# [phenixbb] d99 beyond Nyquist?

Ricardo Righetto ricardorighetto at gmail.com
Sun Jun 3 04:00:11 PDT 2018

```Dear Sacha,

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.
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 :-)

Best wishes,

--
Ricardo Diogo Righetto

2018-06-01 21:38 GMT+02:00 Alexandre OURJOUMTSEV <sacha at igbmc.fr>:

> Dear Ricardo,
>
>
>
> 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).
>
>
>
> 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) !
>
>
>
> 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.)
>
>
>
> 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.
>
>
>
> 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.
>
>
>
> 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.
>
>
>
> With best wishes,
>
>
>
> Sacha Urzhumtsev
>
>
>
> *De :* phenixbb-bounces at phenix-online.org [mailto:phenixbb-bounces@
> phenix-online.org] *De la part de* Ricardo Righetto
> *Envoyé :* vendredi 1 juin 2018 19:21
> *À :* PHENIX user mailing list <phenixbb at phenix-online.org>
> *Objet :* [phenixbb] d99 beyond Nyquist?
>
>
>
> Hi,
>
>
>
> 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.
>
>
>
> 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?
>
> I tried supplying unfiltered, masked and unmasked versions of the maps
> with barely any variation in the d99 results.
>
>
>
> Thanks in advance for helping figuring this out!
>
>
>
> Best wishes,
>
>
>
>
> --
> Ricardo Diogo Righetto
>
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