fourier transform of MRC file

[pappu]

I am trying to do Fourier transform of an electron microscopy density map to compare with the fiber diffraction pattern. Let me know if it is possible in EMAN2 or I have to use any other program. Thank you.

[Steven Ludtke]

Electron density maps are 3-D. Certainly you can take the Fourier transform of one in EMAN, but the result will be a 3-D Fourier transform. I haven't done fiber diffraction myself, but I suspect what you're after is the 2-D power spectrum of this transform after azimuthal averaging.  However, that raises the question of what sort of density map you're referring to. If you're talking about the results of a helical reconstruction procedure, the 3-D map you have may not have the correct long-range periodic behavior if you simply take its power spectrum directly. It is also possible to impose extended helical symmetry in 3-D in EMAN2, using e2proc3d.py with the --sym option, and specifying the correct helical symmetry. You may also need to increase the box-size with --clip

e2help.py symmetry -v2

With this caveat, if you want to try it anyway, I would try something like this:

1) make sure that your 3-D density map has the helical axis aligned along Z. If not, you can use e2proc3d.py with the --rot option to manually rotate it.

2) use e2project3d.py to generate ~azimuthal projections

e2project3d.py mymap.mrc --outfile=proj.hdf --orientgen=eman:alt_min=88:delta=3:perturb=0 -v2

(note if it is an N-start helix, you could add --sym=cN to speed the process)

3) use e2proc2d to compute the average 2-D power spectrum

e2proc2d.py proj.hdf tmp.hdf --apix=<A/pix of map> --fftavg=powspec.hdf

4) e2display.py powspec.hdf

On Apr 10, 2014, at 3:46 AM, pappu <fraternit...@gmail.com> wrote:

I am trying to do Fourier transform of an electron microscopy density map to compare with the fiber diffraction pattern. Let me know if it is possible in EMAN2 or I have to use any other program. Thank you.

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[pappu]

Thank you very much for your detailed explanation. I tried your code but only obtain a very small pixelated image. I am wondering how to improve the quality of the obtained 2D power spectra since I need to match the layer lines. In fiber diffraction, many helical filaments are aligned to each other with few degrees of disorientation which improves the signal/noise.

[Steven Ludtke]

Unfortunately you aren't really giving us enough information to understand precisely what data you're basing your comparison on. Where did the volume you're using come from? How long is the filament it represents?  What are you trying to accomplish?

In diffraction experiments you are making your measurements directly in Fourier space. That is the Fourier transform is being "computed" experimentally and as a continuous function, which you are then sampling with your X-ray detector.  In Cryo-EM, you are reconstructing a short length of the helix representing at least the short-range, and possibly the long-range order in the filament. As the final reconstruction is finite, so the Fourier transform is discrete, with the sampling determined by the length of the helical fragment you're using. If you want better sampling in the FFT, you have to make the filament you're taking the FFT of longer. 

Of course, if you do this strictly by imposing known helical symmetry, you aren't really adding any new information. The existing coarsely sampledFFT will already represent an envelope under which any more complex structural patterning will lie. Anyway, my comment below about using e2proc3d with the --sym option to impose/extend the helical symmetry is how you could accomplish this. However, if you desire very fine sampling, this approach will not be very efficient (your 3-D volume will get very large), and it really isn't gaining you any new knowledge. 

That is, someone could write a more efficient program which computes a simulated 2-D diffraction pattern pixel by pixel at any level of sampling you prefer, taking the periodicity and everything else into account. Someone may well have done this, but I've never had a need myself, so I've never looked around. Ed Egelman is probably the best person to ask about it.

[pappu]

Thank you very much for taking time to clarify various aspects of cryoEM and fibre diffraction. I got the volume from EMDB which represents one helical repeat. I heard that averaging can be done in intensity space without real space projections. I am wondering how it can be done in EMAN2.

[Steven Ludtke]

Again, unsure of how much background you have in crystallography theory, or exactly what you're trying to accomplish. A single helical repeat contains the information about the structure of the protein. When the filament has many helical repeats, you also have the structure of the repeats coming into the scattering pattern. The periodicity of the crystalline (helical) repeat will sample the information in the Fourier transform of a single repeat at discrete points representing the periodicity of the structure. In this situation, the Fourier transform of a single unit cell acts as an envelope function for this uniform sampling effect caused by the periodicity.

There are a few issues here. In a cryoEM map, there is a box. The size of the box is not normally going to exactly match the periodicity of the helix (leaving aside additional issues of helical repeat vs pitch). Since periodic boundary conditions are implicit in FFTs, this means you will have a discontinuity at the edge of the box. The more repeats you have in the box, the less of an effect this becomes, and there are other strategies to minimize this effect. If your goal is the most accurate pattern for comparison against a fiber diffraction pattern, one should probably forego the FFT and simply compute out the integral long-form, perhaps taking knowledge of the helical pitch/repeat into account. While not extraordinarily complex, I have never written such a program for EMAN2.  You can get an approximate solution using the methods I described.

Yes, it is possible to simply integrate in Fourier space rather than generating 2-D projections and averaging them. Projections can be generated in either real or Fourier space, so the two processes are equivalent as long as the averaging is weighted correctly in both cases (FFT artifacts aside). I was simply suggesting a procedure you could use with existing programs. I have never tried to do a direct comparison with fiber diffraction, so I don't know what "gotchas" might exist. Again, I'd suggest that Ed Egelman would probably have more useful knowledge in this area.

[Paul Penczek]

I would say if the structure was taken from the data base the helical symmetry must be known. It is thus very easy to determine whether a given layer line pattern adheres to thus symmetry or on as long as meridional rise can be seen. So, there is really no need to compute a diffraction pattern from the model. If you insist, it can be computed very easily as Steve described. The tools are in sxhelicon_utils.py. The basic idea is that be generating a longer 3D structure (multiple rises) one can get a decent LL pattern from one orthoaxial projection. No averaging is needed. One has to be careful though when azimuthal angle is 90 degrees. Regards, Pawel Penczek

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From: Steven Ludtke <slud...@gmail.com>;
To: <em...@googlegroups.com>;
Subject: Re: [EMAN2] fourier transform of MRC file
Sent: Fri, Apr 11, 2014 12:21:53 PM