[3dem] what is the ideal B factor?

Wed Aug 26 17:20:07 PDT 2020

Likely the more important assumption here is that proteins are rigid, and one could just use a single conformation to generate a SPR-like map with just accurate scattering factors. It may be that one would instead have to average more than one conformation to get to something more similar to a cryoEM map.

Greg

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From: 3dem <3dem-bounces at ncmir.ucsd.edu> on behalf of Paulina Dominiak <pdomin at chem.uw.edu.pl>
Sent: Wednesday, August 26, 2020 3:53 AM
To: Alexis Rohou <a.rohou at gmail.com>; 3dem <3dem at ncmir.ucsd.edu>
Subject: Re: [3dem] what is the ideal B factor?

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!TUGGdRhvSlAGMA-83Z_1nLukNebAtogqAA1J4gijI_954wfTdTrF6tzMzW4Y7wKMBQ$ <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.
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Electron Density Modelling Group
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