<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><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">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">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>
<fieldset></fieldset>
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</blockquote>
<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">pdomin@chem.uw.edu.pl</a>
Phone: (48) 22 55 26 714</pre>
</div>
</blockquote></div>