[3dem] [ccpem] Differences EM CP maps vs Xray ED Maps
Benjamin Himes
himes.benjamin at gmail.com
Sat Oct 21 05:53:35 PDT 2023
Well, if Joachim is adding only 1c, I guess I will perhaps add some crypto
coin*
One distinction to start with: the amplitude contrast from scattering
outside the aperture is distinct from the amplitude contrast generated by
using an energy filter, as Rasmus mentions. The latter leads to an even
more convoluted discussion, and here, I will only refer to aperture
contrast.
I agree with Joachim that a per-element consideration for amplitude
contrast is required to consider the topic seriously. We began to explore
this in “*cryo-TEM simulations of amorphous radiation-sensitive samples
using multislice wave propagation, Himes & Grigorieff 2021.” *A more
accurate description of this contrast would almost certainly improve
techniques that only require an accurate *forward model*, such as template
matching.
How exactly to handle such information is not so clear for techniques that
require a solution to the inverse problem, e.g., cryoEM reconstructions.
That is to say, I believe one reason the additional phase shift (or cosine
term) for the CTF was adopted is it is the only way, ad hoc as it may be,
to account for amplitude contrast in *linear *image formation. It would be
fine if we found some way to include the quadratic terms in how we relate
the Fourier Transform of the experimental image and the Fourier Transform
of the object. This was not at all lost on the author’s Marin mentions.
However, as is often the case, the neat biological paper (1971 paper Marin
calls out) was prioritized in publication, while the nuanced theory paper
(1973 *“The Fourier Transform of an Electron Micrograph – First Order and
Second Order theory of Image Formation”) *received little attention***. *In
this paper, Harold shows nicely how second-order (quadratic) terms in the
expansion give rise to aperture-based amplitude contrast***.
I’m unsure precisely what Marin means by “*In reality, however, the
amplitude contrast and phase contrast two separate properties of the
complex transmission function of the object, and these are associated with
different physical properties*.” There is no special magic here; the
amplitude contrast (from the aperture losses) is produced by the same
phase-object via elastic scattering as the phase contrast. As with many
confusing theoretical issues, it is not nature that is confused; it is our
math.
While the discussion on the proper application of amplitude contrast is
quite interesting, I’m not sure it gets to the heart of Bernhard’s original
question. To paraphrase, “Should one be able to use standard deviations of
voxel values to compare different maps?” I’m not sure it should. Consider
just the ability to compare two cryoEM maps at a standard isosurface
threshold:
Let’s imagine we’ve sorted out CTF issues and other errors in the inverse
image reconstruction problem, so we’ve got a “perfect” reconstructed 3D.
What do you expect if you now imagine gradually decreasing the voxel
sampling (larger pixel size)? The value in each voxel will tend toward the
average value of the map, and you will have an approximately uniform
distribution of voxel values. What about the opposite case with finer
sampling up until we have on average one atom/voxel? Would the distribution
then be Gaussian? Probably not. Would it be comparable between, say a
Ribosome (RNA + protein) and Apoferritin (protein)? Almost certainly not as
the distribution of atom types; hence, the potential well “seen” by the
imaging electrons would not be similar. So, variable sampling rate is one
(of several) things that may confound direct comparison of maps of even the
same molecule. Even normalizing for this, there is no apparent reason I can
see why the distribution should be the same between different molecules, or
Gaussian for any.
*0 cents, eh?
* ***I had to email H.P. Erickson years ago to get a copy. If would like a
copy, feel free to email me.
*****Quadratic terms are a minimum. In a full forward simulation, there is
no approximation via power-series expansion and *all* terms are included in
the calculations.
cheers,
ben
On Wed, Oct 18, 2023 at 12:12 PM <3dem-request at ncmir.ucsd.edu> wrote:
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> 1. Re: [ccpem] Differences EM CP maps vs Xray ED Maps
> (Schroeder, Rasmus)
> 2. Re: [EXTERNAL] Re: [ccpem] Differences EM CP maps vs Xray ED
> Maps (Frank, Joachim)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 18 Oct 2023 11:00:32 +0200
> From: "Schroeder, Rasmus"
> <rasmus.schroeder at bioquant.uni-heidelberg.de>
> To: Marin van Heel <marin.vanheel at googlemail.com>
> Cc: 3dem <3dem at ncmir.ucsd.edu>, CCPEM at jiscmail.ac.uk
> Subject: Re: [3dem] [ccpem] Differences EM CP maps vs Xray ED Maps
> Message-ID:
> <FE068B80-64AC-40BC-AE88-2E2CB08E5B10 at bioquant.uni-heidelberg.de>
> Content-Type: text/plain; charset="utf-8"
>
> Dear Marin - and all others here,
>
> I would not be so harsh with that paper from 1971, there is always a
> certain level of experimental data, and - as far as I understand it - at
> that time and resolution level obtainable it looked as if amplitude and
> phase potentials could be identical.
>
> As you point out correctly, this is not the case, and I may add a study we
> did many, many years ago looking into the CTF for an energy filtered TEM
> (Angert et al., Ultramicroscopy 81 (2000) 203-222).
> Here a correct CTF needs to include yet another cos-term ?.. and the zeros
> in the experimental and theoretical CTF only fit, if an additional
> cos-contrast (amplitude contrast produced by the energy filter) is added ?
> (And yes, I apologize for the quality of the data, but it was the best we
> managed to get with that very old hardware at that time ?)
>
> And I may add a bit of relief to all here: Do not get too excited that
> nobody uses this additional cos-term at present. The explanation is simple:
> Nobody cares for the extra bit of very low resolution data when fitting a
> CTF going out to better than a few Angstroms ?.. But the problem with the
> density and the phase at ?zero? remains ?.
>
> My 2 cent ?.
>
> Best,
>
> Rasmus
>
>
> > On 15. Oct 2023, at 22:22, Marin van Heel <marin.vanheel at googlemail.com>
> wrote:
> >
> >
> > Dear All,
> >
> > Unfortunately, a fundamental mistake has been made in the much-cited
> paper by Erickson and Klug [Erickson & Klug 1971] more than 50 years ago.
> They assumed that the EM amplitude contrast of the (stained ) biological
> object to be proportional to the phase contrast of the same object over all
> spatial frequencies. If that were indeed the case, one single transfer
> function would suffice to describe how the linear imaging device would
> generate an output image. In reality, however, the amplitude contrast and
> phase contrast two separate properties of the complex transmission function
> of the object, and these are associated with different physical properties
> [Van Heel 1978] . The problem is that that proportionality error has crept
> into almost all popular CTF determination programs where, say, 10% or 15%
> amplitude contrast is suggested ab initio. Any percentage of amplitude
> contrast erroneously causes the average density of the cryo-EM 3D
> reconstruction to deviate from zero. Any phase-con
> trast image must yield a zero average as it should be for any phase
> contrast image where what is measured is the difference in phase between
> any point in the back focal plane of the system with respect to the phase
> at the origin! That thus means that the phase at the origin must be zero.
> (Zero being the average density over the image around which the phase
> information is modulated) . Adding a cosine component to the CTF (a sine)
> will shift the zeroes of the CTF and therewith shift the defocus values
> found in most programs (no longer the real defocus!). That makes such
> results no longer comparable to each other and will also complicate any
> comparison with zero-average density maps in X-ray crystallography.
> >
> > Two more cents added!
> >
> > Marin
> >
> > Erickson HP, Klug A (1971). Measurement and Compensation of Defocusing
> and Aberrations by Fourier Processing of Electron Micrographs. Phil. Trans.
> R. Soc. Lond. B. 261; 105-118.
> >
> > van Heel, M. (1978). On the imaging of relatively strong objects in
> partially coherent illumination in optics and electron optics. Optik. 49,
> 389?408.
> >
> > https://mail.ncmir.ucsd.edu/pipermail/3dem/2014-July/003454.html
> >
> >
> >
> > On Sun, Oct 15, 2023 at 10:01?AM Guillaume Gaullier <
> guillaume.gaullier at kemi.uu.se <mailto:guillaume.gaullier at kemi.uu.se>>
> wrote:
> >> Hello Bernhard,
> >>
> >> According to PDB/EMDB validation reports, this spike in the voxel
> values histogram is caused by masking. One validation report I have says "A
> spike in this graph at zero usually indicates that the volume has been
> masked". You can probably also find this note in validation reports of
> released PDB/EMDB entries.
> >>
> >> Opening a map from 3D refinement and one of the two half-maps from the
> same job seems to confirm this. The map?s histogram shows this spike at
> zero, but the half-map?s histogram doesn?t. Half-maps are never filtered
> nor masked, whereas the main map is masked (in cryoSPARC this is done by
> default, unless one turns off automatic masking and doesn?t provide any
> mask). See the attached histograms.
> >>
> >> The fact that there is no absolute scale for contour level in cryoEM
> maps is indeed annoying (I would like to compare maps without worrying that
> maybe I chose inadequate contour levels). My understanding is that it is
> caused at least in part by the fact that the size of the box enclosing the
> particle is arbitrary. Different amounts of low-value voxels between
> different maps give them different voxel value histograms, therefore
> choosing a contour level in terms of a certain number of standard
> deviations above the mean produces different results with different maps.
> Electron density maps from crystallography don?t have this variability
> because the box always spans a full unit cell, without this variable
> padding around the region of high density.
> >> At least this is how I understand Tom Goddard?s explanation in this
> discussion from last month on the chimerax-users list:
> https://urldefense.com/v3/__https://mail.cgl.ucsf.edu/mailman/archives/list/chimerax-users@cgl.ucsf.edu/thread/3RNL6ODNP6QAL3BTHIPPQS2VE2B2YSVO/__;!!Mih3wA!F167aMQKY0npO0mDM2XnYUJMsI5KHiM2qByj0oICNWHtqYI1ub4ZRnTZOBwdK6UPjLGFDKL4R9ffbkAWKNY1BDEpbgUKIZYrTBIUZbKBW_r9pOE$
> <
> https://urldefense.com/v3/__https://mail.cgl.ucsf.edu/mailman/archives/list/chimerax-users@cgl.ucsf.edu/thread/3RNL6ODNP6QAL3BTHIPPQS2VE2B2YSVO/__;!!Mih3wA!BGIjNxSHKX_ICKU_6CFanyPV1Mdi8YchWr8HV5aQnLt4dvOJSmWTZyuazSRj4rRmTlL8O2gx5mA3rFLt4AbnqbMPdEMJ_w$
> >
> >> Maybe there are other reasons adding to this.
> >>
> >> I hope this helps.
> >> Cheers,
> >>
> >> Guillaume
> >>
> >>
> >>> On 15 Oct 2023, at 13:05, <Nonameavailable> <br at RUPPWEB.ORG <mailto:
> br at RUPPWEB.ORG>> wrote:
> >>>
> >>> Dear EM Experts,
> >>>
> >>> Some of my crystallographer colleagues and I wonder about the
> fundamentally different appearance of density histograms in EM Coulomb
> potential maps vs the X-ray Electron density maps. Here is the question:
> >>>
> >>> ?What I've noticed is that they are on different scales. That is
> understandable, a e/A^3 is different than V. But there are papers showing
> that these values are somewhat proportional to each other for lower
> resolutions. But the other thing that I have noticed is that electron
> density maps have close to normally distributed value distributions,
> whereas cryoEM maps have a sharp spike and a very long tail. As a result,
> an electron density blob in an X-ray map looks nice somewhere around
> 3sigma, whereas for cryoEM it's sometime 10sigma, 17sigma, 20sigma, all
> over the place. I'm thinking of using thresholds based on percentiles
> rather than sigmas, but my main question is: shouldn't the values on cryoEM
> maps be also approximately normally distributed? what is the cause of this
> non-normality? sharpening? the raw experimental data themselves??
> >>>
> >>> And here a potential partial answer:
> >>>
> >>> ?In cryo-EM, there is no absolute scaling, which means that density
> values can vary significantly. This variability can explain why you
> consistently encounter different sigma values. I can confirm that the
> density value distribution behaves as you described, and I have also
> observed this. However, I cannot provide a definitive answer as to why this
> occurs. My best guess is that it may be related to B factor weighting in
> motion correction, but I cannot provide a conclusive explanation, I'm
> afraid.?
> >>>
> >>> What are we missing here?
> >>>
> >>> Thx, BR
> >>>
> >>> -----------------------------------------------------------------
> >>> Bernhard Rupp (Hofkristallrat a. D)
> >>> K.k. Hofkristallamt
> >>> CA 92084 San Diego
> >>> 001 (925) 209-7429
> >>> +43 (676) 571-0536
> >>> br at ruppweb.org <mailto:br at ruppweb.org>
> >>> hofkristallamt at gmail.com <mailto:hofkristallamt at gmail.com>
> >>>
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>
> >>> -----------------------------------------------------------------
> >>> All models are wrong but some are useful
> >>> -----------------------------------------------------------------
> >>>
> >>>
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> >> <Screenshot 2023-10-15 at 14.22.31.png>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
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> --
> ############################################################
>
> Rasmus R. Schroeder
>
> Cryo Electron Microscopy
> Heidelberg University / Medical Faculty
> BioQuant, Im Neuenheimer Feld 267
> 69120 Heidelberg, Germany
>
> Tel. +49-(0)6221-5451350
> e-mail rasmus.schroeder at bioquant.uni-heidelberg.de
>
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> ------------------------------
>
> Message: 2
> Date: Wed, 18 Oct 2023 16:11:41 +0000
> From: "Frank, Joachim" <jf2192 at cumc.columbia.edu>
> To: "Schroeder, Rasmus" <rasmus.schroeder at bioquant.uni-heidelberg.de>,
> Marin van Heel <marin.vanheel at googlemail.com>
> Cc: 3dem <3dem at ncmir.ucsd.edu>, "CCPEM at jiscmail.ac.uk"
> <CCPEM at jiscmail.ac.uk>
> Subject: Re: [3dem] [EXTERNAL] Re: [ccpem] Differences EM CP maps vs
> Xray ED Maps
> Message-ID:
> <
> SA3PR02MB932735E3C16CCEED814C104780D5A at SA3PR02MB9327.namprd02.prod.outlook.com
> >
>
> Content-Type: text/plain; charset="utf-8"
>
>
> Hi Rasmus,
>
> I?m in agreement with Marin about the necessity of using a correct
> element-specific spectral distribution of the amplitude contrast. But
> blaming a single paper is as you say unfair; the problem is rather the
> uncritical adoption of an initial oversimplification by the users. There
> have been plenty of misjudgments like that.
>
> Related to amplitude contrast, see my proof-of-concept paper on
> heavy/light atom discrimination using Peter Schiske?s method in Biophys. J.
> (1972), and a later paper with Pawel Penczek (Frank and Penczek, Optik
> 1995) where we tried to use Schiske?s algorithm on the cryo-EM ribosome
> dataset collected in Heidelberg. The funny thing was, the L1 stalk lit up
> in the amplitude contrast image, so we thought something must have gone
> wrong since, to our knowledge then, the L1 stalk was all protein and not,
> as we know now, part protein and part RNA.
>
> my 1c,
>
> --Joachim
>
> Dr. Joachim Frank
> Professor, Biochemistry and Molecular Biophysics & Biological Sciences,
> Columbia University Irving Medical Center,
> Hammer Health Sciences Center, Room 616,
> 701 West 168th Street, New York, NY 10032 -- jf2192 at cumc.columbia.edu
> <mailto:jf2192 at cumc.columbia.edu>
> 2017 Nobel Prize in Chemistry
> Admin. Coordinator: Masgan Saidi 917 232 6545 ms4597 at cumc.columbia.edu
> <mailto:ms4597 at cumc.columbia.edu>
> Science:
> https://urldefense.com/v3/__https://joachimfranklab.org__;!!Mih3wA!Bg_Dt6-kIGGiCCVVKZc1MojKob6HpUPWS1D4XotzwDkNbu_UXbEJZDgQ8OD7NLiLt9z8iFlcSC1ells-0Xn8ptPLhg$
> <
> https://urldefense.proofpoint.com/v2/url?u=https-3A__joachimfranklab.org&d=DwMFAw&c=G2MiLlal7SXE3PeSnG8W6_JBU6FcdVjSsBSbw6gcR0U&r=WMEZpdnKefeJBKIRE4HFMD03dG6F5_6w7sRzzvkLMXQ&m=TYKF4If_gfUQerpbfW2d6Wtduj37ZOB7qemjTwlcxFU&s=imQWuSOK3f7uZgiFTjoAp76cDLVvhB8UwOJ3lnX6618&e=>
> -- Fiction: franxfiction.com
>
>
>
> From: 3dem <3dem-bounces at ncmir.ucsd.edu> on behalf of Schroeder, Rasmus <
> rasmus.schroeder at bioquant.uni-heidelberg.de>
> Date: Wednesday, October 18, 2023 at 5:02 AM
> To: Marin van Heel <marin.vanheel at googlemail.com>
> Cc: 3dem <3dem at ncmir.ucsd.edu>, CCPEM at jiscmail.ac.uk <CCPEM at jiscmail.ac.uk
> >
> Subject: [EXTERNAL] Re: [3dem] [ccpem] Differences EM CP maps vs Xray ED
> Maps
> Dear Marin - and all others here,
>
> I would not be so harsh with that paper from 1971, there is always a
> certain level of experimental data, and - as far as I understand it - at
> that time and resolution level obtainable it looked as if amplitude and
> phase potentials could be identical.
>
> As you point out correctly, this is not the case, and I may add a study we
> did many, many years ago looking into the CTF for an energy filtered TEM
> (Angert et al., Ultramicroscopy 81 (2000) 203-222).
> Here a correct CTF needs to include yet another cos-term ?.. and the zeros
> in the experimental and theoretical CTF only fit, if an additional
> cos-contrast (amplitude contrast produced by the energy filter) is added ?
> (And yes, I apologize for the quality of the data, but it was the best we
> managed to get with that very old hardware at that time ?)
>
> And I may add a bit of relief to all here: Do not get too excited that
> nobody uses this additional cos-term at present. The explanation is simple:
> Nobody cares for the extra bit of very low resolution data when fitting a
> CTF going out to better than a few Angstroms ?.. But the problem with the
> density and the phase at ?zero? remains ?.
>
> My 2 cent ?.
>
> Best,
>
> Rasmus
>
>
>
> On 15. Oct 2023, at 22:22, Marin van Heel <marin.vanheel at googlemail.com>
> wrote:
>
>
> Dear All,
> Unfortunately, a fundamental mistake has been made in the much-cited paper
> by Erickson and Klug [Erickson & Klug 1971] more than 50 years ago. They
> assumed that the EM amplitude contrast of the (stained ) biological object
> to be proportional to the phase contrast of the same object over all
> spatial frequencies. If that were indeed the case, one single transfer
> function would suffice to describe how the linear imaging device would
> generate an output image. In reality, however, the amplitude contrast and
> phase contrast two separate properties of the complex transmission function
> of the object, and these are associated with different physical properties
> [Van Heel 1978] . The problem is that that proportionality error has crept
> into almost all popular CTF determination programs where, say, 10% or 15%
> amplitude contrast is suggested ab initio. Any percentage of amplitude
> contrast erroneously causes the average density of the cryo-EM 3D
> reconstruction to deviate from zero. Any phase-contr
> ast image must yield a zero average as it should be for any phase
> contrast image where what is measured is the difference in phase between
> any point in the back focal plane of the system with respect to the phase
> at the origin! That thus means that the phase at the origin must be zero.
> (Zero being the average density over the image around which the phase
> information is modulated) . Adding a cosine component to the CTF (a sine)
> will shift the zeroes of the CTF and therewith shift the defocus values
> found in most programs (no longer the real defocus!). That makes such
> results no longer comparable to each other and will also complicate any
> comparison with zero-average density maps in X-ray crystallography.
> Two more cents added!
> Marin
> Erickson HP, Klug A (1971). Measurement and Compensation of Defocusing and
> Aberrations by Fourier Processing of Electron Micrographs. Phil. Trans. R.
> Soc. Lond. B. 261; 105-118.
> van Heel, M. (1978). On the imaging of relatively strong objects in
> partially coherent illumination in optics and electron optics. Optik. 49,
> 389?408.
> https://mail.ncmir.ucsd.edu/pipermail/3dem/2014-July/003454.html<
> https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd.edu_pipermail_3dem_2014-2DJuly_003454.html&d=DwMFaQ&c=009klHSCxuh5AI1vNQzSO0KGjl4nbi2Q0M1QLJX9BeE&r=wsoQjtpZ1rSBXeWc4Du-lO_6zaO7RA_HHVekUqQDowc&m=v_q3j9BRkOXQXVB_GGY6fjq8tAIBsPrdF8yYMFHB985rPAuC2c6lyIT_OU-2tl6i&s=0L2C6HNg3dI9xHXtUcSJXvrxQifPj0IQTR59uhdQd4w&e=
> >
>
>
> On Sun, Oct 15, 2023 at 10:01?AM Guillaume Gaullier <
> guillaume.gaullier at kemi.uu.se<mailto:guillaume.gaullier at kemi.uu.se>>
> wrote:
> Hello Bernhard,
>
> According to PDB/EMDB validation reports, this spike in the voxel values
> histogram is caused by masking. One validation report I have says "A spike
> in this graph at zero usually indicates that the volume has been masked".
> You can probably also find this note in validation reports of released
> PDB/EMDB entries.
>
> Opening a map from 3D refinement and one of the two half-maps from the
> same job seems to confirm this. The map?s histogram shows this spike at
> zero, but the half-map?s histogram doesn?t. Half-maps are never filtered
> nor masked, whereas the main map is masked (in cryoSPARC this is done by
> default, unless one turns off automatic masking and doesn?t provide any
> mask). See the attached histograms.
>
> The fact that there is no absolute scale for contour level in cryoEM maps
> is indeed annoying (I would like to compare maps without worrying that
> maybe I chose inadequate contour levels). My understanding is that it is
> caused at least in part by the fact that the size of the box enclosing the
> particle is arbitrary. Different amounts of low-value voxels between
> different maps give them different voxel value histograms, therefore
> choosing a contour level in terms of a certain number of standard
> deviations above the mean produces different results with different maps.
> Electron density maps from crystallography don?t have this variability
> because the box always spans a full unit cell, without this variable
> padding around the region of high density.
> At least this is how I understand Tom Goddard?s explanation in this
> discussion from last month on the chimerax-users list:
> https://urldefense.com/v3/__https://mail.cgl.ucsf.edu/mailman/archives/list/chimerax-users@cgl.ucsf.edu/thread/3RNL6ODNP6QAL3BTHIPPQS2VE2B2YSVO/__;!!Mih3wA!Bg_Dt6-kIGGiCCVVKZc1MojKob6HpUPWS1D4XotzwDkNbu_UXbEJZDgQ8OD7NLiLt9z8iFlcSC1ells-0Xm3pfu--w$
> <
> https://urldefense.com/v3/__https:/mail.cgl.ucsf.edu/mailman/archives/list/chimerax-users@cgl.ucsf.edu/thread/3RNL6ODNP6QAL3BTHIPPQS2VE2B2YSVO/__;!!Mih3wA!BGIjNxSHKX_ICKU_6CFanyPV1Mdi8YchWr8HV5aQnLt4dvOJSmWTZyuazSRj4rRmTlL8O2gx5mA3rFLt4AbnqbMPdEMJ_w$
> >
> Maybe there are other reasons adding to this.
>
> I hope this helps.
> Cheers,
>
> Guillaume
>
>
>
> On 15 Oct 2023, at 13:05, <Nonameavailable> <br at RUPPWEB.ORG<mailto:
> br at RUPPWEB.ORG>> wrote:
>
> Dear EM Experts,
>
> Some of my crystallographer colleagues and I wonder about the
> fundamentally different appearance of density histograms in EM Coulomb
> potential maps vs the X-ray Electron density maps. Here is the question:
>
> ?What I've noticed is that they are on different scales. That is
> understandable, a e/A^3 is different than V. But there are papers showing
> that these values are somewhat proportional to each other for lower
> resolutions. But the other thing that I have noticed is that electron
> density maps have close to normally distributed value distributions,
> whereas cryoEM maps have a sharp spike and a very long tail. As a result,
> an electron density blob in an X-ray map looks nice somewhere around
> 3sigma, whereas for cryoEM it's sometime 10sigma, 17sigma, 20sigma, all
> over the place. I'm thinking of using thresholds based on percentiles
> rather than sigmas, but my main question is: shouldn't the values on cryoEM
> maps be also approximately normally distributed? what is the cause of this
> non-normality? sharpening? the raw experimental data themselves??
>
> And here a potential partial answer:
>
> ?In cryo-EM, there is no absolute scaling, which means that density values
> can vary significantly. This variability can explain why you consistently
> encounter different sigma values. I can confirm that the density value
> distribution behaves as you described, and I have also observed this.
> However, I cannot provide a definitive answer as to why this occurs. My
> best guess is that it may be related to B factor weighting in motion
> correction, but I cannot provide a conclusive explanation, I'm afraid.?
>
> What are we missing here?
>
> Thx, BR
>
> -----------------------------------------------------------------
> Bernhard Rupp (Hofkristallrat a. D)
> K.k. Hofkristallamt
> CA 92084 San Diego
> 001 (925) 209-7429
> +43 (676) 571-0536
> br at ruppweb.org<mailto:br at ruppweb.org>
> hofkristallamt at gmail.com<mailto:hofkristallamt at gmail.com>
>
> https://urldefense.com/v3/__http://www.ruppweb.org/__;!!Mih3wA!Bg_Dt6-kIGGiCCVVKZc1MojKob6HpUPWS1D4XotzwDkNbu_UXbEJZDgQ8OD7NLiLt9z8iFlcSC1ells-0XmQcgWZfQ$
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> -----------------------------------------------------------------
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> ############################################################
>
> Rasmus R. Schroeder
>
> Cryo Electron Microscopy
> Heidelberg University / Medical Faculty
> BioQuant, Im Neuenheimer Feld 267
> 69120 Heidelberg, Germany
>
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> e-mail rasmus.schroeder at bioquant.uni-heidelberg.de
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