[3dem] [ccpem] GroEL best resolution map. (FSC RESOLUTION ??)

[Marin van Heel]

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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