Hi Tom, thank you vey rmuch for the fast and elaborate response. I believe I understand it much better now and see why the resolution per se is not what I am after. My intention is to visualize/model the appearance of a lower resolution map using a higher resolution map. While this should in principal be possible (the other way around not) but would then require an appropriate noise model. So the gaussian filtering only dampens the amplitudes of the frequencies in Fourier space. The dampening can be controlled by the standard deviation of the used gaussian function. The dampening affects signal and noise equally. Does this correspond to a gaussian lowpass filter? Because I was thinking about removing the high frequencies and setting the cutoff at different frequencies then corresponding to different "resolutions". While the resulting map probably has a higher signal-to-noise ratio at lower frequencies (lower than the cutoff) than an experimental map of a resolution that this map tries to depict it may still be a good visual approximation. So I guess my question is whether there is a good way to mimick/visualize a lower resolution experimental map using a higher resolution experimental map without considering a sophisticated noise model. Thanks again for your help. Best Dennis Quoting Tom Goddard <goddard@sonic.net>:
Hi Dennis,
I don't know the answer to your question, but here are some thoughts about it. The Gaussian convolution filter just scales the Fourier space coefficients by a Gaussian making the higher frequencies have lower amplitudes. That is reversible, the high frequencies can be scaled back up. So although the real-space smoothed map looks lower resolution, it still has the same high resolution content. The noise and the signal have both been scaled down at high resolutions so the signal-to-noise is just as good at those high resolutions. If you did this smoothing on two half-maps used to compute the resolution by Fourier shell correlation it would still give 2 Angstroms, the smoothing did not change the FSC resolution! If you were for example testing a fitting method it could easily extract that high resolution information and use it. In order to really lower the resolution you would need to add noise at high frequencies so the high-frequency signal is lost.
That said you could ask if the noise at high frequencies was not scaled down, only the signal, then what would the reduced resolution be. We know at the FSC resolution the signal-to-noise ratio is some specific value that gives the cutoff correlation. But you would need a model of the noise amplitude at other lower frequencies to know how attenuating just the signal but not the noise would change the resolution. Maybe there is a pretty reliable noise model for these cryoEM maps, I'm not sure.
Tom
On Jan 9, 2024, at 2:41 PM, Dennis Dannecker via ChimeraX-users <chimerax-users@cgl.ucsf.edu> wrote:
Hello,
I would like to ask a question regarding the gaussian filtering.
I filtered a given map (downloaded from the emdb with the "open" command from chimerax) in chimerax using the following command:
vop gaussian #1 sDev X
with X taking different values ranging from 0.25 to 20 with different steps.
Now I would like to know the resolutions these maps actually correspond to after this gaussian filtering. The originally loaded map is stated to have nominal resolution of 2 Angstroms (GSFSC). sDev defines the standard deviation in Angstrom of the 3D Gaussian function that is used for the filtering. How can one now calculate the resolution these filtered maps correspond to? Is it possible to calculate or state a resolution for these maps that is related to the resolution given for the original map (here 2 Angstroms).
Thank you very much.
Kind regards
Dennis
Dennis Dannecker Master Student of Biochemistry Department of Chemistry Faculty of Mathematics and Natural Sciences University of Cologne Albertus-Magnus-Platz 50923 Cologne, Germany _______________________________________________ ChimeraX-users mailing list -- chimerax-users@cgl.ucsf.edu To unsubscribe send an email to chimerax-users-leave@cgl.ucsf.edu Archives: https://mail.cgl.ucsf.edu/mailman/archives/list/chimerax-users@cgl.ucsf.edu/
-- Dennis Dannecker Master Student of Biochemistry Department of Chemistry Faculty of Mathematics and Natural Sciences University of Cologne Albertus-Magnus-Platz 50923 Cologne, Germany