Proc. Nail. Acad. Sci. USAVol. 83, pp. 9040-9044, December 1986Cell Biology

Tomographic three-dimensional reconstruction of ciliaultrastructure from thick sections

(high-voltage electron microscopy/image processm'g/microtubule)

B. F. MCEWEN*, M. RADERMACHER*, C. L. RIEDER*t, AND J. FRANK*t*Wadsworth Center for Laboratories and Research, New York State Department of Health, Albany, NY 12201; and tSchool of Public Health Sciences,State University of New York at Albany, Albany, NY 12201

Communicated by Hans Ris, August 18, 1986

ABSTRACT We have applied a computer-based tomo-graphic technique to reconstruct the three-dimensional ultra-structure of newt lung cilia. Epon-embedded samples were cutinto 0.25-,im-thick sections that were imaged at 1 MV with ahigh-voltage electron microscope. For the reconstructionshown, a tilt series of 53 micrographs was taken at tilt anglesbetween -54° and +50°. The reconstruction was accomplishedfrom these projections using a weighted back-projection algo-rithm. The 12-nm resolution of the reconstruction was suffi-cient to resolve the outer doublet and central pair microtubules,dynein arms, radial spokes, and central sheath structures. Thereconstruction can be viewed from various angles and withappropriate parts cut away to reveal structural features ofinterest. The sense of depth in these views can be enhanced bystereo viewing of shaded surface images. From this reconstruc-tion, we determined that newt lung cilia contain the morecommon triplet grouping of radial spokes.

In the past, high-resolution three-dimensional (3D) informa-tion concerning the structure of cells was primarily obtainedfrom serial thin (50- to 70-nm) sections. This approach istechnically difficult, laborious, and plagued with inherentproblems (reviewed in refs. 1-3). Artifacts can arise from: theassumption that structural features are constant throughoutthe depth of the section, the structural discontinuity betweenadjacent sections, and the loss of information about materialthat is not clearly visible in thin sections. In some cases alimited amount of 3D information can be obtained from thequick-freeze deep-etch method (e.g., ref. 4), scanning elec-tron microscopy (e.g., ref. 5), and other techniques based onsurface shadowing. Unfortunately, these methods only re-veal surface features, and one must first fracture, crack, orotherwise disrupt the structure to obtain internal information.With intermediate- and high-voltage electron microscopes

(HVEM) high-resolution images can be obtained from sec-tions as thick as 5 ,m (reviewed in refs. 3 and 6). Suchsections contain an appreciable amount of 3D structuralinformation. However, since electron micrographs are two-dimensional projections of the object, structural detailswithin the thickness of a section appear superimposed. Thisoverlapping of cell constituents often hides or obscurescomplicated substructure even when viewed in stereo. Theproblem of overlap in thick sections was overcome by eitherchoosing a section thickness "in accordance with the degreeof complexity of the structure to be observed" (7) or byselectively staining the structure of interest (reviewed in refs.3 and 6). The limited number of selective staining proceduresapplicable to electron microscopy restricts the usefulness ofthe latter approach, while the former approach necessitatesthe use of thinner sections that contain a more limited amountof 3D information.

In the study reported here, we use a computer-basedtomographic technique to obtain the quantitative 3D recon-struction of in situ newt lung cilia in thick sections. Althoughthe theory for tomographic 3D reconstruction is well estab-lished for electron microscopy (8-11), its primary applicationhas been the study of macromolecules or isolated smallmacromolecular assemblies (reviewed in ref. 11). Only a fewstudies report the reconstruction of larger cellular compo-nents such as chromatin (12, 13) and Balbiani rings (14, 15).Chromosomes, however, are not the ideal object with whichto assess the value of applying tomographic methods tothick-section reconstructions because their structure lacksclearly defined features, is not well established, and varieswith the isolation procedure. Resulting reconstructions can-not, therefore, be compared to a known structure. Thecilium, on the other hand, is well suited for developingtomographic methods and testing their applicability. Ciliahave been studied by a variety of approaches (e.g., refs.16-20), they contain a wealth of easily recognizable struc-tural features (reviewed in refs. 21 and 22), they can bestudied in situ, and their structure is stable and reproduciblyobserved in a wide variety of conditions. There also remainseveral controversial and undetermined features of ciliumultrastructure (e.g., refs. 16-18; 4, 20) that tomography mayultimately help to resolve.

MATERIALS AND METHODS

Sample Preparation. Lysed and reactivated newt lungmucociliary epithelial sheets were prepared, fixed, and em-bedded as described by Hard and Rieder (19). The demem-branated cilia were functionally unaltered. Sections approx-imately 250 nm thick were cut and stained for the HVEM asdescribed (1, 19).

Electron Microscopy. Each tilt series was recorded with anaccelerating voltage of 1 MV using the Wadsworth Center'sAEI EM7 HVEM. All micrographs were recorded at 20,000xusing DuPont Lo'dose mammography film. The response ofthis film to 1-MV electrons has been characterized by Kingand Parsons (23). Those cilia chosen for reconstruction hada typical appearance with no evidence of fragmentation, anorientation approximately perpendicular to the section plane,and no neighboring material that would overlap the structureat high-tilt angles. The specimen was tilted on a single-axis tiltstage designed for the HVEM by Turner and Ratkowski (24).Each tilt series was recorded in successive 1- or 2-degreeintervals starting from the maximum negative tilt angle ofabout -54° and finishing with a maximum positive angle ofabout 500. To minimize the magnification and rotationalchanges caused by the use ofa noneucentric stage, specimenswere chosen that were near the tilt axis of the stage.

Abbreviations: HVEM, high-voltage electron microscope; 3D, threedimensional.

9040

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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The tilt axis direction was determined by using recogniz-able features in several cilia as fiducial markers. Magnifica-tion changes in the tilt series were detected by measuring thedistance between fiducial markers that lay along a lineparallel to the tilt axis. Rotational changes in the series weredetected by measuring the angle this line made to the edge ofthe micrographs. From high-negative to high-positive tiltangles, the magnification was found to vary by 2.5%, and therotational alignment drifted smoothly by 60. Thus, all imageswere found to be rotationally aligned to within ±30 of the 00

image.To minimize radiation-induced changes in the specimen

during data collection, the specimen was preirradiated forabout 5 min, and the tilt series was then recorded with aminimal exposure to the specimen. Minimal exposure wasaccomplished by the use of low magnifications, mam-mography film and off-sample focusing. Each image wasrecorded with approximately 210 e/nm2. A careful check ofthe digitized images showed that, at this exposure level, boththe minimum and the maximum OD levels (relative to the foglevel) found on each micrograph were within the linear rangeof the mammography film.Image Processing. The micrographs of each tilt series were

digitized with a Perkin-Elmer flatbed microdensitometerusing a 50-grm scanning step that yields a 2.5-nm pixel size.All computations were carried out using the SPIDER imageprocessing software system developed by Frank et al. (25).The resolution of the micrographs was checked by digitizingto a 1.25-nm pixel size, a micrograph showing an axial viewof a cilium. Across the boundary between background andheavy stain, the digital image changed from maximum tominimum OD values within 4 pixels. This result indicates thatthe resolution of our micrographs is better than 5 nm.

Translational alignment of the digital tilt series images(relative to an approximately centered 00 image) was accom-plished using a cross-correlation procedure (26). The 3Dreconstruction was carried out by a weighted back-projectionmethod (9, 11), and the resultant reconstruction was con-tained in a volume of 128 x 128 x 128 voxels (volumeelements). The reconstruction was then low-pass filtered inFourier space to the calculated resolution limit (8) using a

filtering function with a Fermi distribution profile (27). Thisfunction produces a smooth cutoff, thereby reducing artifactsin the final result. A surface-shading representation devel-oped by Radermacher and Frank (28) was used to view the 3Dreconstruction.

RESULTS

We have collected five tilt series of cilia in thick section andtwo of these have been carried through the full 3Dtomographic reconstruction procedure. One of the recon-structions, which is representative ofboth, is presented in fullin this report. The tilt series used to calculate this recon-struction is shown in Fig. 1. Each of the 53 projections in thisseries has been rotated to align its y axis (vertical in Fig. 1)to the specimen-tilt axis, normalized so that the average ODis the same for all of the projections, and translationallyaligned relative to the 00-tilt projection.The major factor limiting the resolution of a 3D recon-

struction from projections is the number of views available.For a single-axis tilt series with even angular increments, asused in our reconstruction, the resolution may be calculatedusing the formula of Crowther et al. (8). However, this valuefor the resolution applies only in the direction perpendicularto the tilt axis and parallel to the specimen plane (x axis)because the full angular range of -90° to +90° is not availablein electron microscopy due to geometric limitations. Theresolution in the direction perpendicular to the specimenplane (z axis) is degraded (29). In the present example, whichuses an angular increment of 2° and an angular range of -54°to +50°, the resolution was calculated to be 12 nm in the x

direction and 20 nm in the z direction. Because many of thecomputational steps involved in the reconstruction proce-dure may degrade the resolution of the original data, theresolution of the micrographs used should be better by a

factor of 1.5-2.0 than the resolution expected in the finalresult. Thus, to achieve a 12-nm resolution in the final 3Dreconstruction, the micrographs should have a resolution thatis better than 6-8 nm. We estimate that the resolution of ourmicrographs is better than 5 nm. Resolution in micrographscan be lost, however, when the information is converted intodigital form. To prevent this, the sampling step size must beno larger than half the smallest distance to the resolved (30),or 3-4 nm in the present example. The sampling may bechosen to be finer for the visualization of the result and theminimization of cumulative calculation errors. However, a

finer sampling grid does not improve the resolution of theresult, beyond the limit set by the number of projections, buthas the sole effect that details that can be interpreted withconfidence are represented by a larger number of volumeelements. In the present study, we used a sampling size of 2.5nm.

FIG. 1. The tilt series (afteralignment) usedforthe tomograph-ic 3D reconstruction shown inFigs. 2-4. The tilt range of theseries is from -540 to 500, and themicrographs were recorded at 20intervals. The 53 images in thisgallery are 128 x 128 digital arrayswith a pixel size of 2.5 nm. Thecilium chosen for the tilt serieswas embedded with its cylindricalaxis about 9° from normal to thesection plane and, for this reason,the 80 and 100 images rather thanthe 00 image appear as the axialview (marked with *).

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9042 Cell Biology: McEwen et al.

FIG. 2. A stereo view of the3D reconstruction represented asa shaded surface. This surfacerepresentation has the effect ofreversing the contrast (compare toFig. 1). The cilium shown wasreconstructed from a 250-nm thicksection, and a central 125-nm por-tion of this depth is shown here.

Because the data are always sampled at a resolution finerthan is required by the final resolution limit, these recon-structions contain details that are not supported by theexperiment and do not correspond to structural features (11).To eliminate these details, we have applied a 3D Fourier filterthat limits the resolution to 12 nm (see refs. 11 and 27 for adiscussion of filtering 3D reconstructions).A shaded surface representation of the reconstruction is

displayed in Figs. 2-4. In this representation, a selectedsurface of the 3D density distribution is defined by a thresh-old value. A viewing plane is chosen, and shading is appliedto each element of the surface according to its distance fromthis plane and according to its inclination to a virtual lightsource. For cilia, the threshold level that defines the objectboundary can be determined by trial and error so that familiarstructural features, such as dynein arms and radial spokes,appear with adequate volume but are still distinct fromneighboring material. For an object whose structure is notwell known, the optimal threshold should be determined froma display of a contoured section through the reconstruction.The optimal threshold density level lies in the region ofgreatest density change in the transition from stained tounstained material (31).The diameter of the reconstructed cilium shown in Fig. 2

measures 220 nm. The counterclockwise attachment ofdynein arms to outer doublet microtubules and the slightskew of these doublets establishes that the cilium shown is

being viewed from tip to base (21, 22). Dynein arms, radialspokes, and the central sheath are all clearly visible, eventhough the resolution of this reconstruction is limited to 12nm. However, because these structural elements are only 5-7nm in diameter, they appear blurred, and their exact positionsin the reconstruction are uncertain.A portion can be selected ("windowed") from the recon-

struction and rotated to change the direction from which it isviewed as is illustrated in Fig. 3. Three cuts were used toproduce this figure. One was used to cut away the right sideofthe reconstruction so that the internal features ofthe ciliumwould be visible in the rotated views. The other two wereapplied to the ends of the cilium, perpendicular to itscylindrical axis, to eliminate artifacts at the boundaries of thereconstructed volume. These artifacts arise because thereconstruction was calculated from a tilt series that did nothave the full 180-degree angular range. After windowing, thereconstruction was rotated about the y axis (vertical axis) togenerate a gallery in which neighboring images form stereopairs. Once one stereo pair is fused, the whole gallery isperceived as a stereo array showing the structure rotatedfrom 00 to 90°. The rotation axis used in Fig. 3 correspondsto the tilt axis of the original projections. Each of the first fivestereo pairs in Fig. 3, therefore, roughly correspond to one ofthe images in Fig. 1. However, the views in Fig. 3 are notprojections, and structural details are no longer superim-posed as in Fig. 1.

FIG. 3. Array of overlapping ste-reo pairs showing a portion of thereconstructed cilium in different ori-entations. Material was cut away sothat internal features of the ciliumwould be visible in the rotated viewsand artifacts would be eliminatedfrom the boundaries of the recon-

_ft9 struction. The depth of the ciliumsegment shown in this gallery is 170nm. The windowed reconstructionwas rotated about the y axis (verticalaxis), from -5.13°to 95.130 in 11.250increments, to obtain the views

s 33:shown (the views at the end of the firstand second rows are repeated at thebeginning of the second and thirdrows, respectively). Neighboring im-ages of this gallery form stereo pairsand, once one pair is fused, the wholegallery becomes visible as a stereoarray. Nine distinct stereo views rep-resent the structure in the range from

_0 to 900 in 11.250 increments. Arrowsindicate the longitudinal repeat of ra-dial spokes attached to outer doublemicrotubule 1.

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The periodicity ofradial spokes connected to outer doublet9 is shown by arrows in Fig. 3. The periodic attachment ofspokes to outer doublets 1 and 6 can also be discerned, buta less obstructed view of the spokes attached to doublet 1 isseen when the window is placed deeper into the cilium (Fig.4A). Periodic attachment of material to central pair microtu-bule 3 is evident in Fig. 4B where the reconstruction wasrotated 450 before windowing. Even though this materialappears to be attached to the central pair microtubule, itsaverage spacing of 30 nm suggests that it does not representcentral sheath projections but rather spoke heads, eithersingle or attached to central sheath projections. Finally, aview of the cilium outer surface is shown in Fig. 4C. In thisview, the outer doublet microtubules are distinct, and theperiodic arrangement of dynein arms is indicated althoughnot clearly resolved.

DISCUSSIONTo fully exploit the potential of tomographic 3D reconstruc-tion methods in cell biology, electron microscopes operatingin the high or intermediate voltage range are required so thatthick and semi-thick sections can be imaged. It is alsonecessary to record an extensive tilt series, using 1- or

2-degree intervals, to obtain an adequate sampling of the

A S _a :

FIG. 4. Three additional stereo pairs representing different ori-entations and cutting windows. The small key to the left of eachstereo pair indicates, in face-on view, the orientation of the ciliumand the placement of the cutting surface chosen for each represen-tation. (A) The window was placed so as to cut between the centralpair microtubules. Arrows indicate radial spokes attached to outerdoublet microtubule 1. (B) The reconstruction was rotated clockwise450 about the cylindrical axis ofthe cilium before windowing. Arrowspoint to material appearing with a periodic attachment to central pairmicrotubule 8. (C) The reconstruction was rotated in the oppositedirection about the vertical axis to reveal the outer wall ofthe cilium.

structure (8, 11), Although a sampling limitation to resolutionis introduced by the digitization of the electron micrographs,the resolution of tomographic reconstructions is generallylimited by the number of projections used and not bydigitization. In our cilia reconstructions, the resolution limitis set at 12 nm by the number of projections availablecompared with a 5-nm limit set by digitization. We stress theimportance of filtering the reconstruction to the theoreticalresolution limit so that only structural features supported bythe experimental data are represented. Representations ofthe results where this step has been omitted (14, 15) maycontain artifacts at higher resolution.For the validity of our reconstruction method, it is critical

that the electron micrographs present true projections of thestructure. Of possible concern is the lateral spread of elec-trons, due to chromatic aberration and multiple scatteringthat would destroy the linear relationship between object andprojections and limit the interpretable resolution. However,for the section-thickness range used in this study (0.2-0.3Am), multiple scattering in plastic results in lateral diffusionof less than ± 1.5 nm, and the effect of chromatic aberrationis even smaller (M. Isaacson, personal communication).Other possible technical limitations to the resolution of the

reconstruction arise from thinning of the plastic sections inthe electron beam (32) and the use of a noneucentric stage. Asdescribed, the change in magnification and the image rota-tion, due to use of a noneucentric stage, were determined tobe 2.5% and ±30, respectively. Since the correlation methodsused align the projections to a center of mass, both of theseerrors have their maximal effect at the periphery of thestructure. The maximal errors were calculated to be 3 nmfrom the magnification change and 6 nm from the imagerotation. Since neither of these is close to the 12-nm resolu-tion of the reconstruction, we did not correct for either effect.Thinning of the sections was estimated by comparing the

lengths of the -300 and +50° tilted images. These images aretilted ±40° from the axial view of the cilia (which occurs ata + 100 tilt of the section). Although the exact length of thecilia is hard to determine in tilted views, it was found to be10% larger in the -30° view than the +500 view. Themagnitude of section thinning can also be estimated from thedepth of the mass of the reconstructed volume. This is alsodifficult to determine because the use of an incomplete tiltrange in the reconstruction results in a blurring of the top andbottom boundaries. Nevertheless, we were able to estimatethe depth of the reconstruction to be 215 nm, which wouldindicate a 14% thinning of the section during the exposure.Thus, if the sections shrink uniformly all longitudinal mea-surements (e.g., radial-spoke periodicities) will be 10-15%shorter than their actual values.Our reconstructions agree well, within their resolution

limits, with the established features of cilia ultrastructure.The central pair and outer double microtubules, the dyneinarms, the radial spokes, and the central sheath are all readilyidentified (Figs. 2-4). The central pair microtubules appearfused in many views, but this is because their walls are onlyseparated by 9 nm whereas the resolution of the reconstruc-tion is 12 nm. That the radial spokes in newt lung cilia formthe more common triplet pattern of 3 spokes per 96 nm isindicated by the measurement of a longitudinal periodicity of90-96 nm. This had not been previously determined for newtlung cilia, and our values agree well with measurements fromcilia of other species (reviewed in refs. 21 and 22).A surprising feature in the reconstruction is that the 24-nm

longitudinal repeat of the dynein arms is not more clearlyvisible on the outer cilium wall (Fig. 4C). A partial reason forthis is the degradation of resolution, to about 20 nm, in thelongitudinal (z axis) direction due to the use of a tilt range ofless than 1800 (29). A conical tilting geometry would help toreduce this limitation, as would obtaining higher tilt angles

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9044 Cell Biology: McEwen et al.

such as 600 or 650 (11, 29). However, this anisotropicresolution limitation cannot be the full explanation, since thelongitudinal repeat of the radial spokes, which is close to 24nm, is well resolved. We believe that the main reason for theabsence of a distinguishable repeat is the in situ configurationof the dynein arm. Several studies show that dynein is a thinstructure that is considerably spread out along the z-axisdirection (16-18). At the resolution of this reconstruction,such a structure would produce a blurred image that may notbe distinctly visible against the complex background of thecilium wall.We have shown in this report that tomographic techniques

are capable of rendering a comprehensive 3D representation,including that of internal substructures, of large complexorganelles such as cilia. At the present level of developmentthe technique should be applicable to a variety of structuralproblems in cell biology. Higher resolution (i.e., 5-7 nm) isrequired, however, to address unresolved issues of ciliaultrastructure such as the arrangement of central sheathcomponents (22), the dynein arm configurations (16-18), thehelical handedness of the radial spoke arrangement (4, 20),and the structure of the basal body and its connection to thecilium (19). Feasible approaches to increasing the resolutionof the reconstructions include the use of thinner sections,more projections (a 1'-tilt interval), different sample orien-tations, and the inexact reconstruction method of Crewe etal. (33).We thank Dr. R. Hard for supplying us with reactivated and

embedded newt lung material. We are grateful to Dr. MichaelIsaacson ofCornell University for a discussion ofmultiple scattering.This work was supported by Biotechnology Resource-Related GrantNIH-RR02033 (to J.F.) and by Biotechnology Resource Grant PHS01219, awarded by the Division of Research Resources, PublicHealth Service/Department of Health and Human Services, tosupport the Wadsworth Center's HVEM as a National Biotechnol-ogy Resource Facility.

1. Rieder, C. L., Rupp, G. & Bowser, S. S. (1985) J. ElectronMicrosc. Technol. 2, 11-18.

2. Gaunt, W. A. & Gaunt, P. N. (1978) Three-Dimensional Re-construction in Biology (University Park Press, Baltimore).

3. Rieder, C. L. (1981) Methods Cell Biol. 22, 215-249.4. Goodenough, U. W. & Heuser, J. E. (1985) Cell Biol. 100,

2008-2018.5. Tanaka, K. (1980) Int. Rev. Cytol. 68, 97-109.6. King, M. V., Parsons, D. F., Turner, J. N., Chang, B. B. &

Ratkowski, A. J. (1980) Cell Biophys. 2, 1-95.7. Nagata, E., Hama, K. & Porter, K. R. (1969) J. Electron

Microsc. 18, 106-109.

8. Crowther, R. A., DeRosier, D. J. & Klug, A. (1970) Proc. R.Soc. London Ser. A 317, 319-340.

9. Gilbert, P. F. C. (1972) Proc. R. Soc. London Ser. B 182,89-102.

10. Hoppe, W. & Hegerl, R. (1980) in Computer Processing ofElectron Microscope Images, ed. Hawkes, P. W. (Springer,Berlin and New York), pp. 127-185.

11. Frank, J. & Radermacher, M. (1986) in Advanced Techniquesin Biological Electron Microscopy, ed. Koehler, J. (Springer,Berlin and New York), pp. 1-72.

12. Subirana, J. A., Sebastian, M.-G., Radermacher, M. & Frank,J. (1983) J. Biomol. Struct. Dyn. 1, 705-714.

13. Subirana, J. A., Sebastian, M.-G., Aymami, J., Radermacher,M. & Frank, J. (1985) Chromosoma 91, 377-390.

14. Olins, D. E., Olins, A. L., Levy, H. A., Durfee, R. C.,Margle, S. M., Tinnel, E. P. & Dover, S. D. (1983) Science220, 498-500.

15. Olins, A. L., Olins, D. L., Levy, H. A., Durfee, R. C.,Margle, S. M., Tinnel, E. P., Hingerty, B. E., Dover, S. D. &Fuchs, H. (1984) Eur. J. Cell Biol. 35, 129-142.

16. Johnson, K. A. & Wall, J. S. (1983) J. Cell Biol. 96, 669-678.17. Goodenough, U. W. & Heuser, J. E. (1984) J. Mol. Biol. 180,

1083-1118.18. Avolio, J., Lebduska, S. & Satir, P. (1984) J. Mol. Biol. 173,

389-401.19. Hard, R. & Rieder, C. L. (1983) Tissue Cell 15, 227-243.20. Baccetti, 13., Porter, K. R. & Ulrich, M. (1985) J. Submicrosc.

Cytol. 17, 171-176.21. Warner, F. D. (1974) in Cilia & Flagella, ed. Sleigh, M. A.

(Academic, New York), pp. 11-37.22. Gibbons, I. R. (1981) J. Cell Biol. 91, 107s-124s.23. King, M. V. & Parsons, D. F. (1977) Ultramicroscopy 2,

371-384.24. Turner, J. N. & Ratkowski, A. J. (1982) J. Microsc. 127,

155-159.25. Frank, J., Shmikin, B. & Dowse, H. (1981) Ultramicroscopy 6,

343-358.26. Guckenberger, R. (1982) Ultramicroscopy 9, 167-174.27. Frank, J., Verschoor, A. & Wagenknecht, T. (1985) in New

Methodologies in Studies of Protein Configuration, ed. Wu,T. T. (Van Nostrand Reinhold, New York), pp. 36-89.

28. Radermacher, M. & Frank, J. (1984) J. Microsc. 136, 77-85.29. Radermacher, M. & Hoppe, W. (1978) Proc. Ninth Int. Cong.

Electron Microsc., ed. Sturgess, J. M. (Microscopial Soc.Canada, Toronto), Vol. 1, pp. 218-219.

30. Shannon, C. E. (1949) Proc. IRE NY 37, 10-21.31. Verschoor, A., Frank, J., Radermacher, M., Wagenknecht, T.

& Boublik, M. (1984) J. Mol. Biol. 178, 677-698.32. Bennett, P. M. (1974) J. Cell Sci. 15, 693-701.33. Crewe, A. V., Crewe, D. A. & Kapp, 0. H. (1984) Ultrami-

croscopy 13, 365-372.

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