[3dem] [ccpem] Which resolution?

Thu Feb 13 06:55:40 PST 2020

Dear Teige,

Many questions at once!  This requires a salami-slice piece-wise response,
which is why I had started my #WhyOWhy series to clarify such topics
separately!
The issue of the Abbe resolution criterion that some people believe is the
non-plus-ultra in resolution assessment
(because-they-learned-that-in-school), is discussed in my tweet #WhyOWhy
#10 (@marin_van_heel): The Instrumental versus the Results Resolution. The
Abbe resolution is the instrumental resolution that you can only achieve if
you: a) dont forget to switch on the illumination, and you....  (see:
#WhyOWhy #10 ).

More later (if time permits)

Two more cents by

Marin

<https://twitter.com/hashtag/WhyOWhy?src=hash>

On Thu, Feb 13, 2020 at 8:12 AM Matthews-Palmer, Teige <
t.matthews-palmer14 at imperial.ac.uk> wrote:

> Dear All,
> To Daniel’s comment that we want something like an Abbe criterion - well
> we have a point resolution for the microscope itself, but it’s so high, and
> the SNR of our single images is so low that it’s irrelevant in the
> reconstructions - the sampling rate (Nyquist) is more relevant. Can there
> be an Abbe-like point resolution for the reconstruction…? Others have
> pointed out the sampling rate, filtering and sharpening change how the map
> looks. Does low-pass filtering the map at a very conservative resolution,
> and over-sampling to have lots of map voxels, give you something like a
> point-resolution in your map? :-/
>
> To Marin & others, could you critique my understanding of why we even use
> FSC to talk about ‘resolution’ in 3DEM? (No worries if not.)
>
> It seems to me that we want to estimate the ‘resolution limit’ in this
> figure from Rosenthal & Henderson 2003.
> Can anyone precisely define what this ‘resolution’ limit is?
> Intuitively, it’s the spatial frequency in our reconstruction where the
> [signal from scattering of the beam by our molecule / structure factors of
> our molecule] meets the amplitude of the noise in the reconstruction.
> But I don’t think I understand it in a way that precisely relates to our
> methods.
>
> I figure we use FSC between half-maps to estimate something like that
> ‘resolution limit’ - using a threshold as a marker of where we
> have confidence to claim that up to this spatial frequency, our (FT) map's
> amplitudes and phases [reflect/describe/are determined by] the scattering
> of the electron beam by the molecule.
> I.e. the FSC threshold is our estimate of where the half-map correlation
> significantly exceeds what can be expected for noise, and therefore we
> claim it’s due to common structure factors really existing in the molecule.
> (Assuming the half-maps don’t have correlated noise thanks to
> gold-standard reconstruction and phase-randomisation check)
> *P.S. Am I oversimplifying if I say that we claim the map features are
> totally due to the molecule’s electron scattering up to the resolution
> limit? After all we filter our maps to the threshold res and then boost the
> amplitudes (sharpen the map). Does the ‘reliability’/relationship of the
> resulting map's features to the molecule’s structure factors trail off
> gradually in the range where amplitudes have been boosted? I was thinking
> as if it doesn’t.*
>
> How to determine where we are confident the map is determined by the
> molecule’s scattering?
> Marin’s sigma-factor curves? Van Heel 1987
> https://doi.org/10.1016/0304-3991(87)90010-6
> *"A rough significance threshold value of two standard deviations
> above the expected random background is normally used in this application.
> This threshold value has no absolute validity, but rather serves to compare
> the quality of the results of similar experiments”*
>
> Marin’s half-bit threshold? Van Heel & Schatz 2005
> https://doi.org/10.1016/j.jsb.2005.05.009
> It seems fair to say that the half-bit criterion is calibrated to a 0.5
> figure of merit (like the 0.143 threshold but properly accounting for the
> number of voxels).
> *"Whereas σ-factor curves indicate the resolution level at which one has
> collected information significantly above the noise level, the information
> curves indicate the resolution level at which enough information has
> been collected for interpretation.”*
>
> Shouldn’t, ideally, the questions of "whether information is significantly
> above the noise level", or "is enough for interpretation” be the exact same
> question? What’s so great about that 0.5FOM calibration?
> Presumably because we have so much prior information about the chemical
> structure of proteins, EM maps at high resolution could be judged for their
> ‘interpretability’ against what we expect of proteins. I haven’t read about
> the Q-score yet, is it better than 0.5FOM?
> If we completely ignore prior information about what proteins look like -
> what does the ‘interpretability' of an EM map mean? Surely that would have
> to involve distinguishing ‘signal’ from ‘noise’ without relating it to
> 0.5FOM, i.e. a sigma factor FSC threshold.
>
> I guess my questions are:
> - Is the 0.5FOM calibration the only or best thing linking the ‘resolution
> limit’ concept from attached figure to the half-map FSC?
> - Is the ‘resolution limit’ something useful in relation to our
> experimental methods, anyway?
> - Imagine an EM map with uniform resolution (haha..) Would placing a sharp
> FSC threshold at the ‘resolution limit’ and fourier filtering there
> perfectly separate map features arising from the molecule’s electron
> scattering, from noise? Or do the structure factors get smeared in to the
> noise gradually across fourier shells and does that screw up the map
> features?
>
> Thanks & all the best,
> Teige
>
>
> [image: page39image1280]
>
>
> On 13 Feb 2020, at 16:45, Tim Gruene <tim.gruene at univie.ac.at> wrote:
>
>
> *******************
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> Hi Marin,
>
> crystallography has long moved away from the term 'resolution', see e.g.
> https://www.cell.com/structure/fulltext/S0969-2126(18)30138-2. It is
> merely a
> ballpark number, and it is good to know whether crystallographic data were
> cut
> at 1, 2, or 3 Angstrom, but not very important.
>
> What counts is the interpretation of the model and conclusion that can be
> drawn on the system under study. It requires a broader understanding of
> crystallography in order to understand whether the conclusions are
> justified.
> Resolution plays only a minor role in this. It is more useful to take a
> look
> at the crystallographic map itself in order to understand.
>
> EM is totally different from crystallography, and why would one mix
> concepts
> between the fields?
>
> Best,
> Tim
>
> On Thursday, February 13, 2020 12:07:15 AM CET Marin van Heel wrote:
>
> Hi Tim,
> Good to hear from you!  No longer at PSI??
> See... You are already touching upon one of the logical breaking points in
> the resolutiton story...!  X-ray crystallography resolution criteria like
> R-factors make absolutely no sense outside the field of crystallography and
> of structural biology.  It is the result of a hybrid iterative optimisation
> process between the phases of a model structure and the measured amplitudes
> of a diffraction experiment!  The FRC/FSC resolution criteria, in contrast,
> are universal quality metrics not at all coupled to Cryo-EM or structural
> biology.  Using structural biology arguments like how well I see an alpha
> helix or how well I see the hole in an aromatic ring as an assessment
> criterion of whether a metric is good or not is a waste of time!  (Moreover
> filtering a map can completley change its appearance without changing its
> information contents). Even some my own (ex-)students and (ex-)postdocs
> sometimes completely miss this fundamental point. The FRC and FSC criteria
> are now used as quality metrics in all walks of image science like X-ray
> tomography and super-resolution light microscopy, fields of science where
> atomic coordinates of proteins are not an issue. The FRC / FSC functions
> are universal and very direct metrics that compare both the amplitudes and
> the phases of two independent measurements of images or 3D-densities of the
> same object. For more details, see the 2017 bioRxiv paper and references
> therein (https://www.biorxiv.org/content/10.1101/224402v1) and check my
> #WhyOWhy tweets (@marin_van_heel). See also: van Heel - Unveiling ribosomal
> structures: the final phases - Current opinion in structural biology 10
> (2000) 259-264.
>
> Cheers,
> Marin
>
> On Wed, Feb 12, 2020 at 11:22 AM Tim Gruene <tim.gruene at univie.ac.at>
> wrote:
>
> Dear Marin,
>
> I did not read the enire thread, nor the manuscript you point at -
> apologize
> in case this has been discussed before.
>
> What about a practical approach to determine the resolution of a cryoEM
> map:
> one could take a feature with scales of interest, e.g. an alpha-helix, and
> shift and/or rotate it in steps of, say, 0.3A in several directions to
> see, at
> which magnitude (degree / distance) refinement does not take the helix
> back to
> its original position (within error margins).
>
> One could also take a Monte-Carlo approach and do an arbitrary number of
> random re-orientations of such a helix, refine, and calculate the
> variation in
> position and rotation.
>
> This would reflect my understanding of resolution, much more than any
> statistical descriptor.
>
> Best regards,
> Tim
>
> On Wednesday, February 12, 2020 1:46:48 PM CET Marin van Heel wrote:
>
> Hi Laurence,
>
> One thing is certain: the 0.143 threshold is RUBBISH and all CC50 etc
> are
> also based on the same SLOPPY STATISTICS  as are all  fixed-valued  FSC
> thresholds. This controversy has been ragings for a long long time and
>
>
> the
>
> errors made were extensively described (again) in our most recent paper
> (Van Heel & Schatz 2017 BioRxiv:
> https://www.biorxiv.org/content/10.1101/224402v1) which has been
>
>
> downloaded
>
> more than 3000 times. Further papers on the issue are in the pipeline.
>
>
> The
>
> math BLUNDER behind this controversy is simple:  the inner product
>
>
> between
>
> a signal vector and a noise vector is NOT zero (but rather proportional
>
>
> to
>
> SQRT(N) where N is the length of the vectors) and cannot be left out of
>
>
> the
>
> equations. This error goes back to a paper published in Nature in 1975
>
>
> and
>
> has since been repeated frequently, including in the first paper
>
>
> promoting
>
> the erroneous 0.143 FSC threshold. The consequences of this blunder in
> current processing are serious especially when these erroneous metrics
>
>
> are
>
> used as an optimisation criterion in iterative refinements at
> resolutions
> close to Nyquist.  I get tired of facing this systematic misuse of the
>
>
> FSC
>
> function, which I myself have introduced into the literature in
>
>
> 1982/1986,
>
> and people nevertheless feel they know better (with no scientific
>
>
> arguments
>
> to support!) and they feel justified to use it beyond its definition
>
>
> range,
>
> and to continue to ignore the correct math. To counter this systematic
> abuse of my brain child - over decades - I feel the need to use CLEAR
> LANGUAGE!
> Have fun!
> Marin
>
>
> --
> --
> Tim Gruene
> Head of the Centre for X-ray Structure Analysis
> Faculty of Chemistry
> University of Vienna
>
> Phone: +43-1-4277-70202
>
> GPG Key ID = A46BEE1A
>
>
> --
> --
> Tim Gruene
> Head of the Centre for X-ray Structure Analysis
> Faculty of Chemistry
> University of Vienna
>
> Phone: +43-1-4277-70202
>
> GPG Key ID = A46BEE1A
>
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