[3dem] [ccp4bb] FW: [ccp4bb] Which resolution?

[Marin van Heel]

Dear Colin

Great that you mention the Rose equation and its consequences for cryo-EM!
I have actually written a paper on that topic some 40 years ago [Marin van
Heel: Detection of object in quantum-noise limited images. Ultramicroscopy
8 (1982) 331-342].  I honestly have not thought about it for a long time
but I have recently been thinking about revisiting the topic. It remains
one of the very first particle-picking papers ever, and certainly still one
of the very best (and reference free) ones [Afanasyev 2017].

I remember I was very pleased when I realised one could calculate local
variances rapidly using fast convolutions! I remember the very moment in
December 1979, while visiting my parents in their house in Spain and
catching a bit of winter sunshine, leaning against the wall of their house
with my eyes half closed, that the “Aha-Erlebnis” struck.  Thank you for
reminding me to go back to that issue!

Cheers

Marin

On Mon, Feb 17, 2020 at 2:36 PM colin.nave at diamond.ac.uk <
colin.nave at diamond.ac.uk> wrote:

>
>
> Dear Marin
>
> For electron microscopy, the Rose criterion (a measure of contrast/noise)
> is sometime used to distinguish low contrast features within polymers (see
> for example Libera, M. & Egerton, R. (2010). *Polymer Reviews*. *50*,
> 321-339.). A particular value of the Rose criterion implies a particular
> information content.
>
> I think this can be directly related to a particular threshold for FSC or
> FRC. If you can comment on this in your *Why-o-Why didactical crusade, I
> might even register for a twitter account!*
>
> *Regards*
>
> *Colin*
>
>
>
> *From:* CCP4 bulletin board <CCP4BB at JISCMAIL.AC.UK> *On Behalf Of *Marin
> van Heel
> *Sent:* 17 February 2020 13:29
> *To:* CCP4BB at JISCMAIL.AC.UK
> *Subject:* Re: [ccp4bb] [3dem] Which resolution?
>
>
>
>
>
>
>
> Dear Petrus Zwart (and all other X-ray crystallographers and EM-ers)
>
>
>
> Resolution in the sense of the Abbe Diffraction Limit or the Rayleigh *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].  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)·O(f)}. *
>
>
>
> *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)!   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…     *
>
>
>
> *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 *some
> hydrogen bond length in a cryo-EM density. The FRC/FSC actually make more
> sense than the indirect and hybrid X-ray ones.  *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! *
>
>
>
> *I guess I cannot yet terminate my #Why-o-Why didactical crusade:  I will
> need at least one more on just this linear-transfer theory issue alone…*
>
>
>
> *Marin van Heel, CNPEM/LNNano, Campinas, Brazil  *
>
>
>
>
>
> On Sun, Feb 16, 2020 at 6:51 PM Petrus Zwart <phzwart at lbl.gov> wrote:
>
> Hi All,
>
>
>
> 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?
>
>
>
> 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.
>
>
>
> Regards
>
> Peter Zwart
>
>
>
>
>
>
>
> On Sun, Feb 16, 2020 at 8:38 AM Marin van Heel <
> 0000057a89ab08a1-dmarc-request at jiscmail.ac.uk> wrote:
>
> 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.Penczek at 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.
>
>
>
> Regards,
>
> Pawel Penczek
>
>
>
> Regards,
>
> Pawel
>
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> --
>
> ------------------------------------------------------------------------
> P.H. Zwart
> Staff Scientist
>
> Molecular Biophysics and Integrated Bioimaging &
>
> Center for Advanced Mathematics for Energy Research Applications
>
> Lawrence Berkeley National Laboratories
> 1 Cyclotron Road, Berkeley, CA-94703, USA
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