[3dem] what is the ideal B factor?

Wed Aug 26 00:53:50 PDT 2020

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!XFrT7LmP7kJg8VqmP7uNyW2DIXH7_inhEOkcfkox1FtkIYNtRTfPgrzDrzODiNGDgA$ 

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
>
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-- 
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

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