[3dem] [ccpem] on FSC curve (A can of worms...)

Sun Aug 30 13:50:37 PDT 2015

Hi All,

Signing off or not, I am totally amazed at the level of 
controversy/misunderstanding there is even among experts in our field. 
This just shows how necessary this type of open discussion is!

There are TWO types of resolution in all fields where Fourier Optics 
apply. The two type of resolution are currently probably best defined in 
EM simply because in light optics the FRC-type of criteria have just 
started its entry. In contrast to what Ed suggests, light optics is 
actually lagging behind. The first type of criterion, also the oldest 
type, is the INSTRUMENTAL resolution. This probably first emerged in 
light-microscopy but is in use everywhere, including astronomy and 
electron microscopy. The second type of resolution criterion is related 
to the STATISTICAL REPRODUCIBILITY of an experiment conducted with the 
instrument.

1) The instrumental or geometric resolution: that is, at which 
resolution level does the transfer function of the instrument drop to 
zero (independent of any object being present).  Beyond that level, no 
matter how long we measure, we will not collect any higher resolution 
information about the object. The Raleigh/Abbe formula relating 
numerical aperture and resolution fall in that category.   In 2D EM, 
once the Contrast Transfer function drops to zero there is no further 
information transfer. In 3D, reconstruction, the angular distribution of 
the projections defines the maximum (isotropic) geometric resolution 
achievable. Our contribution on this issue is: (van Heel and Harauz G: 
Resolution criteria for three dimensional reconstructions, Optik 73 
(1986) 119-122. )

But the instrumental/geometric resolution does not mean that you will 
achieve that level of resolution in any one given experiment! If one 
does not switch on the illumination in the light- or electron 
microscope, the data collected in the experiment are rubbish, no matter 
how good your geometric resolution is! Thus the more practical 
statistical significant resolution achieved in one 3D reconstruction 
experiment was introduced. Our contribution here was:

2) Fourier Shell Correlation (Harauz G & van Heel M: Exact filters for 
general geometry three dimensional reconstruction, Optik 73 (1986) 
146-156).  More info in the Wikipedia page: 
(https://en.wikipedia.org/wiki/Fourier_shell_correlation).  As is the 
case with the 2014 paper Gabor is referring to, the 3D version of the 
FSC was actually introduced to show how well 3D reconstruction 
algorithms were performing comparing the reconstruction results with the 
original, known test object.

Still hope this helps,

Marin

================================================

On 30/08/2015 16:27, Edward Egelman wrote:
> And I thought that you were "signing off"! In optics one uses a test 
> image and there is a well-defined definition of lines of resolution. 
> In crystallography one can look for holes in aromatic rings, etc. as 
> an indication of the true resolution. In both of these cases one is 
> starting with a known object and then looking at the "transfer 
> function" of the imaging system. In EM, unfortunately, 
> self-consistency or arguments about SNR (or estimates of SNR) have 
> substituted for a reality-based notion of an instrumental transfer 
> function. That is because such reality-based tests were absent when 
> one has 15, 20 or 30 Angstroms resolution. But we are no longer at 
> that stage...
> Ed
>
> On 8/30/15 2:47 PM, Penczek, Pawel A wrote:
>> Ed and Gabor, I have to respectfully disagree with your statements.
>>
>> Ed - there is no “general” or “absolute” definition of resolution.  What is called resolution differs from field to field
>> so when you say FSC is not a measure of resolution, what resolution do you have in mind?  The one used in optics,
>> or the one used in X-ray crystallography?  They are quite different from each other.
>>
>> For better or worth, definition of FSC allows one to estimate level of SNR in the data and it does just that,
>> assuming that assumptions are fulfilled.
>>
>> These assumptions call, among other things, for full independence of two realizations of the signal.
>> It is easy to see that it follows that thus defined FSC is not applicable to EM protocols as it would be always zero.
>> Simply, a chance that two truly independent refinement processes would magically end up with two structures
>> (or 2D averages) in the exact same orientation is infinitely small.
>>
>> Therefore, in practice we compromise independence to certain degree to make the machinery of FSC applicable to EM.
>> I would submit that most of the confusion arises due to disagreements how much of independence one is allowed to compromise.
>>
>> One kind of “abuse” is some kind of deterministic protocol that increases correlation, as Gabor points out.
>> In helical reconstruction, imposition of helical symmetry is such a step.  However, fundamentally this cannot be avoided
>> if one is to apply FSC at all as pointed out above.  So, we use various tricks to keep two structures in sync.
>> For example, a popular software package simply equates low frequency components between the two, which
>> of course introduces correlations beyond the cut-off point.  How much nobody knows.
>>
>>
>> In closing, as often in life there is a mathematical definition and there is little argument about its meaning and applicability,
>> and then there is life.  Normally there is full understanding that the two differ to a degree and one has to simply live with it.
>> We should keep in mind though that if FSC is applied to an outcome of an image processing protocol, its outcome becomes
>> as function of this protocol, as the ‘purity” of the original definition is compromised.
>>
>> Regards,
>> -
>> Pawel Penczek
>> pawel.a.penczek at uth.tmc.edu
>>
>>
>>
>
> -- 
>
>
> Edward H. Egelman, Ph.D.
>
> Professor
>
> Dept. of Biochemistry and Molecular Genetics
>
> University of Virginia
>
> President
>
> Biophysical Society
>
> phone: 434-924-8210
>
> fax: 434-924-5069
>
> egelman at virginia.edu
>
> http://www.people.virginia.edu/~ehe2n
>
>
>
>
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