<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>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">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!Rn8ptfdW3i-ZJAsyJRtf84MeTMX0gbKZxAVhSD_WbmT6PxiAn3RA49bpffFudf71Mg$" target="_blank">https://journals.iucr.org/d/issues/2018/06/00/ic5102/ic5102.pdf</a>)
provides some clue based on the maximum continuity of the
isosurface.</p>
<p>Finally, we found that a combination of DeepRes (E.
Ramírez-Aportela, J. Mota, P. Conesa, J.M. Carazo, C.O.S. Sorzano.
DeepRes: A New Deep Learning and aspect-based Local Resolution
Method for Electron Microscopy Maps . IUCR J 6: 1054-1063 (2019))
and BlocRes
(<a href="https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S1047847713002086__;!!Mih3wA!Rn8ptfdW3i-ZJAsyJRtf84MeTMX0gbKZxAVhSD_WbmT6PxiAn3RA49bpffHaOthRoQ$" target="_blank">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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