[3dem] [ccp4bb] Which resolution?

Sun Mar 8 21:06:59 PDT 2020

Hi Colin,

It sounds to me like you are mostly asking about whether 1/2-bit is the
"correct" target to aim for, the "correct" criterion for a resolution
claim. I have no view on that. I have yet to read Randy's work on the topic
- it sounds very informative.

What I do have a view on is, once one has decided one likes 1/2 bit
information content (equiv to SNR 0.207) or C_ref = 0.5, aka FSC=0.143
(equiv to SNR 0.167) as a criterion, how one should turn that into an FSC
threshold.

You say you were not convinced by Marin's derivation in 2005. Are you
> convinced now and, if not, why?

No. I was unable to follow Marin's derivation then, and last I tried (a
couple of years back), I was still unable to follow it. This is despite
being convinced that Marin is correct that fixed FSC thresholds are not
desirable. To be clear, my objections have nothing to do with whether
1/2-bit is an appropriate criterion, they're entirely about how you turn a
target SNR into an FSC threshold.

A few years ago, an equivalent thread on 3DEM/CCPEM (I think CCP4BB was
spared) led me to re-examine the foundations of the use of the FSC in
general. You can read more details in the manuscript I posted to bioRxiv a
few days ago (https://www.biorxiv.org/content/10.1101/2020.03.01.972067v1),
but essentially I conclude that:

(1) fixed-threshold criteria are not always appropriate, because they rely
on a biased estimator of the SNR, and in cases where* n* (the number of
independent samples in a Fourier shell) is low, this bias is significant
(2) thresholds in use today do not involve a significance test; they just
ignore the variance of the FSC as an estimator of SNR; to caricature, this
is like the whole field were satisfied with p values of ~0.5.
(3) as far as I can tell, ignoring the bias and variance of the FSC as an
estimator of SNR is _mostly OK_ when doing global resolution estimates,
when the estimated resolution is pretty high (large *n)* and when the FSC
curve has a steep falloff. That's a lot of hand-waving, which I think we
should aim to dispense of.
(4) when doing local resolution estimation using small sub-volumes in
low-res parts of maps, I'm convinced the fixed threshold are completely off.
(5) I see no good reason to keep using fixed FSC thresholds, even for
global resolution estimates, but I still don' t know whether Marin's
1/2-bit-based FSC criterion is correct (if I had to bet, I'd say not).
Aiming for 1/2-bit information content per Fourier component may be the
correct target to aim for, and fixed threshold are definitely not the way
to go, but I am not convinced that the 2005 proposal is the correct way
forward
(6) I propose a framework for deriving non-fixed FSC thresholds based on
desired SNR and confidence levels. Under some conditions, my proposed
thresholds behave similarly to Marin's 1/2-bit-based curve, which convinces
me further that Marin really is onto something.

To re-iterate: the choice of target SNR (or information content) is
independent of the choice of SNR estimator and of statistical testing
framework.

Hope this helps,
Alexis

On Sat, Feb 22, 2020 at 2:06 AM Nave, Colin (DLSLtd,RAL,LSCI) <
colin.nave at diamond.ac.uk> wrote:

> Alexis
>
> This is a very useful summary.
>
>
>
> You say you were not convinced by Marin's derivation in 2005. Are you
> convinced now and, if not, why?
>
>
>
> My interest in this is that the FSC with half bit thresholds have the
> danger of being adopted elsewhere because they are becoming standard for
> protein structure determination (by EM or MX). If it is used for these
> mature techniques it must be right!
>
>
>
> It is the adoption of the ½ bit threshold I worry about. I gave a rather
> weak example for MX which consisted of partial occupancy of side chains,
> substrates etc. For x-ray imaging a wide range of contrasts can occur and,
> if you want to see features with only a small contrast above the
> surroundings then I think the half bit threshold would be inappropriate.
>
>
>
> It would be good to see a clear message from the MX and EM communities as
> to why an information content threshold of ½ a bit is generally appropriate
> for these techniques and an acknowledgement that this threshold is
> technique/problem dependent.
>
>
>
> We might then progress from the bronze age to the iron age.
>
>
>
> Regards
>
> Colin
>
>
>
>
>
>
>
> *From:* CCP4 bulletin board <CCP4BB at JISCMAIL.AC.UK> *On Behalf Of *Alexis
> Rohou
> *Sent:* 21 February 2020 16:35
> *To:* CCP4BB at JISCMAIL.AC.UK
> *Subject:* Re: [ccp4bb] [3dem] Which resolution?
>
>
>
> Hi all,
>
>
>
> For those bewildered by Marin's insistence that everyone's been messing up
> their stats since the bronze age, I'd like to offer what my understanding
> of the situation. More details in this thread from a few years ago on the
> exact same topic:
>
> https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003939.html
>
> https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html
>
>
>
> Notwithstanding notational problems (e.g. strict equations as opposed to
> approximation symbols, or omission of symbols to denote estimation), I
> believe Frank & Al-Ali and "descendent" papers (e.g. appendix of Rosenthal
> & Henderson 2003) are fine. The cross terms that Marin is agitated about
> indeed do in fact have an expectation value of 0.0 (in the ensemble; if the
> experiment were performed an infinite number of times with different
> realizations of noise). I don't believe Pawel or Jose Maria or any of the
> other authors really believe that the cross-terms are orthogonal.
>
>
>
> When N (the number of independent Fouier voxels in a shell) is large
> enough, mean(Signal x Noise) ~ 0.0 is only an approximation, but a pretty
> good one, even for a single FSC experiment. This is why, in my book,
> derivations that depend on Frank & Al-Ali are OK, under the strict
> assumption that N is large. Numerically, this becomes apparent when Marin's
> half-bit criterion is plotted - asymptotically it has the same behavior as
> a constant threshold.
>
>
>
> So, is Marin wrong to worry about this? No, I don't think so. There are
> indeed cases where the assumption of large N is broken. And under those
> circumstances, any fixed threshold (0.143, 0.5, whatever) is dangerous.
> This is illustrated in figures of van Heel & Schatz (2005). Small boxes,
> high-symmetry, small objects in large boxes, and a number of other
> conditions can make fixed thresholds dangerous.
>
>
>
> It would indeed be better to use a non-fixed threshold. So why am I not
> using the 1/2-bit criterion in my own work? While numerically it behaves
> well at most resolution ranges, I was not convinced by Marin's derivation
> in 2005. Philosophically though, I think he's right - we should aim for FSC
> thresholds that are more robust to the kinds of edge cases mentioned above.
> It would be the right thing to do.
>
>
>
> Hope this helps,
>
> Alexis
>
>
>
>
>
>
>
> On Sun, Feb 16, 2020 at 9:00 AM Penczek, Pawel A <
> Pawel.A.Penczek at uth.tmc.edu> wrote:
>
> Marin,
>
>
>
> The statistics in 2010 review is fine. You may disagree with assumptions,
> but I can assure you the “statistics” (as you call it) is fine. Careful
> reading of the paper would reveal to you this much.
>
> Regards,
>
> Pawel
>
>
>
> On Feb 16, 2020, at 10:38 AM, Marin van Heel <marin.vanheel at googlemail.com>
> wrote:
>
> 
>
> ***** EXTERNAL EMAIL *****
>
> Dear Pawel and All others ....
>
> This 2010 review is - unfortunately - largely based on the flawed
> statistics I mentioned before, namely on the a priori assumption that the
> inner product of a signal vector and a noise vector are ZERO (an
> orthogonality assumption).  The (Frank & Al-Ali 1975) paper we have refuted
> on a number of occasions (for example in 2005, and most recently in our
> BioRxiv paper) but you still take that as the correct relation between SNR
> and FRC (and you never cite the criticism...).
>
> Sorry
>
> Marin
>
>
>
> On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A <
> Pawel.A.Penczek at uth.tmc.edu> wrote:
>
> Dear Teige,
>
>
>
> I am wondering whether you are familiar with
>   Resolution measures in molecular electron microscopy.
>
> Penczek PA. Methods Enzymol. 2010.
> Citation
>
> Methods Enzymol. 2010;482:73-100. doi: 10.1016/S0076-6879(10)82003-8.
>
>
>
> You will find there answers to all questions you asked and much more.
>
>
>
> Regards,
>
> Pawel Penczek
>
>
>
> Regards,
>
> Pawel
>
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