<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<div class="moz-cite-prefix"><br>
For the first time in my life I fully agree with what Steven says
here! Does that mean we are both getting old Steven or is that
just me? <br>
<br>
Have fun!<br>
<br>
Marin<br>
<br>
<br>
<br>
On 02/09/2018 23:38, Ludtke, Steven J wrote:<br>
</div>
<blockquote type="cite"
cite="mid:51D4D9E7-4323-49FE-9FD6-5FDBEB755D96@bcm.edu">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
Ok, can't resist chiming in any more.
<div class=""><br class="">
</div>
<div class="">The basis of this general consensus, IS
mathematical. The specific threshold (2/3 Nyquist) which pretty
much everyone agreed on back in the 90's, is empirical. The
reason (at least the one I've always used) is that you do not
have a complete representation of data at Nyquist. Nyquist
corresponds to a +1/-1/+1/-1 sequence in adjacent pixels, if you
phase shift this pattern by 90 degrees, it becomes 0,0,0,0. At
1/2 Nqyuist, you can still represent arbitrary sinusoidal
waveforms with arbitrary phase. Between 1/2 Nyquist and Nyquist,
you get patterns which are dependent on position within the
"box". </div>
<div class=""><br class="">
</div>
<div class="">When you do X-ray crystallography, you are measuring
the Fourier intensities experimentally, and provided that you
can get the correct phase, you can then oversample the
real-space representation of the crystal pattern (with specified
phases), such that it is fully sampled. In CryoEM, we image in
real-space, and between 1/2 Nyquist and Nyquist the phases and
amplitudes are convolved in spatially dependent ways, such that
information is actually lost, and over-sampling cannot recover
the information fully.</div>
<div class=""><br class="">
</div>
<div class="">This is NOT saying you cannot achieve FSC curves
that remain close to 1 all the way to Nyquist. You can, of
course, but the resulting reconstruction will not be properly
sampled and features will be distorted from what you would see
if you had the same structure measured with 2x finer sampling.</div>
<div class=""><br class="">
</div>
<div class="">Try this little experiment. Take a PDB model and
convert to electron density with 1.5 Å/voxel sampling, repeat
the same process, but translate the PDB by 0.75 Å in x/y/z
before doing the conversion. Finally, generate a PDB with 0.75
Å/pixel sampling. All 3 of these should have the same
"resolution" which should extend to 3 Å. Look at the 3-maps.
Overlay the PDB. Take a look at the sidechains. Ostensibly,
these 3 maps are all "identical", but you will see that they are
definitely not...</div>
<div class="">
<div class=""><br class="webkit-block-placeholder">
</div>
<div class="">PS - please note that I am NOT saying that the FFT
is a lossy process. It is not, of course. Information is
exactly preserved by the FFT. The point, is that an arbitrary
real-space periodicity requires 4 pixels, not 2 pixels, to
unambiguously represent. </div>
<div class="">
<div dir="auto" style="color: rgb(0, 0, 0); letter-spacing:
normal; text-align: start; text-indent: 0px; text-transform:
none; white-space: normal; word-spacing: 0px;
-webkit-text-stroke-width: 0px; word-wrap: break-word;
-webkit-nbsp-mode: space; line-break: after-white-space;"
class="">
<div dir="auto" style="color: rgb(0, 0, 0); letter-spacing:
normal; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal; word-spacing:
0px; -webkit-text-stroke-width: 0px; word-wrap:
break-word; -webkit-nbsp-mode: space; line-break:
after-white-space;" class="">
<div dir="auto" style="word-wrap: break-word;
-webkit-nbsp-mode: space; line-break:
after-white-space;" class="">
<div style="color: rgb(0, 0, 0); font-variant-caps:
normal; letter-spacing: normal; text-align: start;
text-indent: 0px; text-transform: none; white-space:
normal; word-spacing: 0px; -webkit-text-stroke-width:
0px;">
<font class="" face="Courier"><span style="font-size:
14px;" class=""><br class="">
</span></font></div>
<div style="color: rgb(0, 0, 0); font-variant-caps:
normal; letter-spacing: normal; text-align: start;
text-indent: 0px; text-transform: none; white-space:
normal; word-spacing: 0px; -webkit-text-stroke-width:
0px;">
<font class="" face="Courier"><span style="font-size:
14px;" class="">--------------------------------------------------------------------------------------<br
class="">
Steven Ludtke, Ph.D. <<a
href="mailto:sludtke@bcm.edu" class=""
moz-do-not-send="true">sludtke@bcm.edu</a>>
Baylor College of Medicine <br
class="">
Charles C. Bell Jr., Professor of
Structural Biology<br class="">
Dept. of Biochemistry and Molecular Biology
(<a
href="http://www.bcm.edu/biochem" class=""
moz-do-not-send="true">www.bcm.edu/biochem</a>)<br
class="">
Academic Director, CryoEM Core
(<a
href="http://cryoem.bcm.edu" class=""
moz-do-not-send="true">cryoem.bcm.edu</a>)<br
class="">
Co-Director CIBR Center
(<a
href="http://www.bcm.edu/research/cibr" class=""
moz-do-not-send="true">www.bcm.edu/research/cibr</a>)<br
class="">
<br class="">
</span></font><br class="">
</div>
</div>
</div>
</div>
</div>
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Sep 2, 2018, at 7:27 PM, Dimitry Tegunov
<<a href="mailto:tegunov@GMAIL.COM" class=""
moz-do-not-send="true">tegunov@GMAIL.COM</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div class="">Dear Marin,<br class="">
<br class="">
quoting from the 1997 paper:<br class="">
<br class="">
"The crossing point between the two curves here lies at
about 78% of the Nyquist frequency. The theoretical
limit for all processing lies at the Nyquist frequency;
yet, considerably before that limit, practical
limitations due to the 2D or 3D interpolation procedures
used limit, or at least interfere with, the information
transfer through the processing chain. Moreover, since
both 3D maps are processed by the same programs, with
the same interpolation routines, the same systematic
round-off errors may be introduced in both
reconstructions, which the FSC program may see as common
“information”. It is thus good practice not to interpret
resolution curves at this high end of the resolution
range. The sampling of the data at a sampling interval
of 5 Å, in our experience, effectively limits the
attainable resolution to ∼15 Å rather than to the
theoretical Nyquist limit of 10 Å."<br class="">
<br class="">
You seem to agree that getting close to Nyquist is
possible if sloppy real-space interpolation is avoided.
As the latter has been the case for at least the past
decade, perhaps it is time to let go of an arbitrary
rule derived from personal experience rather than signal
processing fundamentals?<br class="">
<br class="">
Cheers,<br class="">
Dimitry<br class="">
<br class="">
########################################################################<br
class="">
<br class="">
To unsubscribe from the CCPEM list, click the following
link:<br class="">
<a
href="https://urldefense.proofpoint.com/v2/url?u=https-3A__www.jiscmail.ac.uk_cgi-2Dbin_webadmin-3FSUBED1-3DCCPEM-26A-3D1&d=DwIFaQ&c=ZQs-KZ8oxEw0p81sqgiaRA&r=GWA2IF6nkq8sZMXHpp1Xpg&m=F5Rudew3hA-EqzY67760waCGQCsGcLHKXLRjv420UKw&s=oBlVi2P88nOAHy2CQuhxXeHTFSwH9xmKLYJ5Xhl7ViI&e="
class="" moz-do-not-send="true">https://urldefense.proofpoint.com/v2/url?u=https-3A__www.jiscmail.ac.uk_cgi-2Dbin_webadmin-3FSUBED1-3DCCPEM-26A-3D1&d=DwIFaQ&c=ZQs-KZ8oxEw0p81sqgiaRA&r=GWA2IF6nkq8sZMXHpp1Xpg&m=F5Rudew3hA-EqzY67760waCGQCsGcLHKXLRjv420UKw&s=oBlVi2P88nOAHy2CQuhxXeHTFSwH9xmKLYJ5Xhl7ViI&e=</a><br
class="">
</div>
</div>
</blockquote>
</div>
<br class="">
</div>
<br>
<hr>
<p align="center">To unsubscribe from the CCPEM list, click the
following link:<br>
<a
href="https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCPEM&A=1"
target="_blank" moz-do-not-send="true">https://www.jiscmail.ac.uk/cgi-bin/webadmin?SUBED1=CCPEM&A=1</a>
</p>
</blockquote>
<p><br>
</p>
<pre class="moz-signature" cols="72">--
==============================================================
Prof Dr Ir Marin van Heel
Laboratório Nacional de Nanotecnologia - LNNano
CNPEM/LNNano, Campinas, Brazil
tel: +55-19-3518-2316
mobile +55-19-983455450 (current)
mobile +55-19-981809332
(041-19-981809332 TIM)
Skype: Marin.van.Heel
email: marin.vanheel(A_T)gmail.com
marin.vanheel(A_T)lnnano.cnpem.br
and: mvh.office(A_T)gmail.com
--------------------------------------------------
Emeritus Professor of Cryo-EM Data Processing
Leiden University
Mobile NL: +31(0)652736618 (ALWAYS ACTIVE SMS)
--------------------------------------------------
Emeritus Professor of Structural Biology
Imperial College London
Faculty of Natural Sciences
email: m.vanheel(A_T)imperial.ac.uk
--------------------------------------------------
I receive many emails per day and, although I try,
there is no guarantee that I will actually read each incoming email. </pre>
</body>
</html>