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<p>Hi Alexis,<br>
</p>
<div class="moz-cite-prefix">El 27/08/2020 a las 7:05, Alexis Rohou
escribió:<br>
</div>
<blockquote type="cite"
cite="mid:CAM5goXQffdWAQ_5SFu1mzWLesFrVD+bO=JpJZkFPtKXX4vuSkQ@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Thank you Carlos Oscar for summarizing your work so
succinctly!
<div><br>
</div>
<div>I just would like to pick up on your concluding sentence:</div>
<div><br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">In
conclusion, from my point of view, there is not an optimal
decay valid for all proteins, but it depends on each specific
protein. And the shape of the decay is not a straight line,
but arbitrary depending on its shape.</blockquote>
<div><br class="gmail-Apple-interchange-newline">
</div>
<div>If your point of view is correct, this implies that ResLog
plots and the resulting B factors should not be compared to
each other if they were obtained from images of different
proteins. This would be quite a departure from the field's
consensus. </div>
<div><br>
</div>
</div>
</blockquote>
<p>As everything it can be taken to the extreme or not. It is true
that they are strictly not equal, but they can also be compared if
they have similar shapes (globular, rod-like, ...) and similar
molecular masses. For instance, in our paper, Fig. 1 shows the
radial profiles of 4 atomic models with a factor 4 in difference
of weight. The shape and slope are not the same, but they share
the same kind of general trend (up to 2.5A).</p>
<p>Cheers, Carlos Oscar<br>
</p>
<blockquote type="cite"
cite="mid:CAM5goXQffdWAQ_5SFu1mzWLesFrVD+bO=JpJZkFPtKXX4vuSkQ@mail.gmail.com">
<div dir="ltr">
<div>Cheers,</div>
<div>Alexis</div>
<div><br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Aug 26, 2020 at 12:32
AM Carlos Oscar Sorzano <<a href="mailto:coss@cnb.csic.es"
moz-do-not-send="true">coss@cnb.csic.es</a>> wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<p>Dear Alexis and all,</p>
<p>as a very condensed summary of what Jose Luis Vilas and
us showed in the paper you have mentioned below is that:</p>
<p>1. the Fourier spectrum of a single atom is expected to
decay in amplitude with frequency (the only way it can be
flat is that it is infinitely thin). This is well known
and comes from the electron atomic scattering factors.<br>
</p>
<p>2. the Fourier spectrum of a collection of atoms is
mostly determined by the shape of that collection, more
than on the specific nature of the atoms being involved
(we performed extremely harsh modifications to the atoms
and the decay did not change significantly).</p>
<p>3. the reasons normally argued to make the spectrum flat,
do not apply to macromolecules and the reason why B-factor
sharpening produces "nice" structures is mostly a
visualization reason (higher amplitudes at high
frequencies result in sharper edges whose isosurfaces are
easier to track and fit with an atomic model).<br>
</p>
<p>Because of 2, the decay of the radial average of the
Fourier transform of a macromolecule cannot be expected to
follow any particular shape (for instance, a straight
line) a priori, that we can estimate its slope (also a
priori) and force our 3D reconstruction to follow that
slope. In that regard the question of what is the expected
slope is ill-posed. From my point of view, the amplitude
correction is much more meaningful when performed in the
spirit of LocScale of Jakobi and Sachse. You fit an atomic
model to the map, then convert it into a map, estimate its
decay and force the map to follow this decay. In this way,
the shape of the collection of atoms (and their nature) is
explicitly taken into account. This process can be
performed iteratively (with the corrected map, you may
refine the atomic model, refine the map amplitudes again,
...). I also like the idea that this process is performed
locally.</p>
<p>If we do not want to wait for the atomic model to make
the amplitude correction, we have devised an alternative
based on the local resolution (E. Ramirez-Aportela,
J.L.Vilas, A. Glukhova, R. Melero, P. Conesa, M. Martinez,
D. Maluenda, J. Mota, A. Jimenez, J. Vargas, R. Marabini,
P.M. Sexton, J.M. Carazo, C.O.S. Sorzano. Automatic local
resolution-based sharpening of cryo-EM maps.
Bioinformatics 36: 765-772 (2020)). There is no guarantee
that it will follow the correct decay, but in practice we
have observed that it normally approximates the correct
decay quite closely (there are some examples of this in
the paper).</p>
<p>The procedure above of local correction based on local
resolution is local and it does not require an the atomic
model. If we still want to do a global correction without
an atomic model, procedures like the one of phenix (<a href="https://urldefense.com/v3/__https://journals.iucr.org/d/issues/2018/06/00/ic5102/ic5102.pdf__;!!Mih3wA!UIK1bNFdL0BCqMS1yb-nZxvkCa3QeTZ-SaBr9_hcq0N33slQIgQowiEK6VsdfdR6mw$" target="_blank" moz-do-not-send="true">https://journals.iucr.org/d/issues/2018/06/00/ic5102/ic5102.pdf</a>)
provides some clue based on the maximum continuity of the
isosurface.</p>
<p>Finally, we found that a combination of DeepRes (E.
Ramírez-Aportela, J. Mota, P. Conesa, J.M. Carazo, C.O.S.
Sorzano. DeepRes: A New Deep Learning and aspect-based
Local Resolution Method for Electron Microscopy Maps .
IUCR J 6: 1054-1063 (2019)) and BlocRes (<a href="https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S1047847713002086__;!!Mih3wA!UIK1bNFdL0BCqMS1yb-nZxvkCa3QeTZ-SaBr9_hcq0N33slQIgQowiEK6VvbT0kT6g$" target="_blank" moz-do-not-send="true">https://www.sciencedirect.com/science/article/pii/S1047847713002086</a>)
could help to find a B-factor that does not result in
overfitting.<br>
</p>
<p>In conclusion, from my point of view, there is not an
optimal decay valid for all proteins, but it depends on
each specific protein. And the shape of the decay is not a
straight line, but arbitrary depending on its shape.</p>
<p>I hope these reflections helped a bit.</p>
<p>Cheers, Carlos Oscar<br>
</p>
<div>On 8/26/20 7:05 AM, Alexis Rohou wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">Dear colleagues,<br>
<br>
I hope you may be able to help me get my head around
something.<br>
<br>
When considering the radially-averaged amplitudes of an
ideal 3D protein structure, the expectation (as laid out
in Fig1 of Rosenthal & Henderson, 2003 (PMID:
14568533), among others) is that in the
Wilson-statistics regime (q > 0.1 Å^-1, let’s say),
amplitudes will decay in a Gaussian manner, or linearly
when plotted on a log scale against q^2, reflecting the
decay of structure factors.
<div><br>
This expectation is certainly met when simulating maps
from PDB files, as described nicely for example by
Carlos Oscar Sorzano and colleagues recently (Vilas et
al., 2020, PMID: 31911170). Let’s call the rate of
decay of this ideal curve B_ideal, the “ideal” B
factor.<br>
<br>
Assuming for a moment that noise has a flat spectrum
(reasonable so long as shot noise is dominant), one
may follow in Rosenthal & Henderson’s footsteps
and draw a horizontal line on our plot to represent
the noise floor. As more averaging is carried out, the
noise floor is lowered relative to our protein’s
amplitude profile. As more particles are averaged
(without error, let’s say) the intersection between
the protein’s ideal radial amplitude profile and the
noise floor moves to higher and higher frequencies.<br>
<br>
This is the basis for the so-called ResLog plots,
where one charts the resolution as a function of the
number of averaged particles. The slope of the ResLog
plot is related to the slope of the radial amplitude
profile of the protein. Assuming no additional sources
of errors (i.e. ideal instrument and no processing
errors), B_ideal (the slope of the ideal protein
amplitude profile) can be computed from the slope of
the ResLog plot via B_ideal = 2.0/slope.<br>
<br>
Now, to my question. By looking at the slope of a
schematic Guinier plot generated using Wilson
statistics and atomic scattering factors for
electrons, I estimated a B_ideal of approximately 50
Å^2 (decay of ~ 1.37 natural log in amplitude over 0.1
Å^-2). The problem is that recent high-resolution
studies have reported ResLog-estimated B factors of
32.5 Å^2 (Nakane et al., 2020) and 36 Å^2 (Yip et al.,
2020), leading me to wonder what is wrong in the above
model.</div>
<div><br>
I see several possibilities:<br>
<br>
(1) B_ideal is actually significantly less than 50
Å^2. This would be consistent with the empirical
observation that “flattening” maps’ amplitude spectrum
(i.e. assuming B-ideal = 0 Å^2) gives very nice maps.
Either:</div>
<blockquote style="margin:0px 0px 0px
40px;border:none;padding:0px">
<div>a. I mis-estimated B_ideal when reading the
simulated amplitude spectrum plot. Has anyone done
this (i.e. fit a B factor to a simulated map’s
amplitude spectrum, or to a simulated spectrum)?
What did you find?</div>
</blockquote>
<blockquote style="margin:0px 0px 0px
40px;border:none;padding:0px">
<div>b. The simulations using atomic scattering
factors and Wilson statistics do not correctly
capture the actual amplitude profile of proteins,
which is actually much flatter than the atomic
scattering factors suggest.</div>
</blockquote>
<div>(2) B_ideal actually is ~ 50 Å^2, but the
assumption of a flat noise spectrum is wrong. I guess
that if the true noise spectrum were also decaying at
a function of q^2, this would cause the ResLog plot to
report “too small” a B factor</div>
<div><br>
What do you think? <br>
<br>
Cheers,<br>
Alexis</div>
</div>
<br>
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