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Chapter 5 : Computational Image Analysis and Reconstruction from Transmission Electron Micrographs

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Abstract:

In this chapter, some specialized applications are described in which computers are essential for manipulating and enhancing images obtained by using a transmission electron microscope, particularly to understand the tertiary and quaternary structures of biological macromolecules and their complexes. The chapter must be read with some knowledge of the basic principles of transmission electron microscopy (TEM) of biological material. The computational techniques for analyzing and reconstructing macromolecular structures from TEM images are reviewed in monographs. Partial results of single-particle analyses of both frozen-hydrated and negatively stained preparations are illustrated in the chapter. S-layers, the proteinaceous surface arrays found on some gram-positive and gram-negative eubacteria and many archaea, are naturally occurring 2-D crystals that are amenable to image analysis by electron crystallography. TEM, particularly cryoTEM, has become a powerful tool for analyzing the tertiary and quaternary conformations of biological macromolecules and their complexes. Computational image analysis and reconstruction are integral tools in this process. The chapter has illustrated two approaches to manipulating and processing macromolecular TEM images that one would commonly find in the structural and molecular microbiological literature.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5

Key Concept Ranking

Transmission Electron Microscope
0.72778994
Transmission Electron Microscopy
0.5182637
Atomic Force Microscopy
0.5129825
Scanning Probe Microscopy
0.47444028
Bacterial Proteins
0.46784765
0.72778994
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Figures

Image of FIGURE 1
FIGURE 1

Simulated macromolecular complex, consisting of 12 spheres arranged in D6 symmetry, i.e., with one sixfold rotational axis of symmetry (the top-down view) and two twofold rotational axes of symmetry (the side views). In panel a, the 3- D structure is depicted via shaded surface representations. Here, the brighter regions act as a depth cue. In panel b, 2-D projections of the 3-D structure are shown, in which brighter regions represent a greater amount of molecular mass.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 2
FIGURE 2

In transmission electron micrographs of biological macromolecules, noise obscures structural detail severely. Here, the top-down 2-D projection from Fig. 1b has been duplicated a number of times to represent different individual macromolecular complexes lying in the same orientation on a support film. Random noise has been added to each point (pixel) in each image. Thus, the numbered images portrayed here are all different because the noise is different in each, even though the complex's structural information is the same.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 3
FIGURE 3

When noisy images like those in Fig. 2 are averaged together, the signal-to-noise ratio increases roughly according to the square root of the number of images being averaged. The constant structural information in each image is reinforced, whereas the random noise cancels itself out. The number of images being averaged in each panel is as follows: panel 1, 1; panel 2, 2; panel 3, 9; panel 4, 25; panel 5, 100; panel 6, 225; panel 7, 400; panel 8, 625; and panel 9, 900. Each image must represent the same 2-D orientation and the macromolecule must be in the same place in each image in order for the average to make sense. Thus, in single-particle analysis, a large population of images of different macromolecular complexes is aligned in order to facilitate comparison and sorted into homogeneous subgroups for averaging. Details of these processes are found in references , and .

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 4
FIGURE 4

Principles of reconstruction from projections. (a) In this example, a 2-D image is projected into a 1-D image by summing all the density values along a line at a certain angle. (b) The process of reconstruction by back projection involves smearing back the densities of each 1-D projection along the direction in which the projection was collected into a blank 2-D image and adding together all the back projections possible. Here, the reconstructions from 1, 2, 3, ..., 9 different 1-D projections (i.e., collected at different angles of 0, 20, 40, ..., 160°) are shown. In panel b, image 1, the density from each point in a 1-D projection was back projected at an angle of 0° into the 2-D image that will form the reconstruction. The angle 0° is the one at which projection 1 was collected. In panel b, image 2, the 1-D density data are back projected into the 2-D image at the angle 20° associated with this projection and added to the data back projected from projection 1. On it goes, with images 3 and 4, etc., showing the cumulative results of back projecting density data from different angles and adding them to the previously back-projected information. A reasonable representation of the original object, a collection of three disks, is already obtained from nine projections. Reconstruction quality improves with increasing numbers of input projections that span all possible views. The reconstruction approach shown here is called tomography, meaning that 2-D slices of a 3-D object are reconstructed. Tomography requires a specialized geometry in which the 3-D object is tilted about an axis by a certain angle, e.g., using a tilt stage in a transmission electron microscope. In single-particle analysis, such a geometry generally does not apply and 3-D volume images are reconstructed directly (i.e., not slice by slice) from 2-D projection images.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 5
FIGURE 5

Homogeneous preparation of the 2.25-MDa phosphoenolpyruvate synthase from , adsorbed to a thin carbon support, negatively stained with 2% (wt/vol) uranyl acetate to provide contrast, and imaged by TEM. (a) Field of view showing a number of different individual complexes. The scale bar represents 20 nm. (b) A set of smaller images of different individual complexes, extracted from larger micrographs like those in panel a. The scale bar represents 20 nm. These smaller images will be processed by computer programs that perform single-particle analysis to align, sort, average, and reconstruct them. In these images, the lighter regions represent proteinaceous material whereas the darker areas represent negative stain that embeds it. Some individual complexes are circled and denoted by A, B, C, and D.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 6
FIGURE 6

Homogeneous preparation of the 2.25-MDa phosphoenolpyruvate synthase from , encased in a thin layer of vitreous ice and thereby trapped in a native, hydrated state. The sample was kept at liquid-nitrogen temperature in the transmission electron microscope during imaging. Panels a and b represent the same region of the specimen, but the images were recorded at different defocus values. The image in panel a is closer to the true focus position of the microscope than the one in panel b, and is somewhat crisper but shows less contrast. This effect is due to the contrast transfer function, which changes with defocus ( ). Single-particle analyses of such frozen-hydrated material also incorporate contrast transfer function correction (e.g., reference ). In these cryoTEM images, the darker regions represent the proteins. These images, like those in Fig. 5 , were captured in digital form directly from the cryo-transmission electron microscope at a pixel size of 0.344 nm at the object level ( ). Each panel in this figure is 600 by 600 pixels in size and thus spans a region on the specimen that is 206.4 nm in extent.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 7
FIGURE 7

In cryoTEM images of frozen-hydrated preparations, biological macromolecules can exhibit a greater variety of orientations than those adsorbed to a support film. Single-particle analyses of contrast transfer function-corrected cryo-transmission electron micrographs (as those in Fig. 6 ) of the phosphoenolpyruvate synthase yield projection averages viewed along twofold (a), threefold (b), and fourfold (c) rotational symmetry axes, consistent with an underlying octahedral shape. Singleparticle analyses of TEM images of negatively stained preparations (as those in Fig. 5 ) yield primarily the threefold rotationally symmetric view (d) because this is the stablest way in which this complex can lie on the support film. In all of these images, contrast is such that lighter regions represent proteinaceous material. The scale bar represents 5 nm for all panels. Panels a through c are reproduced from reference 23 by permission of Academic Press.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 8
FIGURE 8

Projection averages at many different orientations, including those in Fig. 7 , were used to reconstruct the 3-D structure of the archaeal phosphoenolpyruvate synthase from negatively stained preparations (1,028 input images) (a) and frozenhydrated preparations (b through d) at high defocus (2,467 input images) (b) and low defocus (5,419 input images) (c) and after contrast transfer function correction (3,776 input images) (d). Here, the reconstructed 3-D objects are represented by shaded surfaces and are viewed from different orientations. This particular macromolecular complex has an octahedral shape and thus has fourfold, threefold, and twofold axes of rotational symmetry. There are always subtle differences among reconstructions from different preparations, and one must be cautious not to overinterpret details that might be spurious.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 9
FIGURE 9

Basic principles of 2-D electron crystallography in general and of Fourier filtering in particular. (a) Simulated macromolecular complex, as shown in Fig. 1 , arranged in a 2-D planar array (one complex thick). (b) Random noise has been added to each point in the image. (c) A Fourier transform of the image in panel a reveals a set of bright spots representative of the underlying regularity of the structure. Crystallographers are able to extract a great deal of information from the intensities and patterns of these spots. (d) A Fourier transform of the noisy image in panel b also reveals a set of bright spots, but now there is a diffuse background due to the noise, and the spots farther away from the origin are obscured. (e) The image in panel d can be filtered by computationally selecting only those values around the bright peaks and discarding all other values which represent primarily image noise. The bright peaks are arranged in a pattern that can be predicted by the way the repeating motifs are arranged with respect to one another, i.e., distances and angles between them. (f) By inverse Fourier transformation of the image in panel e, an improved image of the crystalline array is obtained for comparison with the original noisy image in panel b and the noise-free image in panel a.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 10
FIGURE 10

Specimens in the transmission electron microscope can be tilted about a single axis (or sometimes about two orthogonal axes) at defined angles and then imaged. In modern transmission electron microscopes, this entire process is computer controlled and automated. Here, a partial tilt series around a vertical axis of a segment of a simulated 2-D crystal is shown at tilt angles of 0° (a), 15° (b), 30° (c), 45° (d), and 60° (e). In practice, most transmission electron microscope specimen stages are limited to tilt angles of ±60°, where 0° represents the untilted specimen, but one would collect data at finer tilt increments such as every 3 or 5°. The limitation is the cumulative electron dose that the specimen can withstand before being distorted or destroyed. The object being tilted can be reconstructed tomographically as shown in Fig. 4 . The Venetian blind effect of specimen grid bars makes it difficult to go any higher. This effect is already visible here via the confusing superimposition of repeating motifs at 60°. Since the object is not imaged fully from all possible orientations, the resolution of the final 3-D reconstruction is limited (the so-called missing-cone effect).

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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Image of FIGURE 11
FIGURE 11

Example of 2-D electron crystallography. (a) S-layer from the eubacterium with p4 symmetry (with unit cell dimensions = = 12 nm), negatively stained with 2% (wt/vol) uranyl acetate and imaged by TEM. The various possible planar symmetry groups are defined in references such as 16, 19, and 26. The distance between the center of each repeating motif and its neighbor along the lattice line (i.e., not diagonally) is thus 12 nm. (b) Fourier transform of the image in panel a. The arrangement of peaks is not as good as that in the simulated image in Fig. 9 , reflecting the underlying imperfections of the 2-D array. (c) After filtering of the image in panel b and inverse Fourier transformation, an improved image of the bacterial surface array is obtained. The regional imperfections of the crystal, in terms of degree of staining and distortion, are evident. (d) Magnified view of a region of the filtered crystal. In panel a, the proteinaceous material is dark and the negative stain is light, as it would appear on the original electron micrograph recorded on film. In panels b through d, the contrast has been inverted.

Citation: Harauz G. 2007. Computational Image Analysis and Reconstruction from Transmission Electron Micrographs, p 82-95. In Reddy C, Beveridge T, Breznak J, Marzluf G, Schmidt T, Snyder L (ed), Methods for General and Molecular Microbiology, Third Edition. ASM Press, Washington, DC. doi: 10.1128/9781555817497.ch5
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References

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1. Frank, J. (ed.). 1992. Electron Tomography: Three- Dimensional Imaging with the Transmission Electron Microscope. Plenum Press, New York, N.Y..
2. Frank, J. 1996. Three-Dimensional Electron Microscopy of Macromolecular Assemblies. Academic Press, New York, NY. Both references 1 and 2 are good, albeit specialized, overviews of computerized 3-D electron microscopy, the first one edited and the second one written by a pioneer in the field. Reference 1 describes 3-D reconstruction techniques that are applicable to any structures that can be imaged by TEM, even those as large as organelles and whole cells. Reference 2 is devoted to singleparticle analysis like that described here.
3. Glasel, J. A.,, and M. P. Deutscher (ed.). 1995. Introduction to Biophysical Methods for Protein and Nucleic Acid Research. Academic Press, San Diego, CA. An overview in one volume of the myriad techniques for probing the structures of biological macromolecules.
4. Häder, D.-P. (ed.). 2001. Image Analysis: Methods and Applications, 2nd ed. CRC Press, Boca Raton, FL. A compendium of papers describing various applications of image analysis in the biological sciences, including electron microscopy.
5. Harris, J. R. 1997. Negative Staining and Cryoelectron Microscopy. Bios Scientific Publishers, Oxford, United Kingdom. A lot of excellent examples of high-quality TEM images of biological macromolecules are presented here. A good place to see what to aim for in one’s own work, especially for cryoTEM.
6. Hayat, M. A. 2000. Principles and Techniques of Electron Microscopy. Biological Application, 4th ed. Cambridge University Press, Port Chester, United Kingdom. General, standard reference that should be in every TEM lab.
7. Hayat, M. A.,, and S. E. Miller. 1990. Negative Staining. McGraw-Hill, Toronto, Canada. More detailed description of a common preparation technique, of interest to the experienced practitioner.
8. Hoppert, M.,, and A. Holzenburg. 1998. Electron Microscopy in Microbiology. Bios Scientific Publishers, Oxford, United Kingdom. A good resource written specifically for microbiologists.
9. Misell, D. L. 1978. Practical Methods in Electron Microscopy, vol. 7. Image Analysis, Enhancement, and Interpretation. North-Holland, Amsterdam, The Netherlands. An excellent classic in the field and a good review of techniques such as helical reconstruction.
10. Nasser Hajibagheri, M. A. (ed.). 1999. Electron Microscopy Methods and Protocols. Humana Press, Totowa, NJ. Another general reference that every TEM lab should have available; includes techniques for macromolecules as well.
11. Russ, J. C. 1998. The Image Processing Handbook, 3rd ed. CRC Press, Boca Raton, FL. Although image processing is encountered by everyone daily, most books on the subject are written by and for physicists, engineers, and computer scientists and combine a great deal of mathematics with trivial examples such as models’ faces. This book helps nonspecialists get an appreciation of the tricks of the trade, presents a variety of real microscopic examples, and is accompanied by software to help put principles into practice..
12. Sommerville, J.,, and U. Scheer (ed.). 1987. Electron Microscopy in Molecular Biology: a Practical Approach. IRL Press, Oxford, United Kingdom.A standard reference book on preparing biological macromolecules, including DNA.
13. Cicicopol, C.,, J. Peters,, A. Lupas,, Z. Cejka,, S. Müller,, R. Golbik,, G. Pfeifer,, H. Lilie,, A. Engel,, and W. Baumeister. 1999. Novel molecular architecture of the multimeric archaeal PEP-synthase homologue (MAPS) from Staphylothermus marinus. J. Mol. Biol. 290:347361. References 13 and 23 are intended to provide background for the specific example used here to illustrate single-particle analysis of a large macromolecular complex.
14. Czarnota, G. J.,, D. R. Beniac,, N. A. Farrow,, G. Harauz,, and F. P. Ottensmeyer,. 2001. Three-dimensional electron microscopy of biological macromolecules: quaternionassisted angular reconstitution of single particles, p. 275294. In D. Häder (ed.), Image Analysis: Methods and Applications, 2nd ed. CRC Press, Boca Raton, FL. References 14 and 25 describe two slightly different approaches to angular reconstitution, i.e., the computational determination of relative angular orientations amongst different projections of asymmetric macromolecules.
15. Ellis, M. J.,, and H. Hebert. 2001. Structure analysis of soluble proteins using electron crystallography. Micron 32:541550.
16. Engelhardt, H. 1988. Correlation averaging and 3-D reconstruction of 2-D crystalline membranes and macromolecules. Methods Microbiol. 20:357413. This review does for Fourier filtering and correlation averaging what references 14, 25, 31, and 33 do for single-particle analysis— it brings together the important concepts for a biologically oriented reader without obscuring them by excessive use of equations.
17. Frank, J.,, P. Penczek,, R. K. Agrawal,, R. A. Grassucci,, and A. B. Heagle. 2000. Three-dimensional cryoelectron microscopy of ribosomes. Methods Enzymol. 317:276291. The research groups of Frank and van Heel were pivotal both in developing techniques of single-particle analysis and in elucidating the structures of ribosomal subunits to high resolution in work spanning well over the past two decades. Reference 33 ranks also with references 2, 14, 25, and 31 in terms of reviewing single-particle analysis and cryoTEM and summarizes this group’s work on ribosomes. Reference 17 is dedicated to reviewing contemporary progress in structural ribosomology.
18. Frank, J.,, M. Radermacher,, P. Penczek,, J. Zhu,, Y. Li,, M. Ladjadj,, and A. Leith. 1996. SPIDER and WEB: processing and visualization of images in 3D electron microscopy and related fields. J. Struct. Biol. 116:190199. References 18, 24, 27, and 34 describe software packages available for analysis of TEM images of macromolecules.
19. Hammond, C. 1992. Introduction to Crystallography. Oxford University Press and Royal Microscopical Society, Oxford, United Kingdom. This is handbook 19 of the series produced by the Royal Microscopical Society, other volumes of which are noted in chapter 4. References 19 and 26 provide the reader with explanations of symmetry groups found in macromolecular crystals, including planar ones.
20. Hasler, L.,, J. B. Heymann,, A. Engel,, J. Kistler,, and T. Walz. 1998. 2-D crystallization of membrane proteins: rationales and examples. J. Struct. Biol. 121:162171. References 20 and 35 review some of the exciting advances in the field of structure determination of membrane proteins by cryoTEM.
21. Henderson, R.,, J. M. Baldwin,, T. A. Ceska,, F. Zemlin,, E. Beckmann,, and K. H. Downing. 1990. Model for the structure of bacteriorhodopsin based on high-resolution electron cryo-microscopy. J. Mol. Biol. 213:899929. One of the classic milestones of biological macromolecular TEM.
22. Jap, B. K.,, P. J. Walian,, and K. Gehring. 1991. Structural architecture of an outer membrane channel as determined by electron crystallography. Nature 350:167170. A good example of the power of electron crystallography in elucidating membrane protein structure, of direct interest to structural and molecular microbiologists.
23. Li, W.,, F. P. Ottensmeyer,, and G. Harauz. 2000. Quaternary organization of the Staphylothermus marinus phosphoenolpyruvate synthase: angular reconstitution from cryoelectron micrographs with molecular modelling. J. Struct. Biol. 132:226240.
24. Ludtke, S. J.,, P. R. Baldwin,, and W. Chiu. 1999. EMAN: semiautomated software for high-resolution single-particle reconstructions. J. Struct. Biol. 128:8297.
25. Radermacher, M., 2001. Three-dimensional reconstruction of single particles in electron microscopy, p. 295327. In D. Häder (ed.), Image Analysis: Methods and Applications, 2nd ed. CRC Press, Boca Raton, FL..
26. Rhodes, G. 1993. Crystallography Made Crystal Clear: a Guide for Users of Macromolecular Models. Academic Press, San Diego, CA..
27. Saxton, W. O. 1996. SEMPER: distortion compensation, selective averaging, 3-D reconstruction, and transfer function correction in a highly programmable system. J. Struct. Biol. 116:230236.
28. Sleytr, U. B.,, and T. J. Beveridge. 1999. Bacterial S-layers. Trends Microbiol. 7:253260. An overall review of bacterial surface arrays, including TEM.
29. Stewart, M., 1990. Electron microscopy of biological macromolecules: frozen hydrated methods and computer image processing, p. 939. In P. J. Duke, and A. G. Michette (ed.), Modern Microscopies—Techniques and Applications, Plenum Press, New York, N.Y. Quick “big picture” review.
30. Stewart, M.,, T. J. Beveridge,, and T. J. Trust. 1986. Two patterns in the Aeromonas salmonicida A-layer may reflect a structural transformation that alters permeability. J. Bacteriol. 166:120127. This reference is intended to provide background to the specific example used here to illustrate 2-D electron crystallography.
31. Thuman-Commike, P.,, and W. Chiu. 2000. Reconstruction principles of icosahedral virus structure determination using electron cryomicroscopy. Micron 31:687711. Of interest to virologists; a good recent review of single-particle analysis of highly symmetric objects.
32. Unwin, N.,, and R. Henderson. 1984. The structure of proteins in biological membranes. Sci. Am. 250:7894. A popular review intended for a general audience and of value for a beginner because of the clarity of the illustrations.
33. van Heel, M.,, B. Gowen,, R. Matadeen,, E. V. Orlova,, R. Finn,, T. Pape,, D. Cohen,, H. Stark,, R. Schmidt,, M. Schatz,, and A. Patwardhan. 2000. Single-particle electron cryomicroscopy: towards atomic resolution. Q. Rev. Biophys. 33:307369.
34. van Heel, M.,, G. Harauz,, E. Orlova,, R. Schmidt,, and M. Schatz. 1996. The next generation of the IMAGIC image processing system. J. Struct. Biol. 116:1724.
35. Walz, T.,, and N. Grigorieff. 1998. Electron crystallography of two-dimensional crystals of membrane proteins. J. Struct. Biol. 121:142161.

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