[3dem] what is the ideal B factor?
Carlos Oscar Sorzano
coss at cnb.csic.es
Thu Aug 27 08:56:18 PDT 2020
Dear all,
El 27/08/2020 a las 6:47, Alexis Rohou escribió:
> 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?
My impression is that the radial average should not change too much by
using more accurate structure factors. In our paper (J.L. Vilas, J.
Vargas, M. Martínez, E. Ramírez-Aportela, R. Melero, A. Jiménez-Moreno,
E. Garduño, P. Conesa, R. Marabini, D. Maluenda, J.M. Carazo, C.O.S.
Sorzano. Re-examining the spectra of macromolecules. Current practice of
spectral quasi B-factor flattening. J. Structural Biology 209: 107447
(2020)) we made extremely harsh modifications to the atom descriptions
(Fig. 1) and the slope almost did not change independently of the kind
of atom.
A note on Wilson statistics, it assumes that the atoms are uniformly
distributed in the "unit cell" of the macromolecule. Proteins largely
violate this assumption, the effect is especially visible at low
frequency where the shape of the protein departs the most from the
uniform distribution in the unit cell (our Fig. 2), but at middle or
high frequency the slope of the Wilson approximation and the one of the
protein coincide.
Kind regards, Carlos Oscar
>
> 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
> <mailto: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!Wo-0feJNyN6SB8F0-VNIZChLRRLjFn8kgj3qd55sRlnZnfuvrPRhawoxpU2eo6C87w$
> <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
>>
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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 <mailto:pdomin at chem.uw.edu.pl>
> Phone: (48) 22 55 26 714
>
>
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