[3dem] what is the ideal B factor?

Wed Aug 26 21:47:18 PDT 2020

Dear Paulina,

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.

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?

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.

Cheers,
Alexis

On Wed, Aug 26, 2020 at 12:24 AM Paulina Dominiak <pdomin at uw.edu.pl> wrote:

> Dear colleagues,
>
> 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.
>
> 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,
> https://urldefense.com/v3/__http://scripts.iucr.org/cgi-bin/paper?S2053273319015304__;!!Mih3wA!QYmYdkLbYrZEU5IV3t_6eqD_D0Fo7WOZZS2ej0vYl22csigpsYVYEWOaxcxBbdLWKA$ 
>
> 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.
>
> With regards,
>
> Paulina
>
>
>
> W dniu 26.08.2020 o 07:05, Alexis Rohou pisze:
>
> 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
>
> _______________________________________________
> 3dem mailing list3dem at ncmir.ucsd.eduhttps://mail.ncmir.ucsd.edu/mailman/listinfo/3dem
>
> --
> 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: pdomin at chem.uw.edu.pl
> Phone: (48) 22 55 26 714
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.ncmir.ucsd.edu/pipermail/3dem/attachments/20200826/cabcea74/attachment.html>