Tomogram orientation and tilt angle inversion

[Doulin Shepherd]

Hi EMAN2 team,

This is a question related to the recent AreTomo transformation matrix thread.

I have been performing some checks with different software pipelines to determine the defocus handedness, and I have become confused about the "correct" orientation of the tomograms.

I collected a few tilt series of carbon with fiducials and I am using them to check defocus handedness and CTF estimates. I am seeing a discrepancy between the EMAN2 and IMOD-related protocols.

For EMAN2:

1. I import the tilt series and run a reconstruction using the rawtlt files generated by Imod or without 

2. During reconstruction, the tilt axis is reported as −94.5 degrees

3. However, when I run the CTF handedness check, it suggests the tilt axis should be −274.5 degrees resulting in a -180 degree rotated tomogram with respect to Imod reconstructions

For IMOD-related protocols:

1. I import and align the same data with a tilt axis of −94.5 degrees.

2. I then check the defocus gradient in Warp and use defocusgrad to check the handedness

Defocusgrad checks the defocus values of the right versus the left side of the aligned tilt series. It follows the convention that for positive angles, the right side should have a higher defocus value than the left. This process confirms that the tilt axis of −94.5 degrees is correct (according to my understanding of this convention).

Following the suggestion in another thread, I tried inverting the tilt axis angles in the rawtlt file given to EMAN2. When I did this, the EMAN2 reconstruction became identical to the IMOD reconstruction, and the EMAN2 CTF handedness check reports that the −94.5 degrees tilt axis is now correct.

While I have a vague idea of why inverting the angles worked, I don't understand where the original discrepancy came from or how can I diagnose which orientation is "correct" without "brute-forcing" it by collecting and processingn an apoferritin or a ribosome dataset.

I would greatly appreciate your inshight into my third? tomogram orientation problem.

Cheers,
Doulin

[Steve Ludtke]

Hi Doulin,

A) consider this from the perspective of the specimen in the microscope. The structure of the specimen is absolute, the line along-which tilting occurs is absolute, and the (mostly orthogonal) direction along which the defocus changes is absolute.

B) How that 3-D structure is mapped into the 3-D space of the reconstruction is completely arbitrary, and a matter of convention. Once you have mapped the 3-D structure into the volume of the 3-D reconstruction the direction of the defocus gradient and tilt axis are fixed by the orientation of the reconstructed volume. 

However, getting from A->B can be a little tricky.

- If we ignore the defocus gradient for a moment and assume the tilt axis is perfectly orthogonal to the beam direction (just to get started), the direction of the tilt axis can be determined from the data, but the direction of the rotation about that axis (clockwise or counterclockwise) cannot be determined directly from the data. Also, rotating the tilt axis by 180 degrees is equivalent to swapping the direction of the rotation about the tilt axis.

- In EMAN2 the direction of the tilt axis is fixed in the reconstruction, meaning if you change the orientation of the tilt axis, you are changing its orientation in the plane of the tilt series, but it always winds up in the same place in the reconstruction. This is why rotating the tilt axis by 180 degrees causes a 180 degree rotation of the 3-D reconstruction (and a flipping of the handedness unless you also invert the tilt handedness).

- this is complicated by the fact that in reality the "tilt axis" often isn't perfectly orthogonal to the beam direction causing so called "out of plane tilt". This means that as the specimen rotates it follows the path of a narrow cone in Fourier space rather than a common-line. This makes the approach of searching for a common-line in Fourier space to find the tilt-axis a little ambiguous, which is one reason iterative refinement of the geometry is necessary.

- The only way to resolve the question of absolute handedness directly from the data is to determine the direction of the defocus gradient in the data. I believe EMAN2 was the first package to manage to make this approach actually work. Previous approaches to this problem involved computing the CTF along strips of the image parallel to the tilt axis. However, as this involves averaging over the gradient within the strip and the thickness of the specimen, results were historically a little marginal in real data. EMAN2's approach is to model the defocus gradient and compare the result to the individual tilt images. Even with this method, it only works because direct detectors now provide sufficient contrast at high resolution 

- It is not mathematically possible to get an optimal 3-D map by phase-flipping applied to the 2-D tilt series, since the specimens have some thickness associated with them, Modern subtomogram averaging procedures (including EMAN2) work by knowing the final geometry determined above and extracting subtilt series from the original tilt series for each particle. The precise knowledge of the geometry allows each tilt for each particle to have its own defocus value at the center of the particle to be reconstructed. While this defocus will still be inaccurate for the portions of the image which are well above or well below the target particle, the particle itself should be coherently corrected out to high resolution, and all of that peripheral stuff just becomes incoherent noise. 

As you can see, all of these transformations are very tricky to get right, and most software just strives for internal self-consistency such that the final tomograms and "subtomogram" averages are optimal. It can be very challenging to look at another software package and figure out all of the mathematical details of these choices and try to match them. There are also historical decisions made by specific packages due to computational limitations at the time, which no longer make sense. For example, the default orientation in IMOD doesn't put the beam direction along Z, I think it's along X? or Y?  The reason for this was (as I understand it) memory limitations on computers when IMOD was written.

The question of how to try and solve this mess so users could theoretically move back and forth between different software packages was the major topic of a meeting called by the CZII/EBI last year, with the goal of defining a common well-defined standard that the various packages could map to.   This is a _much_ harder problem than getting single particle reconstruction packages to interconvert, and that's why we have very reliable interconversion of single particle data between EMAN2, Relion and CryoSPARC, but interconversion among tomography software is still hit and miss. It takes a lot of effort just to figure out the math to convert properly from one package to one other package, and it's a bit of a thankless job. Indeed, you're more likely to get yelled at than thanked if there are any tiny mistakes, so people who tackle this tend to put large disclaimers on their solutions.

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[Pranav Shah]

"Indeed, you're more likely to get yelled at than thanked if there are
any tiny mistakes"

This is true for so many different things! :)
Best,
Pranav
--
Pranav Shah
Postdoctoral Research Fellow.

Division of Structural Biology,
Wellcome Trust Centre for Human Genetics,
University of Oxford,
Roosevelt Drive, Oxford OX3 7BN,
UK

> To view this discussion visit https://groups.google.com/d/msgid/eman2/2B159769-E805-4C50-8765-A239F12BEF2A%40gmail.com.

[Doulin Shepherd]

Hi Steve,

Thanks for the detailed reply, as always.

My goal was to make sure the metadata going into EMAN2 was correct and understand why the tomograms might look different even when using the same parameters in different software.

With your explanation, I have a much better understanding of why things flip and rotate at different stages. This wasn't a major issue, since the particles had the correct handedness even when the tomograms were rotated or flipped. However, I was trying to determine if this was a situation where:

(1) There was a mistake that just happened to look okay on the surface, or

(2) It is simply a matter of different conventions, and everything is fine and internally consistent.

Thanks again!