[3dem] B-factors

Fri Jan 19 13:03:07 PST 2024

Dear colleagues,

I just want to clarify the usage of the ResLog plots from my perspective. Our intent with ResLog was to provide an empirical metric for assessing reconstruction and data quality. We noticed that plots of the spatial frequency vs. the log of the numbers of particles were linear, which makes it very convenient to compare reconstructions in terms of the ResLog slope and intercept. The units were also sensible with respect to our understanding of structure (Å and particles) which fits with how we think about structures. Our claim was that the ResLog slope related to the overall B factor while the the intercept (or rather nptlcs=1 since 0 is undefined) relates to reconstruction quality, but we never provided a theoretical formulation for determining B factor from the plots. I agree that the most conventional formulation (though not only) for determining the B factor is the Guinier plot etc as described in Rosenthal and Henderson with units of Å^2. It is also has the same units at the crystallographic B factor, which is quite sensible.

Regarding ResLog slopes and intercepts, they remain very convenient ways of comparing reconstructions and datasets. I have always intended to go back and determine what particular values for ResLog intercepts tell us about the reliability of a given reconstruction. There is definitely a number below which the reconstruction is questionable. The idea is that the ResLog intercept is another metric for reconstruction validation and/or can tell a given investigator whether or not there are issues with their data that need further investigation.

Best regards,
Scott

Scott Stagg
Professor
Institute of Molecular Biophysics
Department of Biological Sciences
Florida State University
Tallahassee, FL 32306-4380
w: 850-645-7872
f: 850-644-7244
sstagg at fsu.edu
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On Jan 19, 2024, at 2:38 AM, Takanori Nakane <tnakane.protein at osaka-u.ac.jp> wrote:

Hi,

This is a tricky point.

Indeed poses obtained from fewer numbers of particles are
less accurate, because the reference volume is of lower quality.
Thus, RELION's way is more solid from a theoretical point of view.
But we have to recall that other parameters have been optimised against
ALL particles in earlier CtfRefine and Polish jobs.
To make it *really* solid, one would have to repeat everything from
raw movies! But this is computationally unrealistic.

In reality, fortunately, the difference is tiny (if any) unless
you are looking at the fewest particle region.

Also note that stochasticity in random sampling introduces
variations in the resolution. To be precise (e.g. you are
writing a paper comparing two datasets), one should perform
3 or 5 trials for each data point.

Best regards,

Takanori Nakane

On 2024/01/19 16:23, Hagen, Wim J. wrote:
Dear Henning,
You mention “ResLog B-factor”, but could that be mixing up two things?
Reslog Analysis, at least in cryoSPARC, uses reconstruction-only for the subsets of particles to build the plot, based on the poses of the particles from 3D-refinement of the full dataset.
https://urldefense.com/v3/__https://guide.cryosparc.com/processing-data/all-job-types-in-cryosparc/post-processing/job-reslog-analysis__;!!Mih3wA!BM4AIXXXnt06QSHnQoyitzFlmTy7NoSqPwgDL5IG1eNvFyk_quTjvF_cYd5UQMCoinBzzHHHUhuutKBlhCs5OPvkGQ3aHh-54Zo$  <https://urldefense.com/v3/__https://guide.cryosparc.com/processing-data/all-job-types-in-cryosparc/post-processing/job-reslog-analysis__;!!Mih3wA!AgY5dBQd-XhHY1O0m5MdiahCiXuZaFNiqzSWPxClQ6CMYaws6iEctqqslya3plYhyszAACzLOR0t1m9fwFWVKVud0Q$>
The Rosenthal-Henderson B-factor plot, at least in the Relion bfactor_plot.py script, uses 3D-refinement for the subsets of particles.
https://urldefense.com/v3/__https://github.com/3dem/relion/blob/master/scripts/bfactor_plot.py__;!!Mih3wA!BM4AIXXXnt06QSHnQoyitzFlmTy7NoSqPwgDL5IG1eNvFyk_quTjvF_cYd5UQMCoinBzzHHHUhuutKBlhCs5OPvkGQ3aADj7CPU$  <https://urldefense.com/v3/__https://github.com/3dem/relion/blob/master/scripts/bfactor_plot.py__;!!Mih3wA!AgY5dBQd-XhHY1O0m5MdiahCiXuZaFNiqzSWPxClQ6CMYaws6iEctqqslya3plYhyszAACzLOR0t1m9fwFU1HQk4_g$>
This makes the outcome of both procedures different, regardless of the units used for fitting the plotted line. Reslog Analysis still serves the quality assessments discussed in Stagg et al, but one could argue that it is not the best indicator for how many (more) particles on needs to get to a certain resolution.
Best,
Wim
*From:*3dem <3dem-bounces at ncmir.ucsd.edu> *On Behalf Of *Alexis Rohou
*Sent:* 19 January 2024 00:45
*To:* Henning Stahlberg <henning.stahlberg at epfl.ch>
*Cc:* 3dem at ncmir.ucsd.edu
*Subject:* Re: [3dem] B-factors
*CAUTION:*This email originated from outside of Thermo Fisher Scientific. If you believe it to be suspicious, report using the Report Phish button in Outlook or send to SOC at thermofisher.com.
Dear Henning,
Thanks for bringing this to our attention.
I for one hadn't picked up on this discrepancy until you pointed it out. I had assumed that all ResLog plots always used Å^2 units. To my mind this is the only dimensionality that makes sense if we're going to use the "B factor" concept and wording (in analogy to temperature factors) to describe incoherent averaging in our reconstructions. I would have thought we'd always want to give B factors in units of Å^2, following the logic outlined in R&H2003.
Perhaps Scott and/or co-authors could comment as to why they moved from Å^2 to Å.
Cheers,
Alexis
PS. My understanding of this topic is summarized in section 4.7 of this 2021 book <https://urldefense.com/v3/__https:/iopscience.iop.org/book/edit/978-0-7503-3039-8__;!!Mih3wA!EInZgiJTGjny9OeUYvfegswag6cL2aI9L5BOih5sIGlIEB17fQvaYylR2PG7ZLpVAOQHO6FMdGAZKrb0iw$>. I regret that I didn't notice this discrepancy in the units at the time of writing - my text makes the assumption that all ResLog plots use 1/Å^2. Despite this omission, readers who are not familiar with the topic in question may still find it a useful introduction. I'd be happy to share preprints if you do not have access to the final publication.
On Thu, Jan 18, 2024 at 6:27 AM Henning Stahlberg <henning.stahlberg at epfl.ch <mailto:henning.stahlberg at epfl.ch>> wrote:
   Dear Colleagues,
   There are two B-factors used in cryo-EM:
   Rosenthal and Henderson, JMB (2003) discuss the Guinier plot, where
   the amplitude falloff beyond 10A resolution can be fitted with a
   B-factor that has the unit "Angstromˆ2".
   They also discuss the dependency of the resolution d (in Angstroem)
   on the number # of particles, and provide the basis for a ResLog
   B-factor, which is obtained from the slope of 1/dˆ2 as a function of
   ln(#).  The numbers of particles needed to reach a resolution "d" is
   then obtained with:
   # = (1/Nasym) * (<S>/<N>)ˆ2 * (30 pi) / (N_e * sigma_e * d) * exp(B
   / (2 * dˆ2))
   The B-factor also in this case is defined as in Angstromˆ2.
   Stagg et al., JSB (2014) define a dependency of the resolution d
   from ln(#), with
   d = constant * ln(#) + constant.
   So, here, “d” is linear, not to the square. Their ResLog B-factor is
   then presumably obtained from the first "constant" in that equation,
   therefore in Angstrom,  not Angstromˆ2.
   This is also implemented in CryoSPARC, which also plots 1/d as a
   function of ln(#).
   But other papers, such as Yip et al. and Holger Stark, Nature (2020)
   discuss the ResLog B-factor in Aˆ2 again.
   It is interesting for a map to provide all three, the FSC 0.143, the
   Sharpening B-factor in Aˆ2, and the Reconstruction ("ResLog")
   B-factor in Aˆ2.
   But, what is the most commonly used definition of the ResLog
   B-factor, A or Aˆ2 ?
   Best wishes,
   Henning.
   Henning Stahlberg
   Laboratory of Biological Electron Microscopy
   Institute of Physics, School of Basic Sciences, EPFL, and
   Dep. of Fund. Microbiology, Faculty of Biology and Medicine, UNIL,
   Cubotron, BSP421, 1015 Lausanne, Switzerland
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