[3dem] [ccpem] GroEL best resolution map. (FSC RESOLUTION ??)
Marin van Heel
marin.vanheel at googlemail.com
Mon Sep 3 04:47:20 PDT 2018
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?
Have fun!
Marin
On 02/09/2018 23:38, Ludtke, Steven J wrote:
> Ok, can't resist chiming in any more.
>
> 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".
>
> 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.
>
> 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.
>
> 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...
>
> 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.
>
> --------------------------------------------------------------------------------------
> Steven Ludtke, Ph.D. <sludtke at bcm.edu <mailto:sludtke at bcm.edu>>
> Baylor College of Medicine
> Charles C. Bell Jr., Professor of Structural Biology
> Dept. of Biochemistry and Molecular Biology
> (www.bcm.edu/biochem <http://www.bcm.edu/biochem>)
> Academic Director, CryoEM Core (cryoem.bcm.edu
> <http://cryoem.bcm.edu>)
> Co-Director CIBR Center (www.bcm.edu/research/cibr
> <http://www.bcm.edu/research/cibr>)
>
>
>
>> On Sep 2, 2018, at 7:27 PM, Dimitry Tegunov <tegunov at GMAIL.COM
>> <mailto:tegunov at GMAIL.COM>> wrote:
>>
>> Dear Marin,
>>
>> quoting from the 1997 paper:
>>
>> "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."
>>
>> 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?
>>
>> Cheers,
>> Dimitry
>>
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--
==============================================================
Prof Dr Ir Marin van Heel
Laboratório Nacional de Nanotecnologia - LNNano
CNPEM/LNNano, Campinas, Brazil
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