<html>
<head>
<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
<div class="moz-cite-prefix"><br>
Dear Smith Liu,<br>
<br>
You have hit upon a can of worms here… Although the FRC/FSC
metrics we introduced in 1982/1986 [1, 2] are now considered the
"gold standard" cryo-EM resolution criterion, these resolution
issues continue to be heavily debated [3]. Many FSC
add-ons/variants and tangential issues such as “reference bias”
have been inserted into the resolution criterion discussion. These
discussions unfortunately confuse even established researchers
(referees of major journals…), let alone newcomers to the field.
Many believe the resolution issue is better resolved in
X-crystallography. In fact, the FSC is arguably a better metric
than the R-factor, the generally accepted resolution metric in
X-ray crystallography [4]. Fortunately, FRC/FSC criteria are now
slowly also becoming the standard in optical microscopy, X-ray
microscopy, X-ray crystallography, and other fields of 2D/3D
imaging.<br>
<br>
The most controversial part of the FSC discussion is the FSC
threshold value to serve as a resolution criterion (such as the
FSC 0.5 value you mention). It took more than a decade to remove
the mathematically flawed DPR (Differential Phase Residual) from
the literature, after I explicitly discussed its shortcomings and
proposed a corrected phase residual in 1987 [3]. The discussion in
the field was then deviated towards the FSC threshold at which one
defines the average resolution of a 3D structure. The “0.5”
“criterion” was just postulated ad hoc, without any scientific
justification. Ten years ago, we argued that all fixed-valued FSC
threshold criteria (such as: “0.5” and “0.143”) are based on
flawed statistics [5]. Virtually all more formal justifications
for resolution criteria start off referring to the old formula
“SNR = (CCC/(1-CCC))” by Frank & Al-Ali 1975 [6].
Unfortunately this formula is also mathematically incorrect as was
discussed previously [5]. <br>
<br>
Here is another very simple argument to illustrate its flawed
definition: the normalised CCC (or FSC) has values in the range:
-1<=CCC<=+1, whereas the SNR (=S2/N2) is, per definition,
positive. Now insert the value CCC= -1, the case of perfectly
anti-correlated data, into the formula. This yields: SNR = “-0.5”,
a rampant violation of the SNR definition range. The formula could
be valid for the limiting case of CCC is close to unity, but such
high correlation values are not relevant in the
resolution-threshold context. For uncorrelated signals/noise the
CCC oscillates around the zero mark and, through the flawed Frank
& Al-Ali formula, produces as many positive as it does
erroneous negative SNR values.<br>
<br>
Unfortunately, virtually all (~100?) papers on resolution criteria
and validation tests in cryo-EM (from friends and foes) are based
on this formula and are thus based on “flawed statistics” to say
the least. With the great recent success of cryo-EM, everybody
appears to have stopped thinking about the basics, and merrily
continue to refer to incorrect stuff while focusing on “my
resolution is better than yours”. After decades of funny jokes and
verbal FSC controversies at GRC meetings, I don’t find it so funny
anymore: it is time to clean up the mess. I have lost the patience
to discuss these issues with referees who continue to consider the
subject as debatable. Questionable actions are sometimes hidden
behind this controversy such as in Mao & Sodrosky [7], who
cynically accuse us - their critics - of not knowing how to
interpret the FSC: “FSC estimates of resolution are known to be
quite sensitive to statistical bias …” etc. etc. As I said, this
whole issue is no longer amusing; it has become a matter of the
debatable scientific culture (integrity?) in the field of the
cryo-EM field. <br>
<br>
Oh, by the way, Smith Liu, what I really was going to say when I
started typing an answer to your question is that if you are new
to the field it is a good idea to read some basic literature in
Fourier Optics. Maybe my lecture notes can help [8]. The
horizontal axis in the FSC is 1/spatial-frequency (we are in
Fourier space) and the FSC values in the curve indicate the
cross-correlation level at that level of resolution (= inside that
specific 3D Fourier shell).<br>
<br>
Hope this helps,<br>
<br>
Marin<br>
<br>
[1] Van Heel M, Keegstra W, Schutter W, van Bruggen EFJ: Arthropod
hemocyanin structures studied by image analysis
<a class="moz-txt-link-freetext" href="http://singleparticles.org/methodology/MvH_FRC_Leeds_1982.pdf">http://singleparticles.org/methodology/MvH_FRC_Leeds_1982.pdf</a><br>
[2] Harauz G & van Heel M: Exact filters for general geometry
three dimensional reconstruction, Optik 73 (1986) 146-156<br>
[3]Van Heel M: Similarity measures between images. Ultramicroscopy
21 (1987) 95-100.]. [4] Van Heel: Unveiling ribosomal structures:
the final phases. Current Opinions in Structural Biology 10 (2000)
259-264.<br>
[5] Van Heel M & Schatz M: Fourier Shell Correlation
Threshold Criteria, J. Struct. Biol. 151 (2005) 250-262<br>
[6] Frank J & Al-Ali L: Signal-to-noise ratio of electron
micrographs obtained by cross correlation. Nature (1975)<br>
[7] Mao Y, Castillo-Menendeza LR, Sodroski JG: Reply to
Subramaniam, van Heel, and Henderson: Validity of the
cryo-electron microscopy structures of the HIV-1 envelope
glycoprotein complex. PNAS 2013
<a class="moz-txt-link-abbreviated" href="http://www.pnas.org/cgi/doi/10.1073/pnas.1316666110">www.pnas.org/cgi/doi/10.1073/pnas.1316666110</a><br>
[8] Van Heel: Principles of Phase Contrast (Electron) Microscopy.
<a class="moz-txt-link-freetext" href="http://www.single-particles.org/methodology/MvH_Phase_Contrast.pdf">http://www.single-particles.org/methodology/MvH_Phase_Contrast.pdf</a><br>
<br>
===========================================<br>
<br>
<br>
<br>
On 08/08/2015 07:45, Smith Liu wrote:<br>
</div>
<blockquote
cite="mid:10144882.10d59.14f0ceab82b.Coremail.smith_liu123@163.com"
type="cite">
<div
style="line-height:1.7;color:#000000;font-size:14px;font-family:Arial">
<div style="LINE-HEIGHT: 1.7; FONT-FAMILY: Arial; COLOR:
#000000; FONT-SIZE: 14px">
<div>Dear All, </div>
<div><br>
</div>
<div>I know the x-axis of the FSC curve is on the reverse of
the resolution, and the value in the x-axis corresponding
FSC 0.5 is usually regarded as the reverse of the resolution
of the whole EM map.</div>
<div><br>
</div>
<div>Here I do not know the meaning of the resolution in the
X-axis. The Whole map has only one resolution corresponding
FSC 0.5, then why the x-axis is on different resolutions
(for example the x-axis is from resolution 0 to 20 A, or the
reverse of that scope)? Is it because different parts of the
map have different resolutions (caused by different parts of
map have different quality), or it is because the X-axis of
the FSC curve has some relation with Fourier shell? If the
X-axis of the FSC is on the property related to Fourier
shell, then what is in the relation of resolution (or the
reverse of it) in the x-axis with Fourier shell (in
addition, what is the Fourier shell)?</div>
<div><br>
</div>
<div>Best regards.</div>
<div><br>
</div>
<div>Smith</div>
<div> </div>
</div>
<br>
</div>
<br>
<br>
<span title="neteasefooter"><span id="netease_mail_footer"></span></span>
</blockquote>
<br>
<br>
</body>
</html>