[3dem] Is there an asymmetric biological sample out there that reveals handedness at CET resolution?

[Dr .Julio Ortiz]

Handedness determination in Electron Tomography: a trivial problem?

Julio Ortiz, Friedrich Foerster, and Martin Beck
Max Planck Institute of Biochemistry, Department of Structural  
Biology, Am Klopferspitz 18, D-82152 Martinsried, Germany

To illustrate the point of this tutorial, we begin by imagining a  
three dimensional (3D) model of the right hand inside a cube. One  
could imagine that this cube has been divided into slices that  
represent longitudinal cuts through the model of the hand. By  
inverting the order of these slices from the top to the bottom,  
sequentially and without rotating them, a new model of the hand can be  
visualized. This model looks similar to the original, but with a  
significant difference: it is the model of a ‘left’ hand. By altering  
the order of the slices, the handedness of the model has been changed.
Electron tomography has been applied to biological specimens to  
produce astonishing 3D representations, in particular from vitrified  
specimens (cryoelectron tomography - CET)1. Based on tomograms, the  
morphology of viruses, organelles and cells has been described in 3D  
space, retrieving valuable information even in cases in which the  
handedness of the models is unknown. Nevertheless, advanced data  
acquisition equipment and a continuous development of image processing  
methods now allows one to obtain 3D reconstructions in which the  
structure of macromolecular complexes can be resolved (4-6 nm  
resolution)2,3,4. Consequently, it is indispensable to consider the  
handedness of tomograms when analyzing such structures and their  
spatial relations.
CET allows the 3D reconstruction of volumes based on series of two  
dimensional micrographs. Each single micrograph is a projection of a  
specimen that has been tilted to a particular angle inside the  
electron microscope. As projections, these micrographs do not show a  
top or bottom view of the object, but rather a sum of its  
electrostatic potential along the path followed by the electron beam.  
Only with an appropriate comprehension of spatial
relation among micrographs and the real object, together with  
algorithms that take into account these relations, it is possible to  
reconstruct models with the correct handedness. Here we discuss three  
aspects of which one should be aware of in order to obtain the proper  
handedness in a tomogram. Methods for establishing the handedness of  
biological macromolecules from single projections of tilted specimens  
have been described elsewhere 5,6.
Firstly, the micrographs used in CET are recorded on a charge-coupled  
device (CCD) camera and saved digitally. The file format implies a  
specific coordinate system. Depending on the software, the same data  
can be visualized differently. In particular, the pictures could be  
mirrored if the coordinate system of the visualization program does  
not agree with the conventions that were used by the acquisition  
program. In practical terms, the representation of the sample in a  
single projection could correspond to two different views, looking at  
the sample from the top or from the bottom of the microscope.  
Independently of rotations in the plane of the picture (to be  
discussed later), this mirroring problem is critical to defining a  
coordinate system for a 3D reconstruction. A theoretical assignment of  
“point of view” for one’s micrographs could demand information that is  
not available to the microscopist. However, a simple experiment can  
solve the problem. With the help of a light-microscope, a labeled grid  
can be placed on the holder in such a manner that the labels (e.g.  
numbers or letters of a ‘finder’ grid) can be read correctly as seen  
from the top of the holder. A single micrograph of this grid inside  
the electron microscope reveals the “point of view” for the particular  
set of microscope, CCD camera, and acquisition software. When an  
asymmetrical label is read correctly, as for number “2” in Fig 1 a,  
the image corresponds to a view that looks at the sample from the top  
of the microscope.
Secondly, it is necessary to relate the tilt series images to the  
coordinate system used for tilting. Conventionally, the value of tilt  
angle is saved in the header of each image with a
sign that correspond to a right-handed coordinate system, the x-axis  
of which runs through the tilt axis of the holder and points to its  
tip (e.g. a clockwise rotation of the holder can be seen from outside  
the microscope when tilting from negative to positives angles). The  
direction of the tilt axis in each image of a tilt series can be  
described by an angle α, defined as the angle between one axis of  
the micrograph and the projection of the tilt axis onto the  
micrograph. This angle can be determined precisely with appropriate  
algorithms, but with two different values, differing by 180º. That  
means that the “arrow” of a vector indicating the direction of tilt  
cannot be specified from the projections without external information.  
Again, an experimental approach assures the correct solution to this  
issue. We suggest mounting two plastic-covered grids in the same  
holder, one over the other. The grids should be distinguishable, e.g.  
grids with circular holes of different sizes. Knowing the specific  
order in which the grids are placed on the holder, they are useful as  
references for top and bottom motifs when acquiring micrographs. With  
a tilt series of two or three images of this arrangement, it is  
possible to deduce which is the appropriate value of α for the  
corresponding tilt axis. We illustrate such an approach in Fig 1 c-e.  
The small hole on the plastic film moves from the right to the left of  
the tilt axis when tilting from negative to positives angles. Given  
that the grid with smaller holes was placed under the grid with larger  
holes, it can be concluded that the tilt axis points from bottom to  
top in this example. It should be considered that the direction of the  
tilt axis is magnification-dependent.
Finally, a comprehensive understanding of the algorithms applied for  
the 2D alignment of the projections and the 3D reconstruction is  
indispensable. The coordinate system of the applied routines should be  
internally consistent and in agreement with the input data. It is not  
necessary to go into the fine details of the reconstruction program;  
but some simulations are required in order to understand how a tilt  
series, with a specific definition of tilt angles, must be aligned and  
reconstructed in order to get the true handedness (Fig. 1f). In
some cases, e.g. with the softwares EM system or Matlab TOM toolbox,  
the direction of the tilt axis needs to be anti-parallel to the axis  
used by a back-projection algorithm. This may imply a rotation of 180°  
of the projections before reconstruction.
Therefore, the problem of handedness determination is trivial only if  
it is considered systematically. There is only a 50% chance to be right!
References
1. Lučić, V., Förster, F. & Baumeister, W. Structural  
studies by electron tomography: from cells to molecules. Annu. Rev.  
Biochem. 74, 833-865 (2005).
2. Frangakis, A. S. et al. Identification of macromolecular complexes  
in cryoelectron tomograms of phantom cells. Proc. Natl Acad. Sci. USA  
99, 14153-14158 (2002).
3. Beck M. et al. Nuclear pore complex structure and dynamics revealed  
by cryoelectron tomography. Science 306, 1387-1390. (2004).
4. Ortiz, J. O., Forster, F., Kurner, J., Linaroudis, A. A. &  
Baumeister, W. Mapping 70S ribosomes in intact cells by cryoelectron  
tomography and pattern recognition. J Struct Biol. in press (2006).
5. Klug, A. & Finch, J. T. Structure of viruses of the  
papilloma-polyoma type: IV. Analysis of tilting experiments in the  
electron microscope. J. Mol. Biol. 31, 1-12 (1968).
6. Belnap, D. M., Olson, N. H. & Baker, T. S. A method for  
establishing the handedness of biological macromolecules. 120, 44-51  
(1997).




Fig. 1. Determining handedness in electron tomography. a. Electron  
micrographs of an oriented, labeled grid at low magnification  
revealing a “point of view” from the top of the microscope for the  
particular combination of microscope and CCD-camera used. b. Mirrored  
image display in a; this orientation is expected when the opposite  
point of view is valid for the settings under study. c, d, e, Aligned  
micrographs (tilt axis vertical) of a double grid set tilted -2, 0,  
and +2 degrees respectively. The small hole, of the grid placed at the  
bottom of the holder, moves to the left of the tilt axis during  
tilting to positives angles (big holes only partially visible). Only  
if the tilt axis points to the top, the movement of the hole  
corresponds to the angles assigned to each image for a clockwise  
rotation of the holder in a right-handed coordinate system. f.  
Simulated model and corresponding projections. Depending of the  
3D-reconstruction program, the images of a tilt series should be  
aligned in a particular way. In this example, only if the direction of  
the tilt axis in the projections opposes the sense of direction of the  
axis used during reconstruction, does the resulting model recover the  
right handedness.

-- 
Max-Planck Institut für Biochemie
Abteilung Molekulare Strukturbiologie
Am Klopferspitz 18
D-82152 Martinsried
Germany
Tel: +49 (89) 8578 2032
fax: +49 (89) 8578 2641
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Handedness_tutorial.jpg
Type: image/jpeg
Size: 17678 bytes
Desc: not available
Url : https://mail.ncmir.ucsd.edu/mailman/private/3dem/attachments/20120808/e9f8d956/Handedness_tutorial-0001.jpg