<div dir="ltr"><div>Dear Sacha,</div><div><br></div><div>Thank you very much for the detailed explanation. It is now clearer to me what the Fourier terms at the "corner" of the box mean, and how to interpret the results of the d99 method. Indeed I thought my maps would have zero coefficients for d < dhigh in Fourier space but that's not the case.</div><div>And I guess I've got too much used to think in terms of spherical resolution "shells" whereas a 3D FT is just the 1D FT computed successively along each axis :-)</div><div><br></div><div>Best wishes,<br></div></div><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature" data-smartmail="gmail_signature"><br>--<br>Ricardo Diogo Righetto<br></div></div>
<br><div class="gmail_quote">2018-06-01 21:38 GMT+02:00 Alexandre OURJOUMTSEV <span dir="ltr"><<a href="mailto:sacha@igbmc.fr" target="_blank">sacha@igbmc.fr</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div link="#0563C1" vlink="#954F72" lang="FR">
<div class="m_3291058815307323743WordSection1">
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">Dear Ricardo,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">First, let’s note that for an arbitrary map calculated in a ‘3D-box’ its equivalent in reciprocal space is also a ‘box’
(and not sphere!) of respective Fourier coefficients (right, some of them may be zeros, but in general case not).
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">When you talk about the Nyquist limit, you talk about 1D Fourier transformation. Let’s have a cubic unit cell with the
size a*a*a. Let’s for some resolution cut-off the maximal index along each reciprocal space axis be hmax (Nyquist limit). If you calculate a ‘3D-box’ of Fourier coefficients , then the Fourier coefficients in the corners of this box will have the resolution
not dhigh but dhigh/sqrt(3) !<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">Now, formally speaking, for a EM map calculated with the data cut at dhigh all its Fourier coefficients with d < dhigh
(those in the ‘box corners’) are supposed to be 0. However, in practice due to numerous map manipulation this is not always the case. This is exactly what d99 << dhigh tells us. One possible reason is using some sharp mask. Some other data manupulations may
be responsible as well. (obviously, d99 = dhigh-epsilon is not alarming; there are always some rounding errors.)<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">These Fourier coefficients (resolution between d99 and dhigh) may be somehow random and do not produce visible map details
(as you observe). But anyhow such noisy coefficients do exist in your calculations. Probably, it would be better to filter them out explicitly to avoid unexpected surprises in interpretation of map details.
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">Inversely, d99 >> dhigh means that higher-resolution map details are insignificant, near invisible in the total map and
that the formally announced resolution dhigh may be revised. Alternatively, these higher-resolution details may be correct but are too weak and a map with high-resolution data only may be useful to analyze such detailed information and to justify the atomic
model built in the map. <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">Resuming, d99 different from the announces dhigh, being larger or smaller, does not necessary mean that something is definitely
wrong but is a warning to check higher-resolution data.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">With best wishes,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US">Sacha Urzhumtsev<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1f497d" lang="EN-US"><u></u> <u></u></span></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif" lang="EN-US">De :</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif" lang="EN-US"> <a href="mailto:phenixbb-bounces@phenix-online.org" target="_blank">phenixbb-bounces@phenix-<wbr>online.org</a> [mailto:<a href="mailto:phenixbb-bounces@phenix-online" target="_blank">phenixbb-bounces@<wbr>phenix-online</a>.</span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">org]
<b>De la part de</b> Ricardo Righetto<br>
<b>Envoyé :</b> vendredi 1 juin 2018 19:21<br>
<b>À :</b> PHENIX user mailing list <<a href="mailto:phenixbb@phenix-online.org" target="_blank">phenixbb@phenix-online.org</a>><br>
<b>Objet :</b> [phenixbb] d99 beyond Nyquist?<u></u><u></u></span></p><div><div class="h5">
<p class="MsoNormal"><u></u> <u></u></p>
<div>
<div>
<p class="MsoNormal">Hi,<u></u><u></u></p>
</div>
<div>
<p class="MsoNormal"><u></u> <u></u></p>
</div>
<div>
<p class="MsoNormal">I've seen the d99 criterion in phenix.mtriage reporting a resolution value beyond Nyquist (=2.0 A), or very close to Nyquist in another case. For these particular maps, which are from the same dataset processed with two different single-particle
analysis packages (internal benchmarking), half-map FSC-based methods (including blocres) report resolutions in the range of 3.0-3.5 A which are consistent with the features I can see.<u></u><u></u></p>
</div>
<div>
<p class="MsoNormal"><u></u> <u></u></p>
</div>
<div>
<p class="MsoNormal">How can I interpret this? I understand that d99 starts omitting Fourier samples from the corners of the reciprocal box, but does it make sense to report a value beyond Nyquist?<u></u><u></u></p>
</div>
<div>
<p class="MsoNormal">I tried supplying unfiltered, masked and unmasked versions of the maps with barely any variation in the d99 results.<u></u><u></u></p>
</div>
<div>
<p class="MsoNormal"><u></u> <u></u></p>
</div>
<div>
<p class="MsoNormal">Thanks in advance for helping figuring this out!<u></u><u></u></p>
</div>
<div>
<p class="MsoNormal"><u></u> <u></u></p>
</div>
<div>
<p class="MsoNormal">Best wishes,<u></u><u></u></p>
</div>
<div>
<p class="MsoNormal"><u></u> <u></u></p>
</div>
<div>
<div>
<p class="MsoNormal"><br>
--<br>
Ricardo Diogo Righetto<u></u><u></u></p>
</div>
</div>
</div>
</div></div></div>
</div>
</blockquote></div><br></div>