[3dem] what is the ideal B factor?

Wed Aug 26 22:05:47 PDT 2020

Thank you Carlos Oscar for summarizing your work so succinctly!

I just would like to pick up on your concluding sentence:

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.

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.

Cheers,
Alexis

On Wed, Aug 26, 2020 at 12:32 AM Carlos Oscar Sorzano <coss at cnb.csic.es>
wrote:

> Dear Alexis and all,
>
> as a very condensed summary of what Jose Luis Vilas and us showed in the
> paper you have mentioned below is that:
>
> 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.
>
> 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).
>
> 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).
>
> 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.
>
> 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).
>
> 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 (https://urldefense.com/v3/__https://journals.iucr.org/d/issues/2018/06/00/ic5102/ic5102.pdf__;!!Mih3wA!Rn8ptfdW3i-ZJAsyJRtf84MeTMX0gbKZxAVhSD_WbmT6PxiAn3RA49bpffFudf71Mg$ )
> provides some clue based on the maximum continuity of the isosurface.
>
> 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 (
> https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S1047847713002086__;!!Mih3wA!Rn8ptfdW3i-ZJAsyJRtf84MeTMX0gbKZxAVhSD_WbmT6PxiAn3RA49bpffHaOthRoQ$ )
> could help to find a B-factor that does not result in overfitting.
>
> 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.
>
> I hope these reflections helped a bit.
>
> Cheers, Carlos Oscar
> On 8/26/20 7:05 AM, Alexis Rohou wrote:
>
> Dear colleagues,
>
> I hope you may be able to help me get my head around something.
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> I see several possibilities:
>
> (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:
>
> 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?
>
> 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.
>
> (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
>
> What do you think?
>
> Cheers,
> Alexis
>
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