How would one evaluate the information content of systematic absences? JPK
On Feb 26, 2020 8:14 PM, James Holton <jmhol...@lbl.gov> wrote: In my opinion the threshold should be zero bits. Yes, this is where CC1/2 = 0 (or FSC = 0). If there is correlation then there is information, and why throw out information if there is information to be had? Yes, this information comes with noise attached, but that is why we have weights. It is also important to remember that zero intensity is still useful information. Systematic absences are an excellent example. They have no intensity at all, but they speak volumes about the structure. In a similar way, high-angle zero-intensity observations also tell us something. Ever tried unrestrained B factor refinement at poor resolution? It is hard to do nowadays because of all the safety catches in modern software, but you can get great R factors this way. A telltale sign of this kind of "over fitting" is remarkably large Fcalc values beyond the resolution cutoff. These don't contribute to the R factor, however, because Fobs is missing for these hkls. So, including zero-intensity data suppresses at least some types of over-fitting. The thing I like most about the zero-information resolution cutoff is that it forces us to address the real problem: what do you mean by "resolution" ? Not long ago, claiming your resolution was 3.0 A meant that after discarding all spots with individual I/sigI < 3 you still have 80% completeness in the 3.0 A bin. Now we are saying we have a 3.0 A data set when we can prove statistically that a few non-background counts fell into the sum of all spot areas at 3.0 A. These are not the same thing. Don't get me wrong, including the weak high-resolution information makes the model better, and indeed I am even advocating including all the noisy zeroes. However, weak data at 3.0 A is never going to be as good as having strong data at 3.0 A. So, how do we decide? I personally think that the resolution assigned to the PDB deposition should remain the classical I/sigI > 3 at 80% rule. This is really the only way to have meaningful comparison of resolution between very old and very new structures. One should, of course, deposit all the data, but don't claim that cut-off as your "resolution". That is just plain unfair to those who came before. Oh yeah, and I also have a session on "interpreting low-resolution maps" at the GRC this year. https://www.grc.org/diffraction-methods-in-structural-biology-conference/2020/<https://urldefense.com/v3/__https://www.grc.org/diffraction-methods-in-structural-biology-conference/2020/__;!!Eh6p8Q!TK-tIY-zm5coRu74uWMkIJkTFWNz4-1ibr1oaahxT_2BAAetUTMNdfRqUCmIqtYfhDo$> So, please, let the discussion continue! -James Holton MAD Scientist On 2/22/2020 11:06 AM, Nave, Colin (DLSLtd,RAL,LSCI) wrote: Alexis This is a very useful summary. You say you were not convinced by Marin's derivation in 2005. Are you convinced now and, if not, why? My interest in this is that the FSC with half bit thresholds have the danger of being adopted elsewhere because they are becoming standard for protein structure determination (by EM or MX). If it is used for these mature techniques it must be right! It is the adoption of the ½ bit threshold I worry about. I gave a rather weak example for MX which consisted of partial occupancy of side chains, substrates etc. For x-ray imaging a wide range of contrasts can occur and, if you want to see features with only a small contrast above the surroundings then I think the half bit threshold would be inappropriate. It would be good to see a clear message from the MX and EM communities as to why an information content threshold of ½ a bit is generally appropriate for these techniques and an acknowledgement that this threshold is technique/problem dependent. We might then progress from the bronze age to the iron age. Regards Colin From: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK><mailto:CCP4BB@JISCMAIL.AC.UK> On Behalf Of Alexis Rohou Sent: 21 February 2020 16:35 To: CCP4BB@JISCMAIL.AC.UK<mailto:CCP4BB@JISCMAIL.AC.UK> Subject: Re: [ccp4bb] [3dem] Which resolution? Hi all, For those bewildered by Marin's insistence that everyone's been messing up their stats since the bronze age, I'd like to offer what my understanding of the situation. More details in this thread from a few years ago on the exact same topic: https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003939.html<https://urldefense.com/v3/__https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003939.html__;!!Eh6p8Q!TK-tIY-zm5coRu74uWMkIJkTFWNz4-1ibr1oaahxT_2BAAetUTMNdfRqUCmIsJF61uc$> https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html<https://urldefense.com/v3/__https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html__;!!Eh6p8Q!TK-tIY-zm5coRu74uWMkIJkTFWNz4-1ibr1oaahxT_2BAAetUTMNdfRqUCmIPu-nRBo$> Notwithstanding notational problems (e.g. strict equations as opposed to approximation symbols, or omission of symbols to denote estimation), I believe Frank & Al-Ali and "descendent" papers (e.g. appendix of Rosenthal & Henderson 2003) are fine. The cross terms that Marin is agitated about indeed do in fact have an expectation value of 0.0 (in the ensemble; if the experiment were performed an infinite number of times with different realizations of noise). I don't believe Pawel or Jose Maria or any of the other authors really believe that the cross-terms are orthogonal. When N (the number of independent Fouier voxels in a shell) is large enough, mean(Signal x Noise) ~ 0.0 is only an approximation, but a pretty good one, even for a single FSC experiment. This is why, in my book, derivations that depend on Frank & Al-Ali are OK, under the strict assumption that N is large. Numerically, this becomes apparent when Marin's half-bit criterion is plotted - asymptotically it has the same behavior as a constant threshold. So, is Marin wrong to worry about this? No, I don't think so. There are indeed cases where the assumption of large N is broken. And under those circumstances, any fixed threshold (0.143, 0.5, whatever) is dangerous. This is illustrated in figures of van Heel & Schatz (2005). Small boxes, high-symmetry, small objects in large boxes, and a number of other conditions can make fixed thresholds dangerous. It would indeed be better to use a non-fixed threshold. So why am I not using the 1/2-bit criterion in my own work? While numerically it behaves well at most resolution ranges, I was not convinced by Marin's derivation in 2005. Philosophically though, I think he's right - we should aim for FSC thresholds that are more robust to the kinds of edge cases mentioned above. It would be the right thing to do. Hope this helps, Alexis On Sun, Feb 16, 2020 at 9:00 AM Penczek, Pawel A <pawel.a.penc...@uth.tmc.edu<mailto:pawel.a.penc...@uth.tmc.edu>> wrote: Marin, The statistics in 2010 review is fine. You may disagree with assumptions, but I can assure you the “statistics” (as you call it) is fine. Careful reading of the paper would reveal to you this much. Regards, Pawel On Feb 16, 2020, at 10:38 AM, Marin van Heel <marin.vanh...@googlemail.com<mailto:marin.vanh...@googlemail.com>> wrote: **** EXTERNAL EMAIL **** Dear Pawel and All others .... 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...). Sorry Marin On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A <pawel.a.penc...@uth.tmc.edu<mailto:pawel.a.penc...@uth.tmc.edu>> wrote: Dear Teige, I am wondering whether you are familiar with Resolution measures in molecular electron microscopy. Penczek PA. Methods Enzymol. 2010. Citation Methods Enzymol. 2010;482:73-100. doi: 10.1016/S0076-6879(10)82003-8. You will find there answers to all questions you asked and much more. 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