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And just to reinforce another point that I have made previously and
in a recent eLife paper, the FSC measures self-consistency, and not
resolution. The examples I had used involved applying the wrong
helical symmetry, where one can generate an FSC that has no relation
to reality. But what about consistent, reproducible errors in the
reconstruction engine? Imagine a bug that introduces a large peak of
density at the center of every reconstruction. The two half maps
will then show a better FSC than the ones generated by the bug-free
reconstruction engine.<br>
Ed<br>
<br>
<blockquote
cite="mid:493D2D8A-AF33-4460-BE29-630C214C820C@uth.tmc.edu"
type="cite">
<blockquote type="cite">
<pre wrap="">On Aug 30, 2015, at 12:14 PM, Ludtke, Steven J <a class="moz-txt-link-rfc2396E" href="mailto:sludtke@bcm.edu"><sludtke@bcm.edu></a> wrote:
Ok, I've tried to avoid this discussion, as it seems like somewhat pointless rehashing of old debates to little real point. However, based on direct emails I've gotten from some people new to the field, it may be causing a lot of confusion and uncertainty among this group. They lack the historical context to understand the point of the debate. Let me add a couple of minor points to the discussion:
1) Compensating for statistical uncertainty through use of an adjustment to the threshold is confusing to people raised in experimental science. In essence, it is concealing the fact that the FSC values have considerable uncertainty due to counting statistics and other effects. That is, the final resolution plots wind up being the intersection of two lines with no presented uncertainty at all, and we find people looking a specific intersection points between these two lines with ridiculous levels of precision.
A much more sensible way to present this result would be to produce FSC curves with error bars, which do a much better job of expressing the fact that there is considerable uncertainty in the resulting intersection! The difficulty is how to best produce such error bars.
Once you have an FSC with error bars, you still have the question of a threshold value/curve. I would argue that the error bars subsume the uncertainty, and using Alexis arguments about expectation values, you can then use a fixed value threshold. I think Alexis arguments are spot-on in this case (FSC relationship to SNR is an expectation value), and Marin's orthogonality argument is fundamentally incorrect. The cross-terms in the presence of noise do have an expectation value of zero, of course! The cross-terms contribute to the uncertainty in the estimator, not to its asymptotic value.
2) Closely related to point #1 is the issue that our resolution estimates simply are not that precise. They do have considerable uncertainty (which an FSC with error bars would help to express). They also ignore differences in the FSC curve at resolutions lower than the cutoff resolution, which are also significant from the perspective of map interpretation. If I have an FSC curve up close to 1 which smoothly and rapidly falls to zero near some target resolution, the quality of the map is not equivalent to an FSC which begins falling gradually at much lower resolution and undergoes considerable gymnastics before finally falling below the 'threshold' value.
----
Our field takes these resolution numbers MUCH too seriously, and have unwisely turned them into the sole measure of map quality. I do not believe it is possible to make the FSC into a single catch-all measure.
Following the 'error-bar' approach (if we can agree on one) would properly associate an uncertainty with each measured resolution value, to point out the limits of this estimator in a way that a reviewer from any field could easily encompass. Like the X-ray community, we need to adopt additional criteria rather than continue these pointless debates trying to make the FSC more statistically accurate than it is possible for it to be.
----------------------------------------------------------------------------
Steven Ludtke, Ph.D.
Professor, Dept of Biochemistry and Mol. Biol. (<a class="moz-txt-link-abbreviated" href="http://www.bcm.edu/biochem">www.bcm.edu/biochem</a>)
Co-Director National Center For Macromolecular Imaging (ncmi.bcm.edu)
Co-Director CIBR Center (<a class="moz-txt-link-abbreviated" href="http://www.bcm.edu/research/cibr">www.bcm.edu/research/cibr</a>)
Baylor College of Medicine
<a class="moz-txt-link-abbreviated" href="mailto:sludtke@bcm.edu">sludtke@bcm.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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