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<p>Dear all,</p>
<div class="moz-cite-prefix">El 27/08/2020 a las 6:47, Alexis Rohou
escribió:<br>
</div>
<blockquote type="cite"
cite="mid:CAM5goXTzCTS5UqEiQraQNnx1=dnwRp66aexjS_no2dS23S21zA@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Dear Paulina,
<div><br>
</div>
<div>Thank you for your contribution. I am afraid I am not in a
position to truly appreciate your work, but I wonder if you
could answer the following question about simulating Guinier
plots.</div>
<div><br>
</div>
<div>When I computed my idealized Guinier plot of a protein
(well, the part of it beyond 0.1 Å^-1), I used my
understanding of Wilson statistics (that the average intensity
in a frequency band is the sum of the squared structure
factors over all atoms in the structure) to compute
intensities based on the sums of scattering factors, where the
factors I used came from Peng, Ren, Dudarev, Whelan (Acta
Cryst 1996 A52, 257-276, Table 1). I then took the square root
and plotted it on a ln scale as a function of q^2, the squared
spatial frequency. This gave me something very similar to what
can be seen in figure 1 of Rosenthal & Henderson (2003):
an approximately straight line with a negative slope. My
question to you: would you expect this slope (which I
interpret as being a feature of the underlying scattering
factors) to be more, or less, negative if I had used more
accurate structure factors or simulation techniques?</div>
</div>
</blockquote>
<p>My impression is that the radial average should not change too
much by using more accurate structure factors. In our paper (J.L.
Vilas, J. Vargas, M. Martínez, E. Ramírez-Aportela, R. Melero, A.
Jiménez-Moreno, E. Garduño, P. Conesa, R. Marabini, D. Maluenda,
J.M. Carazo, C.O.S. Sorzano. Re-examining the spectra of
macromolecules. Current practice of spectral quasi B-factor
flattening. J. Structural Biology 209: 107447 (2020)) we made
extremely harsh modifications to the atom descriptions (Fig. 1)
and the slope almost did not change independently of the kind of
atom.</p>
<p>A note on Wilson statistics, it assumes that the atoms are
uniformly distributed in the "unit cell" of the macromolecule.
Proteins largely violate this assumption, the effect is especially
visible at low frequency where the shape of the protein departs
the most from the uniform distribution in the unit cell (our Fig.
2), but at middle or high frequency the slope of the Wilson
approximation and the one of the protein coincide.</p>
<p>Kind regards, Carlos Oscar<br>
</p>
<blockquote type="cite"
cite="mid:CAM5goXTzCTS5UqEiQraQNnx1=dnwRp66aexjS_no2dS23S21zA@mail.gmail.com">
<div dir="ltr">
<div><br>
</div>
<div>Sorry if the above question is naive - just trying to
understand the basics and this is not a part of the literature
I am familiar with.</div>
<div><br>
</div>
<div>Cheers,</div>
<div>Alexis</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Aug 26, 2020 at 12:24
AM Paulina Dominiak <<a href="mailto:pdomin@uw.edu.pl"
target="_blank" moz-do-not-send="true">pdomin@uw.edu.pl</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 colleagues,</p>
<p>I am not a single-particle cryoEM practitioner yet and do
not now the answer for Alexis questions. But allow me to
comment on the relation of B-factors and scattering model
used to interpret experimental data. <br>
</p>
<p>I have an expertise in developing new scattering models
for X-ray diffraction, and now for electron diffraction,
which are better than commonly used scattering factors
from Independent Atom Model (IAM). We have discovered
recently than when electron diffraction (ED) data for
small molecules are refined with IAM scattering factors,
obtained B-factors are by far too small (even 70% too
small at atomic resolution depending on the molecule), and
they are getting even smaller when resolution gets worse.
Some of the results are published here: Acta Cryst.
(2020). A76, 92-109, <a
href="https://urldefense.com/v3/__http://scripts.iucr.org/cgi-bin/paper?S2053273319015304__;!!Mih3wA!QYmYdkLbYrZEU5IV3t_6eqD_D0Fo7WOZZS2ej0vYl22csigpsYVYEWOaxcxBbdLWKA$"
target="_blank" moz-do-not-send="true">http://scripts.iucr.org/cgi-bin/paper?S2053273319015304</a><br>
</p>
<p>Usage of wrong scattering factors (which do not take into
account partial charge on atoms, and asphericity of
electron density and electrostatic potential due to
existence of covalent bonds, lone electron pairs, etc.)
may be one of the reason why B-factors from ED and sp
cryoEM are so nonphysical.</p>
<p>With regards,</p>
<p>Paulina</p>
<p><br>
</p>
<p><br>
</p>
<div>W dniu 26.08.2020 o 07:05, Alexis Rohou pisze:<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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<pre cols="72">--
dr hab. Paulina M. Dominiak, prof. ucz.
Group Leader
Electron Density Modelling Group
Laboratory for Structural and Biochemical Research (LBSBio)
Biological and Chemical Research Centre
Department of Chemistry
University of Warsaw
ul. Zwirki i Wigury 101
02-089 Warszawa, Poland
Room: 3.125
E-mail: <a href="mailto:pdomin@chem.uw.edu.pl" target="_blank" moz-do-not-send="true">pdomin@chem.uw.edu.pl</a>
Phone: (48) 22 55 26 714</pre>
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