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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Dear
Petrus Zwart (and all other X-ray crystallographers and EM-ers)<span></span></span></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Resolution
in the sense of the Abbe </span><span class="gmail-st">Diffraction Limit or the
Rayleigh </span><em><span style="font-style:normal">Criterion are part of what we would now call
the theory of linear systems, and are described by a “transfer function”.
“Fourier Optics” covers the theory of linear systems in Optics. These two
(essentially identical) resolution criteria state that the smallest details (let
us call that “A(r)” for “Airy”) you can possible observe in real-space is
inversely proportional to the size of the maximum aperture in Fourier space,
i.e., the extent of the transfer function in Fourier space “T(f)”. This defines
what “Instrumental Resolution” one could possibly achieve in an experiment, “instrumental”
to differentiate it from the “Results Resolution” you actually managed achieve
in your data collection/processing experiment [#Why-o-Why #10].<span> </span>What a linear imaging system will do the
image of the object (under the best of circumstances) is described by a (Fourier-space)
multiplication of the Fourier transform of the object O(r) [= O(f)] with the (Fourier-space)
transfer function T(f) of the instrument, yielding O’(f), which you need to
transfer back to real space to obtain the exit wave in the image plane; that
is: {O’(f)=T(f)</span></em><em><span style="font-style:normal">·</span></em><em><span style="font-style:normal">O(f)}. <span></span></span></em></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:"Times New Roman",serif"><em><span style="font-style:normal">Note, however, that the properties of the sample, that is, of O(r), does
nowhere appear in the transfer function T(f) or in its real-space version A(r)!<span> </span>The very concept of (instrumental) resolution
is exactly that it does NOT depend on the object O(r)! The “results resolution”
[#Why-o-Why #10], on the other hand, obviously depends on the sample; the
illumination; on the radiation dose; the pH of the solvent; the air humidity;
and the mood of the person doing the work on the day of preparation… <span> </span><span> </span><span> </span><span> </span><span></span></span></em></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:"Times New Roman",serif"><em><span style="font-style:normal">The FRC/FSC “results resolution” measures we introduced in 1982/1986, fit
perfectly in the abstract framework of linear systems and Fourier optics. The
X-ray metrics like R-factor and phase-residuals and FOMs do NOT fit into that clean
mathematical framework. Unfortunately, my EM colleagues started using X-ray
metrics like “Differential Phase Residual” and “FOMs” in EM based on some gut feeling
that the X-ray scientists know it better because they achieve a higher
resolution than us EM blobologists. How wrong my EM colleagues were: the quality
of the resolution metric is totally unrelated to the numerical resolution
levels we operate at! Seeing 3mm kidney stones in a patient’s tomogram can be
equally important as seeing </span></em>some hydrogen bond length in a cryo-EM
density. The FRC/FSC actually make more sense than the indirect and hybrid
X-ray ones. <span> </span><em><span style="font-style:normal">This misconception has
introduced a very tainted – and still ongoing – discussion in cryo-EM. Now that
the fields of X-ray crystallography and cryo-EM are merging it is time to get
things right! <span></span></span></em></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:"Times New Roman",serif"><em><span style="font-style:normal">I guess I cannot yet terminate my #Why-o-Why didactical crusade: <span> </span>I will need at least one more on just this linear-transfer
theory issue alone…<span></span></span></em></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:"Times New Roman",serif"><em><span style="font-style:normal">Marin van Heel, CNPEM/LNNano, Campinas, Brazil <span> </span><span></span></span></em></p>
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</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Feb 16, 2020 at 6:51 PM Petrus Zwart <<a href="mailto:phzwart@lbl.gov" target="_blank">phzwart@lbl.gov</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Hi All,<br></div><div><br></div>How is the 'correct' resolution estimation related to the estimated error on some observed hydrogen bond length of interest, or an error on the estimated occupancy of a ligand or conformation or anything else that has structural significance?<br><div><br></div><div>In crystallography, it isn't really (only in some very approximate fashion), and I doubt that in EM there is something to that effect. If you want to use the resolution to get a gut feeling on how your maps look and how your data behaves, it doesn't really matter what standard you use, as long as you are consistent in the use of the metric you use. If you want to use this estimate to get to uncertainties of model parameters, you better try something else.</div><div><br></div><div>Regards</div><div>Peter Zwart</div><div> </div><div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Feb 16, 2020 at 8:38 AM Marin van Heel <<a href="mailto:0000057a89ab08a1-dmarc-request@jiscmail.ac.uk" target="_blank">0000057a89ab08a1-dmarc-request@jiscmail.ac.uk</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Dear Pawel and All others ....
<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:12pt;font-family:"Times New Roman",serif"></p><p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:12pt;font-family:"Times New Roman",serif">This 2010 review is - unfortunately - largely based on the
flawed statistics I mentioned before, namely on the a priori assumption that
the inner product of a signal vector and a noise vector are ZERO
(an orthogonality assumption). The (Frank & Al-Ali 1975) paper we have
refuted on a number of occasions (for example in 2005, and most recently in our BioRxiv paper) but you still
take that as the correct relation between SNR and FRC (and you never cite the criticism...). <span></span></p>
<span></span></div><div>
</div><div></div><div></div><div>Sorry</div><div>Marin<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A <<a href="mailto:Pawel.A.Penczek@uth.tmc.edu" target="_blank">Pawel.A.Penczek@uth.tmc.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="auto">
<div dir="ltr">Dear Teige,
<div><br>
</div>
<div>I am wondering whether you are familiar with</div>
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<h2 style="box-sizing:border-box;font-family:"Lucida Grande","Helvetica Neue",Helvetica,Arial;font-size:20px;margin:8px auto;line-height:24px">
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<h2 style="box-sizing:border-box;font-family:"Lucida Grande","Helvetica Neue",Helvetica,Arial;font-size:20px;margin:8px auto;line-height:24px">
Resolution measures in molecular electron microscopy.</h2>
<div id="gmail-m_-3796767887894287704gmail-m_8609787314343393747gmail-m_-8079088879635535655gmail-m_4473107327319981263gmail-m_-4642610284911275282cit_summary" style="box-sizing:border-box;font-size:14px;color:rgb(39,39,39);font-family:Arial">
<div style="box-sizing:border-box">Penczek PA. Methods Enzymol. 2010.</div>
</div>
<div id="gmail-m_-3796767887894287704gmail-m_8609787314343393747gmail-m_-8079088879635535655gmail-m_4473107327319981263gmail-m_-4642610284911275282cit_full" style="box-sizing:border-box;font-size:14px;color:rgb(39,39,39);font-family:Arial">
<h3 style="box-sizing:border-box;font-family:"Lucida Grande","Helvetica Neue",Helvetica,Arial;color:rgb(0,0,0);margin-bottom:0px;font-size:14px">
Citation</h3>
<p style="box-sizing:border-box;margin:2px 0px">Methods Enzymol. 2010;482:73-100. doi: 10.1016/S0076-6879(10)82003-8.</p>
</div>
<div><br>
</div>
<div>You will find there answers to all questions you asked and much more. </div>
<br>
<div dir="ltr">Regards,
<div>Pawel Penczek</div>
</div>
</div>
</div>
<br>
<br>
<div dir="ltr">Regards,
<div>Pawel</div>
</div>
</div>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div><font size="2">------------------------------------------------------------------------</font><br><font size="1">P.H. Zwart<br>Staff Scientist</font></div><div><font size="1">Molecular Biophysics and Integrated Bioimaging &</font></div><div><font size="1">Center for Advanced Mathematics for Energy Research Applications</font></div><div><font size="1">Lawrence Berkeley National Laboratories<br>1 Cyclotron Road, Berkeley, CA-94703, USA<br>Cell: 510 289 9246</font></div><div><font size="1"><br></font></div><div><font size="1">PHENIX: <a href="http://www.phenix-online.org/" style="color:rgb(17,85,204)" target="_blank">http://www.phenix-online.org</a><br></font></div><div><font size="1">CAMERA: <a href="http://camera.lbl.gov/" target="_blank">http://camera.lbl.gov/</a></font></div><div style="font-size:small">-------------------------------------------------------------------------<br></div></div></div></div></div></div></div></div></div>
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