[3dem] [ccp4bb] Which resolution?

Mon Feb 17 05:29:02 PST 2020

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
>>> _______________________________________________
>>> 3dem mailing list
>>> 3dem at ncmir.ucsd.edu
>>> https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem
>>>
>>
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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
> Cell: 510 289 9246
>
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