International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 2.5, pp. 377-378

Section 2.5.7.3. Electron microscopy and data digitization

P. A. Penczekg

2.5.7.3. Electron microscopy and data digitization

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The electron microscope is a phase imaging system; i.e., in order to create contrast in images, they have to be underfocused. Owing to the particular form of the CTF of the microscope [(2.5.7.4)[link]], not only the amplitudes of the image in Fourier space are modified, but information in some ranges of spatial frequencies is set to zero and some phases have reversed sign. Therefore, in order to obtain possibly uniform coverage of Fourier space, the standard practice is to take pictures using different defocus settings and merge them computationally in order to fill gaps in Fourier space. The problem is compounded by the relation between underfocus and the envelope function of the microscope. Far-from-focus images have high contrast, but the envelope function has a relatively steep fall-off limiting the range of useful spatial frequencies. Conversely, close-to-focus images have little contrast, but the envelope function is decreasing, slowly extending useful information to high spatial frequencies. In effect, it is easier to process computationally far-from-focus data and to obtain accurate alignment of particles, but the results have severely limited resolution. Processing of close-to-focus data is challenging and results tend to be less accurate, but there is the potential to obtain high-resolution information.

The experimental techniques of initial structure determination (random conical tilt, tomography) require collection of tilt data. This is facilitated by dedicated microscope stages that can be rotated inside the microscope column yielding additional views of the same field. However, collection of high-quality tilt images is difficult. The quality of tilted images tends to be adversely affected by charging and drift effects. Moreover, as the stage is tilted the effective ice thickness increases (inversely proportionally to the cosine of the tilt angle, so at 60° the factor is two) and the contrast of the images decreases correspondingly. Finally, the defocus in tilted micrographs varies depending on the position in the field, often forcing users to restrict the particle selection only to regions in the vicinity of the tilt axis. However, tilting establishes geometrical relations between different projections of the same particle, unambiguously allowing for robust determination of an initial 3D model and the handedness of the quaternary structure of the complex.

Electron microscope images can be either recorded on the film and subsequently converted to digital format, or they can be recorded using a charge-coupled device (CCD) camera in a digital format directly on a microscope. In either case, it is necessary to select the magnification of the microscope and the eventual pixel size of the digitized data before the data-collection session. High magnification can potentially yield high-resolution data, but at the same time it decreases the yield of particles. Lower magnification values can be used when images are recorded on film, which does not attenuate high spatial frequencies to the same extent as CCD cameras tend to do.

The pixel size has to be adjusted according to the expected resolution of the final structure. Although it is tempting to adopt a small pixel size (in the hope of achieving high resolution of the results), in most cases this is counterproductive, as it results in very large computer files that are difficult to handle and in excessively long data-processing times. Theoretically, the optimum pixel size is tied to the maximum frequency present in the data by Shannon's sampling theorem, which states that no information is lost if the signal is sampled at twice the maximum frequency present in the signal, and no additional information is gained by sampling using higher frequency. Thus, if the expected resolution is 12 Å, it should be sufficient to use a pixel size (on the specimen scale) of 6 Å. In practice, various image-processing operations performed during alignment of the data and 3D reconstruction of the complex significantly lower the range of useful frequencies. This is because in currently available single-particle reconstruction software packages rather unsophisticated interpolation schemes are employed, which were selected mainly for the speed of calculations. Therefore, it is advisable to oversample the data by a factor of 1.5 or even 3.0. For an expected resolution of 12 Å this corresponds to pixel sizes of 4 and 2 Å, respectively.

The windowed particles have to be normalized to adjust the image densities to a common framework of reference. The reason for this step is that microscopy conditions are never exactly the same and also within the same micrograph field the background densities can vary by a significant margin due to uneven ice thickness and other factors. A sensible approach to normalization is to assume that the statistical distribution of noise in areas surrounding particles should be the same (Boisset et al., 1993[link]). Hence a large portion of one of the micrographs from the processed set is selected and a reference histogram of its pixel values is generated. Next, assuming a linear transformation of pixel values, the two parameters of this transformation are found in such a way that the histogram of the transformed pixel values surrounding the particle optimally matches the reference histogram using χ2 statistics as a discrepancy measure.

References

Boisset, N., Penczek, P., Pochon, F., Frank, J. & Lamy, J. (1993). Three-dimensional architecture of human alpha 2-macroglobulin transformed with methylamine. J. Mol. Biol. 232, 522–529.








































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