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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...<br>
Ed<br>
<br>
<div class="moz-cite-prefix">On 8/30/15 2:47 PM, Penczek, Pawel A
wrote:<br>
</div>
<blockquote
cite="mid:B8A7A8B2-6E80-437B-B048-C295DD654677@uth.tmc.edu"
type="cite">
<pre wrap="">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
<a class="moz-txt-link-abbreviated" href="mailto:pawel.a.penczek@uth.tmc.edu">pawel.a.penczek@uth.tmc.edu</a>
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<div class="WordSection1">
<p class="MsoNormal">Edward H. Egelman, Ph.D.<o:p></o:p></p>
<p class="MsoNormal">Professor<o:p></o:p></p>
<p class="MsoNormal">Dept. of Biochemistry and Molecular
Genetics<o:p></o:p></p>
<p class="MsoNormal">University of Virginia<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">President<o:p></o:p></p>
<p class="MsoNormal">Biophysical Society<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">phone: 434-924-8210<o:p></o:p></p>
<p class="MsoNormal">fax: 434-924-5069<o:p></o:p></p>
<p class="MsoNormal"><a class="moz-txt-link-abbreviated" href="mailto:egelman@virginia.edu">egelman@virginia.edu</a><o:p></o:p></p>
<p class="MsoNormal"><a
href="http://www.people.virginia.edu/%7Eehe2n"><a class="moz-txt-link-freetext" href="http://www.people.virginia.edu/~ehe2n">http://www.people.virginia.edu/~ehe2n</a></a><o:p></o:p></p>
<br>
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