystal diffraction, for example in powder diffraction the resolution of the diffraction pattern is the closest separation of diffraction peaks that can be seen to be separate (resolved), and as such is in large part dependent on the beam divergence, as well as the mosaicity. It has absolutely nothing to do with the d-spacing of the peak or how far the pattern extends in reciprocal space.
On the STARANISO server we have largely deprecated the term 'resolution limit', instead preferring 'diffraction limit' and I always talk about the d-spacing of a reflection (in homage to Max von Laue and W.L. Bragg of course), never its resolution. Cheers -- Ian On Wed, Oct 9, 2024 at 12:48 PM Nave, Colin (DLSLtd,RAL,LSCI) < 000064fdcfc6624b-dmarc-requ...@jiscmail.ac.uk> wrote: > Dear all > Thanks all for these interesting discussions. > > My view is that the issues arise from a convention adopted many years ago > to use the word "resolution" in crystallography to describe the visibility > of features in an electron density map and/or the limit in reciprocal space > where the diffraction intensities were either cut off or deemed to just add > noise. In nearly all other fields, the term resolution is used to describe > the performance of an instrument and would depend on factors such as the > aperture of a telescope or the number of pixels in the sensor of a smart > phone camera. Despite this, the procedures adopted for defining resolution > in the structure determination of proteins are obviously useful. The reason > is that the electron density distributions of different proteins as a > function of spatial frequencies are similar and therefore the distribution > of intensities (e.g. Wilson statistics) are also similar. This means that > the metric adopted (resolution obtained via CC1/2 or FSI ) allows > comparison between different data and different proteins. It is a simple, > easily digested number which proves useful. > > Carrying the procedures over to different fields could be problematic as > this situation might not apply if the distribution of densities varies > between different samples or, for astronomy, different areas of the sky. I > am not sure whether the distribution of densities varies between brain > tumour and/or healthy patients (Marin's example). Capturing an image of the > sky where one can see Orion's belt as 3 sharp stars* but cannot see Orion's > nebula would not be particularly exciting. > > Apologies if some find the above a bit too philosophical. > > Colin > * actually one star is single, another triple and one hextuple. > -----Original Message----- > From: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK> On Behalf Of Randy John > Read > Sent: Tuesday, October 8, 2024 9:05 AM > To: CCP4BB@JISCMAIL.AC.UK > Subject: Re: [ccp4bb] Review: Linearity and Resolution in X-Ray > Crystallography and Electron Microscopy > > [You don't often get email from > 0000eafc0efa8263-dmarc-requ...@jiscmail.ac.uk. Learn why this is > important at https://aka.ms/LearnAboutSenderIdentification ] > > 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%2Fphysics%2Fpeople%2Fschmidt-marius%2F&data=05%7C02%7Ccolin.nave%4 > > 0DIAMOND.AC.UK%7C581b97a1c18d4e462bca08dce76ff9a0%7C9d27ba7401004d0d81 > > ff1d728dae8df6%7C0%7C0%7C638639719183014032%7CUnknown%7CTWFpbGZsb3d8ey > > JWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C400 > > 00%7C%7C%7C&sdata=rbydsH61Xqi3QwWPeUbcDNJoWL2ASdoZoV4lT7booJI%3D&reser > > ved=0 > > https://site/ > > s.uwm.edu%2Fsmarius%2F&data=05%7C02%7Ccolin.nave%40DIAMOND.AC.UK%7C581 > > b97a1c18d4e462bca08dce76ff9a0%7C9d27ba7401004d0d81ff1d728dae8df6%7C0%7 > > C0%7C638639719183028690%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLC > > JQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C40000%7C%7C%7C&sdata=4N > > 63pAEYGiepCmP69ZHxRBrKn2rqcZfk8vfrV8VvdSA%3D&reserved=0 > > https://www/. > > bioxfel.org%2F&data=05%7C02%7Ccolin.nave%40DIAMOND.AC.UK%7C581b97a1c18 > > d4e462bca08dce76ff9a0%7C9d27ba7401004d0d81ff1d728dae8df6%7C0%7C0%7C638 > > 639719183040132%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2 > > luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C40000%7C%7C%7C&sdata=rUdWwnRQCP > > GQ2SLAEEbLpuCbUJ6jbi3vc8MUXN%2F8e1Y%3D&reserved=0 > > Nature News and Views: > > https://www/. > > nature.com%2Farticles%2Fd41586-023-00504-4&data=05%7C02%7Ccolin.nave%4 > > 0DIAMOND.AC.UK%7C581b97a1c18d4e462bca08dce76ff9a0%7C9d27ba7401004d0d81 > > ff1d728dae8df6%7C0%7C0%7C638639719183051470%7CUnknown%7CTWFpbGZsb3d8ey > > JWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C400 > > 00%7C%7C%7C&sdata=TA8XjxxIL3XpRMt442bQNROJQlQIg%2Fzc9CuBObjzCCQ%3D&res > > erved=0 > > > > 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%2F10.31219%2Fosf.io%2F5empt&data=05%7C02%7Ccolin.nave%40DIAMOND.AC > > .UK%7C581b97a1c18d4e462bca08dce76ff9a0%7C9d27ba7401004d0d81ff1d728dae8 > > df6%7C0%7C0%7C638639719183074914%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wL > > jAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C40000%7C%7C%7C > > &sdata=m3IntDjvpQEkQxMHstkCeWi4uRfME%2FNiBbQaO5uDD08%3D&reserved=0 > > > > Have fun reading it! > > > > Marin > > > > > > > > > > > > To unsubscribe from the CCP4BB list, click the following link: > > https://www/. > > jiscmail.ac.uk%2Fcgi-bin%2FWA-JISC.exe%3FSUBED1%3DCCP4BB%26A%3D1&data= > > 05%7C02%7Ccolin.nave%40DIAMOND.AC.UK%7C581b97a1c18d4e462bca08dce76ff9a > > 0%7C9d27ba7401004d0d81ff1d728dae8df6%7C0%7C0%7C638639719183085964%7CUn > > known%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haW > > wiLCJXVCI6Mn0%3D%7C40000%7C%7C%7C&sdata=oP32JFOGcMDsK4Y8LCI1xTss0M8UeM > > eIZU9pEh%2Fr1KU%3D&reserved=0 To unsubscribe from the CCP4BB list, > > click the following link: > > https://www/. > > jiscmail.ac.uk%2Fcgi-bin%2FWA-JISC.exe%3FSUBED1%3DCCP4BB%26A%3D1&data= > > 05%7C02%7Ccolin.nave%40DIAMOND.AC.UK%7C581b97a1c18d4e462bca08dce76ff9a > > 0%7C9d27ba7401004d0d81ff1d728dae8df6%7C0%7C0%7C638639719183098167%7CUn > > known%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haW > > wiLCJXVCI6Mn0%3D%7C40000%7C%7C%7C&sdata=qJqTz9M8bwI1G%2FH8KvQfTRd2D7Ic > > UZlnm6iq9U0QTFs%3D&reserved=0 > > ----- > 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 http://www.jiscmail.ac.uk/CCP4BB, a > mailing list hosted by http://www.jiscmail.ac.uk/, terms & conditions are > available at https://www.jiscmail.ac.uk/policyandsecurity/ > This e-mail and any attachments may contain confidential, copyright and or > privileged material, and are for the use of the intended addressee only. 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