Structural analysis of macromolecular assemblies by image reconstruction from electron micrographs.

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Annu. Rev. Biochem. 1975.44:161-182. Downloaded from www.annualreviews.org Access provided by University of California - San Francisco UCSF on 02/03/15. For personal use only.

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STRUCTURAL ANALYSIS OF MACROMOLECULAR ASSEMBLIESBY IMAGERECONSTRUCTION FROM ELECTRONMICROGRAPHS

:878

R. A. Crowther and A. Klu9 Medical Research Council Laboratory of Molecular Biology,

Cambridge CB2 2QH, England

CONTENTS INTRODUCTION............................................................ Specimen Preservation and Attainable Resolution ...................................... BACTERIOPHAGE T4 ........................................................ Polyheads : Translational Filterin 9 ................................................. Baseplates: Rotational Filteriny ................................................... Phage Tail: Three-Dimensional Reconstruction ....................................... TOBACCO MOSAIC VIRUS: SEPARATE IMAGING OF PROTEIN AND STAIN ....... HEMOCYANIN .............................................................. THE ACTIN-TROPOMYOSIN-MYOSIN COMPLEXFROM MUSCLE ................ SPHERICALVIRUSES ........................................................ CONCLUDING REMARKS ....................................................

161 163 164 164 166 168 171 174 176 177 180

INTRODUCTION Electron microscopyand X-ray diffraction have revealed a wealth of information aboutbiological structures. Thetwo techniquesare frequently complementary. X-ray diffraction is particularly applicable to specimensthat exhibit a high degree of regularity. Theintensity distribution of the diffraction pattern gives information aboutthe periodicities present in the specimen,whichcan frequently be preserved in its native state in an aqueousmedium. Furthermore, if the phasesof the diffraction pattern can be determined, for example, by using isomorphousheavy atom derivatives as in protein crystallography, a three-dimensional image of the specimen can be computedby Fourier synthesis. This mayhave atomic resolution if the order in the specimenis sufficiently good.It is the phasedetermination


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can be used on materials unsuitable for X-ray diffraction. The objective lens of the microscope combines the diffracted beamsfrom the specimen while preserving their relative phases. This phase information is therefore recorded in the intensity distribution of the image and may be retrieved from it optically or computationally. It wouldbe lost if only the electron diffraction pattern were recorded. The image given by the microscope, however, suffers from a numberof limitations, including distortion of the specimen during preparation and damageduring observation. In addition, artificial meansof contrast enhancementhave to be used, as the majority of atoms in biological specimens have an atomic number too low to give sufficient contrast on their own. Furthermore, the depth of focus of the conventional microscope is several thousand angstroms, so that features at different levels in the specimenare superimposedin the two-dimensional image, which is thus essentially a plane projection of the specimenin the direction of view (1). All these factors limit the structural information that can be obtained by direct inspection of the image. Some of these drawbacks may be overcome by various forms of image processing that exploit the spatial symmetriesthat are frequently exhibited by the native biological structure or that can be induced by crystallization or by aggregation. Morereliable structural information can then be retrieved from the image by techniques analogous to those used in X-ray diffraction analysis. Broadly, there are two kinds of analysis performed, namely two-dimensional spatial filtering and three-dimensional image reconstruction. The former may be applied to translationally or rotationally symmetric images and provides an average two-dimensional image of the repeating unit of the structure by combining the manyimages present in the array. This averaging may be realized by direct optical superposition or more reliably by filtering of the optical or computed diffraction patterns. For three-dimensional image reconstruction a series of twodimensional images of the specimen, viewedfrom different directions and therefore giving different projections, must be combined to generate a three-dimensional ¯ image of the specimen, again showingan average of the repeating unit. An important feature of these methods is that the initial step consists of a quantitative assessmentof the reliability of a particular imagebased on its degree of symmetry. Images of well-preserved specimens can then be cross-correlated to check their degree of reproducibility. Finally, the best images that exhibit the maximumdegree of cross correlation may be combined to produce a best two- or three-dimensional image of the specimen. The unaided eye cannot perform such assessment and combination of different images. For example, stereoscopy cannot be used to disentangle the continuously varying density even in a perfect threedimensional specimen viewed in transmission. In such a case it can be shown mathematically that a pair of images is not sufficient to allow unambiguous reconstruction, and perceptually we are not accustomed to viewing images of spatially varying translucent objects. The application of these reconstruction methods has in recent years helped to reveal the molecular architecture of various biological assemblies, such as muscle, viruses, and enzymecomplexes. Wedescribe a limited number of examples, which serve to demonstrate the power of the various techniques and the nature of the

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results they can give. Wedo not go deeply into the theory of reconstruction nor consider the merits of alternative approaches to the Fourier methods by which most results have so far been obtained. First of all, however, we consider briefly the crucial question of specimenpreservation.


Specimen Preservation

and Attainable

Resolution

In order to makethe specimenvisible in the conventional microstope, it is necessary to add heavy metal as an electron dense contrasting medium.Bulk specimens such as muscle may be embedded, sectioned, and stained. In such specimens the degree of preservation seldom extends muchbeyonda resolution of 100 A, although in one favorable case of insect flight musclea 48/~ spacing has been recorded (2). Sectioned crystals can give higher resolution. Alternatively the specimen may be frozen, fractured, and possibly etched, the resulting surface topography then being contrasted by heavy metal shadowing.Details in the range 50-100 A can be visualized, possibly even downto 35 A, as in polyheads for example (3). Finally, specimens may be deposited from solution and embeddedon the grid in a heavy metal salt such as uranyl acetate. Such contrasting is knownas negative staining (4), as the presence of biological material is inferred from the absence of stain. Thedegree of detail revealed is limited by the granularity of the stain and the fidelity with which it follows the surface of the specimen. Although limited to showing the envelope of the structure and accessible internal cavities, this form of contrasting is the most successful so far devised and typically details downto about 20 ,~ can be observed. As weshall see later, the stain serves not only to contrast the biological material but also to stabilize it, at least partially, during the dehydration and intense irradiation that it suffers in the microscope. In talking about the resolution present in an image, we actually meana number of rather different things. First of all, there is the point-to-point resolution, which is set by the electron optical properties and stability of the microscope.For modern instruments correctly operated this should be better than 3 A and is not limiting in the type of workconsidered here. Then, there is the degree to which individual macromoleculesare preserved during dehydration and irradiation and the fidelity with which their shape is mappedout by the stain. Finally, whenone is working with symmetrical structures, one has the problem of distortions in the long range order of the specimen. Whenone is combining data from the different subunits, it is this variation within individual subunits and the departures from their ideal symmetry-related positions which set a limit to the maximumspatial frequency that can usefully be recovered from the image. There will of course be higher spatial frequencies present, arising from the granularity of the stain and the support film. Thus when one speaks, for example, of an image containing information to 20 A, one meansthat spatial frequencies arising from the regular part of the image are detectable above the background noise only for spacings out to 20 A but not beyond. This spatial frequency cutoff can be converted to the classical Rayleigh criterion for resolving two equal pointlike features by multiplying by 0.61 in two dimensions or 0.72 in three. It is also important to note that the positions or changes in position of well-defined features in the image can be estimated much


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moreaccurately than this, possibly to about 0.1 of the spatial frequency cutoff. It is frequently observed for negatively stained specimens that the regular part of the information extends only to spacings of about the diameter D of the structure units in the array. This is not unexpected, since the stain is only mappingout the envelope of the subunit. If the subunit were spherical, its diffraction pattern (or "Airy sphere") would have its first zero at a radius lID and would be weakbeyond this. Thus, in negatively stained images of structures built from globular subunits, one would not expect to obtain muchinformation about spacings shorter than D. This is nevertheless sufficient to discover the packing geometryof the subunits and to maptheir gross shape. The limitation on the results arises from the specimen preparation and not from the reconstruction methods themselves. BACTERIOPHAGE

T4

The various parts of bacteriophage T4 display the applicability of a number of image processing techniques. The DNA-containinghead has a contractile tail with a complexbaseplate structure. The latter serves to attach the phage to the bacterium during infection. Changes in the baseplate trigger contraction of the tail and injection of the phage DNAinto the bacterium. Polyheads : Translational Filterin 9 The native head structure of T4 is difficult to study directly as it is rather smooth and its features are not strongly contrasted in negative stain. Moreover,the bulk of the tightly folded DNAis superimposed on the protein coat. Ghosts, that is heads from which the DNAhas been ejected, are generally poorly preserved and difficult to analyze. Someprogress has been madewith freeze etching on the closely related T2 phage, but the degree of detail in these images is limiting (3). There are, however, a numberof aberrant tubular structures, knownas polyheads, which are related to the native head structure and undergo transformations believed to mimic the complicated process of maturation associated with DNApackaging in the native head (5). These structures are easier to analyze than the native head. Figure la showsa negatively stained ~’coarse" polyhead(6). Thetubular structure has flattened so that the image is of two superimposed, approximately planar layers of protein molecules. This supcrposition plus the granularity of the support film obscures the individual subunits and their arrangement in the structure. Figure 1 b showsits optical diffraction pattern. A coherent optical processing system is used (7), in which the micrograph is illuminated by a laser and its Fraunhofer diffraction pattern recorded in the back focal plane of a lens. The spots occur in pairs, symmetrically related about the center of the pattern, and each pair arises by diffraction from a particular strong sinusoidal wavein the image. Pairs of spots near the center of the pattern arise from low spatial frequencies while spots further out come from increasingly higher spatial frequencies. For images with two-dimensionaltranslational periodicity the spots in the diffraction pattern lie on a regular lattice. The case shownhere closely approximates this situation, and the spots lie on two regular lattices related by an axial mirror line. The spots

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from the two layers are spatially separated, so by placing in the diffraction plane of the optical diffractometer an opaque mask with appropriate holes cut in it, the diffracted beams from one of the layers can be selectively recombined by a further lens to produce a filtered image of a single layer (8), as shown in Figure IC. Besides

Figure 1 (Top) Optical filtering of a coarse polyhead of bacteriophage T4. The centers of the hexagonal rings of subunits seen in the filtered image are approximately 100 .& apart. Figure 2 (Bottom) Computer filtering of a “fine” polyhead of bacteriophage T4, showing

different ranges of averaging. The hexagonal rings of subunits seen in (4are approximately 100 A apart.


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removing one of the layers, a large proportion of the aperiodic noise (that is the irregular part of the image, which gives the speckle between the main diffraction spots) has also been removed. In the filtered image the approximately hexagonal arrangementof individual protein subunits can be clearly seen. It is possible to perform the equivalent operations computationally (9, 10) digitizing the image and calculating its diffraction pattern or Fourier transform in a computer. This is useful in cases where the diffraction spots are close together or wherethe signal-to-noise ratio is particularly low. This is the case with so-called fine grained polyheads; an example is shown in Figure 2a. The filtered image is generated by setting the wholetransform to zero, except in small regions surrounding the diffraction maximaarising from one of the two layers, and then computing the inverse transform. The range of averaging that takes place in the filtering process is controlled by the size of these "apertures"; the smaller the apertures the greater the range of averaging. If the apertures were reduced to single sample points, a perfectly periodic filtered imagewouldresult. Figure 2b-d (9) shows a series of filtered images of Figure 2a in which the respective range of averaging is 3, 6, and 12 unit cells in the longitudinal direction and about half this laterally. Figure 2b resembles the best that could be achieved readily by optical filtering and is uninterpretable. In Figure 2d, however,,a sufficient number of different unit cells have been averaged to enable the fine hexagonal pattern of subunits to be discerned. The patterns are most readily seen at the bottom of the image, and once perceived, can be traced right along this image and also in Figure 2c. It is believed that the protein subunits in the coarse polyhead (Figure 1) have undergone cleavage and rearrangement in forming the fine polyhead of Figure 2. Similar changes occur during the packaging of the DNAinside the native phage head (5), which is thought to have a final structure resembling that of a fine polyhead. Becausethis final structure consists of small units rather uniformly distributed, the low spatial frequencies are very weak comparedwith corresponding terms for the coarse polyhead. The principal coiatributions therefore comefrom the region of high spatial frequencies, wherethe principal noise contributions also occur. Thus, extensive averaging is necessary if the underlying regular pattern is to be seen. Phage ghosts themselves do not provide a sufficiently large and regular specimenfor this averaging to be satisfactorily performed. Baseplates : Rotational Filteriny The baseplate of T4 is a complexstructure containing multiple copies of about a dozen different proteins (11, 12) and, as can be seen in Figure 3a, it appears possess sixfold rotational symmetry.It is not possible to analyze and filter images with rotational symmetryby optical diffraction, as the wanted and unwantedcomponents of the imageare not spatially separated in the diffraction pattern. However, it can be done fairly easily by computer (13). The image is again digitized and then numerically decomposedinto a series of functions representing harmonics of increasing angular and radial frequency. (These are analogous to the plane sinusoidal wavesthat give rise to the pairs of spots in the diffraction pattern of a



167

translationally periodic object ) By plotting the strength or power of the angular harmonics as a function of increasing angular frequency, we obtain a rotational power spectrum of the image which is analogous to the distribution of intensities in the optical diffraction pattern of a translationally periodic image and summarizes the results of the analysis in a convenient form. The power spectrum of the baseplate in Figure 3a is shown in Figure 3c (13). As expected, the harmonics that are multiples of 6 are much stronger than the other harmonics and it is reasonable to say that the image is predominantly sixfold, as is clear from direct inspection in this case. However, we can now recombine just those harmonics whose angular frequencies are multiples of 6 to resynthesize a rotationally filtered image (Figure 3h) The assumption here is that all those harmonics whose angular frequencies are not multiples of 6 arise from distortions, variable staining, and contributions from the support film. The total noise contribution will be reduced by a factor of 6 in this case. Rotational filtering has a number of advantages over the more straightforward technique of rotational superposition using photographic methods (14). In the latter a compound image is produced by superimposing m copies of the original image, each rotated successively by an angle 2n/m, about the supposed symmetry axis. Features related by m-fold or some multiple ofm-fold symmetry are preserved, while features with all other rotational symmetries are suppressed. The disadvantage of this method is that the determination of the symmetry number m and the assessment

Figure 3 Rotational filtering of baseplates of bacteriophage T4. (a) Extended baseplate, approximate diameter 500 8.(b) Sixfold filtered image of (a). (c) Rotational power spectrum of baseplate shown in (a). (d) Contracted baseplate, approximate diameter 550 A. (e) Sixfold filtered image of (d). Micrographs provided by Dr. J. King.


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of the quality of the image are not separated from the production of the final averaged image; only a subjective assessment is possible based on the appearance of the final image. Onthe other hand, the power spectrum such as that shown in Figure 3c enables us to measure the strength of the sixfold componentsand to see to what order or resolution they extend. A quantitative comparison of different images can then be made and the best chosen. Similar remarks apply to the comparisonof filtering (8)as against linear integration (15) of translationally periodic images. The filtered image (Figure 3b) shows that the baseplate has a strong hexagonal periphery with spikes at the corners. The central core is surrounded by hexagonal tracery whichis in turn connected to the periphery by a series of fine bridges. This complexity of structure is certainly consistent with the fact that it contains the dozen or so components found by genetic and biochemical analysis (11, 12). Preliminary image analysis of a number of structural mutants (J. King and R. A. Crowther, unpublished results) suggests that it may be possible to locate the positions of someof the gene products in the baseplate. It is also possible to get images of the baseplates in their contracted state (Figure 3d and e) from which one may be able to deduce what molecular rearrangement takes place on contraction and how this initiates the contraction of the tail structure, which is discussed in the next section. Phage Tail:

Three-Dimensional

Reconstruction

The tail of the T-even phages consists of a hollow core surrounded by a contractile sheath (Figure 4a), which is attached to the baseplate at one end and by a collar structure to the head at the other. The sheath contains a single type of protein subunit arranged in successive annuli whichare rotated with respect to one another, so that the subunits also lie along oblique helical lines. Onattachment to the host cell the baseplate triggers a contraction of the sheath whichrides up the core, causing the core to penetratc the host ccll wall and leading to the injcction of the phage DNA. The symmetryof the sheath can be analyzed (16, 17) by using optical diffraction (Figure 4b). The indexing enables the various strong features in the diffraction pattern to be ascribed to the front or back of the helical structure, in muchthe same way as the contributions from the two planar layers were separated in the case of polyheads.However,filtering of the helical tail structure (Figure 4c) (16) not lead to a simply interpretable image, as did the polyheads, because there is staining at more than one radius in the structure. The filtered image of a single side of the structure still shows a complicated superposition of diflbrent features and it is therefore necessary to undertake a three-dimensional imagereconstruction (16). The optical diffraction pattern records only the intensity of the diffracted beams from the various strong spatial periodicities in the image and not their relative phases, which fix the relative positions of these periodicities in the image. The relative phase information is of course used in optical filtering because the selected diffracted rays themselves are refocused by a lens to form the filtered image. However,it is possible to determinethe relative phases by computingthe diffraction


169


pattern as a complex Fourier transform. The complex numbers give the amplitudes of the various components and also their phases which are lost in optical recording of the transform.

Figure 4 (Top) Optical filtering of the tail of bacteriophage T4. The axial spacing of the annuli in the tail (a) is approximately 3X A, corresponding to the layer line marked 7 in (b). Fkgure 5 (Bottom) Models of three-dimensional reconstructions of ( o ) the extended tail of bacteriophage T4, diameter approximately 240 A. (b)Polysheath which closely resembles the contracted sheath, diameter approximately 300 A.


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The dill?action pattern from a helical structure consists of a series of horizontal layer lines, each arising from a particular set of families of helical grooves in the structure. Indexing of the pattern consists of determining the numberand pitch of the helices in each family. If there is a sufficiently large numberof subunits in the helical repeat, there will be only a single helical family contributing to each layer line in the neighborhoodof the meridian. This not only simplifies the indexing but also the process of three-dimensional reconstruction. For a helical structure with such high symmetrya single image suffices for the reconstruction. In physical terms, this is because a single imageof the specimenpresents manydifferent views of the repeating subunit. These views are, moreover, at knownrelative positions and equally spaced in angle. In the phage tail there are 42 subunits in the axial repeat, since each annulus contains six subunits and the whole structure repeats after seven annuli. There are, however,only 21 distinct views of the subunit, because two views of a subunit from opposite directions give the same projection. The two-dimensional computeddiffraction pattern or Fourier transform of the image is a central section of the three-dimensional transform of the threedimensional specimen. Wemay use the known helical symmetry, established by indexing the diffraction pattern, to generate uniquely from this single section the complete three-dimensional transform out to a limit set by the numberof distinct views of the subunit. A three-dimensional image of the specimen can then be computed by Fourier synthesis from this filled-in transform. In the computer implementation (18) the filling in of the three-dimensional ~ransform is implicit in the mathematical formulation as a Fourier-Bessel transform, which links the amplitude and phase of each layer line contribution to the strength and position of a particular helical family in the three-dimensional structure. The threedimensional image is built from a superposition of a number of these helical families. Close to the meridian on each layer line there is in general only a single helical family contributing, and the necessary information about it can be retrieved from a single view of the structure. As we moveaway from the meridian, other families start to contribute and it is not possible to sort out from a single view the various contributions on each layer line. It is this overlapping that limits the resolution attainable from a single view: the more subunits in the helical repeat, the further out the overlapping starts and the higher the resolution attainable. With more views this limitation can be overcomein a waysimilar to that described later for spherical viruses. A reconstruction of the extended phage tail (16; L. A. Amos,unpublished), combining data from several particles to a cutoff of about 30 A, is shown in Figure 5a. There is a hole of about 15 ~ radius along the axis of the particle and then more or less continuous density representing the tail core which extends to about 45 A radius. Separating this from the main bulk of the sheath is a set of six helical tunnels with bridges between, which link the sheath with the core. At outer radii from about 90-120 A, the surface is divided up apparently into subunits by two strong families of hclical grooves. The contracted sheath itself is too short to make a good reconstruction. However, an aberrant structure, polysheath, made from sheath subunits assembled in a way believed to resemble closely the normal contracted sheath, has been analyzed

IMAGERECONSTRUCTION FROMELECTRON MICROGRAPHS 171 (L. A. Amos,unpublished results) (Figure 5b). A comparisonof the two structures taken together with Moody’sanalysis (19) of the geometrical path of contraction enables the subunit to be tentatively dissected out and its change of configuration to be followed (L. A. Amos,in preparation).


TOBACCO MOSAIC VIRUS: PROTEIN AND STAIN

SEPARATE

IMAGING

OF

The coat protein of tobacco mosaic virus (TMV)can be polymerized in a number of polymorphicforms. Oneof these, the stacked disc aggregate (20), is a long rodshaped particle madefrom discs of protein, successive discs being rotated by 3/10 of2n/17 radians. Thedisc consists of two rings, each containing 17 protein molecules, arranged in a polar manner. Three-dimensional image reconstruction shows that the subunits in the two rings have different conformations. The stacked disc rods have been used for testi~ag a new phase contrast imaging technique, using an electrostatic phase plate (21) that enables the contributions of stain and protein to the image to be separated. This has in turn provided important newinformation on the nature of negative staining and the behavior of the stain when exposed to the beam(22, 23). The electrostatic phase plate (21) consists of an aperture spanned by a thin, poorly conductingthread, whichis placed in the diffraction plane of the microscope. Its effect is analogous to that of an absorbing phase plate in light microscopy. The thread cuts out a large proportion of the unscattered beam, and the charge distribution on it gives an electric field which imparts a more or less uniform phase shift to the various scattered beams. In addition the aperture cuts out most of the electrons scattered by the heavymetal stain. The net effect of all these factors is that the principal contrast in the phase plate image arises from the biological material (24), unlike the conventionalbright field imagein whichthe contrast arises predominantly from the stain. Figure 6a and b shows the appearance of the two types of image. Weconsider first the phase plate images (22). A number of good stretches particles, selected by optical diffraction, were further analyzed by computer. After the relative positions and orientations had been determined by searching for the best correlations betweenthe various sets of layer line data, an average transform wascomputed,in whichthe consistent parts of the data from five different transforms were averaged. This average transform closely resembled the X-ray diffraction pattern from oriented sols of stacked discs (25), suggesting that the structure imaged by the microscope is very similar to the native structure existing in solution. A cylindrically averaged structure was computed(Figure 6c) from just those parts the transform that do not involve azimuthal variations, including data out to spacings of about 8.5 .&. There are striking differences between the two layers comprising the disc, the upper running radially while the lower is bent into a zigzag. This gives rise to a local pairing of the layers within a disc at outer radii but between discs at inner radii. There are significant departures from mirror symmetrybetweenthe two layers, confirming the polar nature of the disc. A model of a full three-dimensional reconstruction is shown in Figure 7 (22).


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Figure 6 (Top) Stacked disc rods of tobacco mosaic virus protein, approximate diameter 180 p\. (a) Bright field image in which contrast comes mainly from the stain. (b) Phase plate image in which contrast comes mainly from the protein. Note that the oblique helical families corresponding to azimuthally varying harmonics are much more visible in (b) than (a). (c) Section through a cylindrically averaged reconstruction from phase plate images, showing differences between the two layers of subunits forming the disc. The axis of the particle is at the left. Figure 7 (Bottom) Model of a three-dimensional reconstruction of the stacked disc rod of tobacco mosaic virus protein. The pictures show a cross section and a view of the outside. There are clear differences in conformation between the subunits in the two layers forming a disc (see text).



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The shapes of the subunits in the two layers are again rather different, the layer markeda running approximate!y radially while the one marked z has a pronounced zigzag. At outer radii the tips of the subunits in the two layers arc separated by grooves of different shape; those in the a layer are broad and shallow while those in the z layer are narrow and angled. By studying various contour mapsof the reconstruction sectionedin different ways,it is possible to follow the course of the subunits in the two layers and to make a tentative correlation between features commonto the two conformations (22). Three such features, two knobs marked u and v and a ridge marked w, are shown in Figure 7. If these identifications are correct, it appears that the conformation in the a layer could be generated by a rotation and slewing of the heads of the subunits in the z layer accompanied by a reduction of the axial zigzag. Comparingthe average computed transform on which this reconstruction is based with the X-ray diffraction pattern from stacked disc rods in solution, it appears that the conformationaldifferences between the two layers of subunits, although existing in solution, may have been somewhat exaggerated in the negatively stained preparation. It is the conformation of the subunits on the a layer that seems most similar to the layer closest to the dyad axis in the structure determinedby X-ray diffraction of crystals of discs (26). This turn is most like the structure of subunits in the virus itself, again as determined by X-raydiffraction (27). There are two significant discrepancies between the reconstruction from phase plate images just described and the reconstruction made earlier (28) from conventional bright field images whichshowthe stain rather than the protein. There is a much weaker axial modulation at the outer surface of the bright field reconstruction, and the slewing of the outer parts of the subunits in the two different rings is muchmore similar in the bright field reconstruction. By analyzing the transforms of bright field imagesof negatively stained specimensexposedto different electron doses, Unwin(23) has shownthat, although the bright field image taken with minimalexposure is similar to the phase plate image, increasing irradiation produces consistent and reproducible changes. A difference reconstruction between the images of a weakly and strongly irradiated specimen shows that the changes occur mainly at the inner and outer surfaces of the particle and are accompanied by an increase in the volumeunpenetratcd by stain. This is explained by a contraction and migration of the stain. Onirradiation the uranyl acetate is converted to the considerably more dense UO2,causing a linear shrinkage of about 15~. Shrinkage alone does not account for all the observed changes, however, and Unwinsuggests that there maybe surface energy effects whichtend to cause the stain to round up. Together these effects can explain the difference between the phase plate reconstruction and the strongly irradiated bright field reconstruction. It is important to note that the contraction and migration of the stain is an orderly affair not accompaniedby significant loss of resolution, so that the biological material must be morphologically preserved to act as a template for the movementsof stain. What is being seen is probably somehighly crosslinked derivative of the original biological material but this must nevertheless bear a close morphologicalsimilarity to the native material because of the close resemblance between the transform

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& KLUG


of the phase plate image and the X-ray diffraction pattern. The stain supports the carbonaceousmaterial while this initial crosslinking to form a morestable radiation product takes place. The latter then serves as a template for the stain movement that occurs on further irradiation. It is clear that caution is necessaryin interpreting bright field images of negatively stained specimens and that minimal exposure (29) should be used wheneverpossible. HEMOCYANIN Hemocyaninsare copper-containing respiratory proteins which occur dissolved in the hemolymphof many invertebrates. Gastropod hemocyanins have molecular weights of about 7-8 x 106 and undergoa series of association-dissociation reactions, depending on pH and ionic strength. Electron microscopy shows the particle to be cylindrical with a diameter of about 300 A and a length of about 360 A. The first dissociation into half particles occurs in a plane perpendicularto the cylindrical axis. Rotational filtering of half particles (30) showsthat at an inner radius there a strong fivefold modulation in density, whereas the outer part is dominatedby a tenfold modulation (Figure 8). In whole particles the central fivefold modulation, though still present, is considerably reduced in strength comparedwith the half particles, and the outer part remains tenfold in character (Figure 8). The reduction in the strength of the fivefold componentsoccurs because the two half particles comprisinga wholeparticle are not in rotational register. The whole particle probably therefore has point group symmetry 52 but this would only allow three-dimensional reconstruction to a cutoff of about 100 A from a single view. However, taking advantage of the tendency of some hemocyanins to aggregate end-to-end, linear polymerswere formed(Figure 9a) (30). The transform of the image showeda set of layer lines characteristic of a helical arrangement with an axial repeat of about 1150 A, which corresponds to the length of three particles, successive particles being rotated by 120° . There are 15 independentprojections of the asymmetric unit within the repeat distance of the polymer, which is therefore suitable for three-dimensional reconstruction to a cutoff of 50 A. Tilting experiments showedthat central rows of particles lying within arrays, such as those shownin Figure 9a, were better preserved than either isolated rows or rows on the edges of arrays. This could be judged both by measuring the apparent widths of the particles in a tilt series and by following the phase variations in the Fourier components on tilting. Four independent reconstructions were made, which were very similar to one another, so an average reconstruction was computed after the relative orientations of the individual polymers had been determined by comparingthe relative phases in the transforms. In all reconstructions the halves of the particle lying on either side of the equator appeared to be related by twofold axes normal to the cylindrical axis, as would be expected from the associationdissociation reactions. The presence of twofold axes was therefore tested for in each of the four transforms individually and also in the average. It was found that the averaged data were more nearly twofold related than any of the individual



175

polymers, leaving little doubt that horizontal twofold axes are present to the resolution of the micrograph. This twofold symmetry was therefore imposed and a final map computed having a cutoff of about 30 8, axially and 50 8, radially. Figure 9b shows a wooden model of a single particle and Figure 9c a section through the cylindrically averaged structure (30). The structure consists of a hollow cylindrical drum closed by fivefold material forming a collar and a central cap. The wall of the drum consists of six layers, each with approximate tenfold rotational symmetry, so that there are 60 morphological units which are of six crystallographically distinct types (two in each layer ofthe halfparticle). They are, however, of similar size, shape, and orientation and appear to be quasi-equivalent. The relative rotation between successive layers, whether within or between half particles, is approximately the same, suggesting that there are approximate twofold axes relating the various HALF PARTICLE

WHOLE PARTICLE

R O T A T W L FREOUENCV

ROTATKNAL FREWENCV

all

(a>

(b>

(0

Figure 8 (Tup) Rotational power spectra and rotationally filtered images of half and whole particles of gastropod hemocyanin. Particle diameter approximately 300 A. Figure 9 (Bottom) Gastropod hemocyanin. (a) Negatively stained array of particles. ( h ) Model of a three-dimensional reconstruction of a particle. (c) Section through a cylindrically averaged reconstruction on the same scale as (b).

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layers, in addition to the strict twofolds relating half particles. This wouldin turn imply twofold axes within each layer, suggesting that the 60 observed morphological units are themselves dimers. This would agree well with chemical evidence that the numberof O2binding sites per particle is approximately 130. The reconstruction suggests that there are actually 120 functional units arranged in pairs to form 60 dimers, which are assembled as shownin the model. The roles of the extra cap and collar are unknownbut they mayplay a part in the assembly of the structure. THE ACTIN-TROPOMYOSIN-MYOSIN FROM MUSCLE

COMPLEX

The basic structural constituents of vertebrate striated muscle are thick and thin filaments, containing myosin and actin respectively, which are interspersed in a parallel and regular manner. Whenthe muscle contracts, the two sets of filaments slide past one another under the influence of cyclically acting crossbridges (31). The myosinmolecule consists of a long tail embeddedin the thick filament joined by a flexible hinge to a protruding globular head. Whenthe muscle is relaxed, the heads lie close to the thick filaments and their attachmentto the thin filaments is inhibited. Uponelectrical stimulation by the motor nerve, calcium ions are released from the sarcoplasmic reticulum and relieve the inhibition of the thin filaments. The myosin heads can then form crossbridges to the actin in the thin filaments. This attachment is followed by a change of the head conformation, which generates tension in the muscle, followed in turn by the release of the crossbridge from the actin. This repeated cycle of events is associated with the splitting of ATP,which provides a source of energy.

(a)

(b)

(c)

Fi.qure 10 Theactin-tropomyosin-myosin interaction. (a) Helical projections of reconstructions of actin (dotted contours) and actin plus tropomyosin(solid contours). (b) view of a slice of a reconstruction of thin filament decorated with the S1 subfragment of myosin,(c) Diagramshowingpositions relative to the actin of the tropomyosinin the active (solid circle) andthe inhibited(dotted circle) state. TheS~subfragment is superimposed in profile, showinghowits binding maybe blocked by the tropomyosinin the inhibited state.



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The globular actin monomersare arranged in a staggered double helix in the thin filament. On its own the actin activates the myosin ATPase activity independently of the calcium concentration. Calciumsensitivity is conferred by the presence in the thin filaments of the tropomyosin-troponin complex. The troponin is a globular molecule responsible for binding calcium and is located at approximately 400 A intervals along the thin filament. The tropomyosin howeveris a twochain coiled coil which forms two continuous strands in the grooves of actin double helix and is present in sufficient amountsto makecontact with each actin monomer. Since the presence of tropomyosin is necessary for the regulation mechanismto work, it is natural to suppose that the influence of the troponin is transmitted to the actin monomersby the tropomyosin strands. Evidence for this type of model comes from X-ray diffraction and from threedimensional imagereconstruction from electron micrograp~hs(32). Figure 10a shows helical projections of three-dimensional reconstructions of pure actin and of actin plus tropomyosin (33). The two large commonfeatures correspond to the double strand of actin while the two smaller features correspond to the tropomyosinlying in the grooves betweenthe actins. Figure 10b showsan end-on view of a reconstruction (34) of a thin filament containing tropomyosin-troponin, which has been "’decorated" with subfragmentl ($1), a proteolytic fragmentof myosincontaining the globular head but with the long tail removed.The Sl fragment, besides being tilted and skewed, is attached to the actin monomerin a tangential fashion so that the end of the subfragmentextends round into the groove in the actin structure, towards the position of the tropomyosin. This suggests that the inhibitory effect of the tropomyosin:troponin complex may be steric and that in the absence of calcium the troponin holds the tropomyosin in a position where it prevents the binding of the myosin heads to the actin. Whenthe troponin binds calcium it undergoes a structural rearrangement, which allows movementof the tropomyosin and the formation ofcrossbridges. Further evidence for this comesfrom studies of the relative positions of the tropomyosin in the active and inhibited complex(T. Wakabayashi, H. E. Huxley, A. Klug, and L. A. Amos,in preparation). The results, summarized in Figure 10c, showthat in the inhibited complexthe tropomyosinis closely bound to the actin in a position that would prevent the myosin head from binding, but that in the active complex the tropomyosin moves away from the actin by about 10 A to a position that wouldpermit the binding of myosin. SPHERICAL

VIRUSES

Theprotein coats of all small spherical viruses so far investigated have icosahedral symmetry, point group 532. They contain multiple copies of one or more proteins. The largest numberof identical subunits that can be arranged in identical environments in a spherical shell is 60. However,by relaxing the requirement for strict equivalenceof all subunits, it is possible to build larger shells containing 60Tsubunits, in whichthe subunits are now only quasi-equivalent (35). The triangulation number,T, can take only certain integer values, of whichthe smallest are 1, 3, 4, and 7. The subunits maylie in special positions in the surface lattice, giving rise


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to dimer, trimer, or hexamer-pcntamerclustering. The resulting morphologicalunits give rise to characteristic features in negatively stained preparations, even though the individual subunits maynot be distinguishable if the stain does not penetrate between them. The first successful attempts at disentangling the complicated patterns that arise from superposition of features on opposite sides of the particle were by building wire models and using them to cast shadowgraphs (36). However,this gives only crude simulation of the image and the models are difficult to makeand alter. A more flexible and sophisticated technique was therefore developed using a computer with a cathode ray tube display (37). Howeverthe process is still inductive, that is, production of a hypothetical model, comparisonwith observed views of the virus, and modification of model where a discrepancy is found. While this may suffice for simple structures (38), it is likely that for a complexstructure no single model can be invented by the simulator to account for all observed views. Even for simple structures, although it may be easy to explain howthe gross features arise, no single simulated model mayaccount for the fine details of the images. Wetherefore need a more powerful and direct method, such as that provided by three-dimensional image reconstruction. For helical structures, as already described, three-dimensional reconstruction can often be performedin a fairly straightforward wayfrom a single view of the structure. For other types of symmetry,such as icosahedral, the situation is more complicated and more than one view is necessary (39). The two-dimensional Fourier transform of each image represents a central section through the three-dimensional transform of the object. Thedifferent viewsgive different sections and so the three-dimensional transform can be filled in plane by plane. Whenthe specimen possesses symmetry, each view gives not only one plane but a whole set of equivalent planes (60 in the case of icosahedral symmetry) generated by the appropriate symmetryoperations. Whena sufficient numberof different views has been included to fill in the threedimensional transform out to the limiting spatial frequency set by the preservation of the specimen, we perform a three-dimensional Fourier inversion to give a threedimensionalimageof the specimen. "Since the particles lie in arbitrary orientations, the three-dimensionaltransformis not filled in uniformlyand it is therefore necessary to perform interpolation in the transform prior to inversion. This interpolation involves the solution of sets of linear equations, which will be solvable only if sufficient views have been included. Tests for the solvability of the equations (in the form of eigenvalue spectra) provide a check that for a particular specimen the selected views do uniquely determine the three-dimensional reconstruction to a fineness of detail set by the specimenpreservation. Typically for small spherical viruses three or four viewsare sufficient. Before including any particular view, its orientation relative to the icosahedral symmetryaxes must be found and its preservation assessed. This can be done by searching its two-dimensionaltransformfor the position of the best set of pairs of socalled commonlines (40). These are pairs of lines along which the transform should have equal values because of the symmetryof the particle. With ideal data the values along the commonlines would agree exactly if the particles were



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icosahedral, so the symmetry can be tested. Because of distortions of the specimen, nonuniform staining, and contributions from the supporting grid, the values will not agree exactly and the resulting discrepancy may be used as a measure of the quality 'of the image. It can moreover be computed as a function of increasing spatial frequency, so that it is possible to tell at what scale of detail features in the image cease to be icosahedrally correlated. Typically for small spherical viruses in negatively stained preparations, some degree of icosahedral correlation extends to spatial periodicities of about 25 A. The structures o f a number of spherical viruses of different T classes and clustering types have been solved (41, 42), demonstrating how the requirement for quasiequivalence is realized in different ways. Here we consider two more recent and interesting examples. The first is an insect virus, Nudaurelia capensis virus, which is the first established case of a T = 4 surface lattice and also the first to exhibit clear trimer clustering (43). Chemical data show that the capsid consists of about 240 copies of a singlc protein species. The three-dimensional reconstruction (Figure 11) shows that at outer radii the protein is confined within the triangular faces of the circumscribing icosahedron, leaving clear grooves along the icosahedral edges. Each icosahedral face contains four Y-shaped features, each of which in conjunction with the chemical evidence may be interpreted as a trimer. These trimers follow the local symmetry of the T = 4 surface lattice at inner radii. At outer radii, however, the packing of subunits within a face is closer than the packing of subunits between two adjacent faces across an icosahedral edge, the respective center-to-center distances being 35 A and 50 8, at a radius of 170 A. These are quite large differences for quasi-equivalent

Figure 11 Nudaurelia capensis virus, approximate diameter 400 A. (a) Contour map of a three.dimensional image reconstruction viewed approximately along a twofold axis of symmetry. (b)Proposed model for the structure, consisting of trimers of subunits arranged on a T = 4 surface lattice, also viewed along a twofold axis.

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2

i

Figure 22 Cowpea mosaic virus, approximate diameter 240 A. (u) Contour map of a three-dimensional image reconstruction, viewed approximately along a threefold axis. (b) Trace of the equator of the image reconstruction in a plane normal to a twofold axis, showing large bumps at the fivefold positions and smaller ones at the threefold positions.

units and it may be that the capsid of this virus is more like a surface crystal with sharp edges than simple quasi-equivalence theory would allow. The second example is a plant virus, cowpea mosaic virus. Chemical evidence shows that the capsid of this virus contains two different proteins with molecular weights of about 49,000 and 27,500, each present in about 60 copies per particle. The three-dimensional image reconstruction (Figure 1 2 4 (44) suggests how this more complicated capsid is organized. The capsid has a rather smooth but modulated surface, not easily described in terms of an arrangement of discrete morphological units. However, there are strong projecting knobs at the fivefold positions with ridges running from the fivefold positions to additional smaller bumps at the threefold positions. This modulation is most easily appreciated by looking at the outer contour of the particle around an equator normal to a twofold axis (Figure 12b). Just under the surface there are five peaks of density around each fivefold position and also three peaks around each threefold position. A plausible interpretation of these features is that the larger of the two proteins forms 12 pentamers at the fivefold positions while the smaller forms 20 trimers at the fivefold positions. However the asymmetric unit of the reconstructed density may be divided in some more complicated way between the large and small chemical subunits.

CONCLUDING REMARKS Three-dimensional image reconstruction is in principle applicable to any object, whether it possesses symmetry or not. All the examples discussed above are


IMAGERECONSTRUCTION FROMELECTRON MICROGRAPHS 18l symmetricalassemblies of molecules. Not only are manysuch structures biologically important, they also possess enormousadvantages for analysis of their images. The symmetrical particle in effect provides manyregularly repeated images of the asymmetricunit from whichit is built. Thusonce the symmetryhas been determined, the relative disposition of these various images is knownand may be used in twodimensional filtering or three-dimensional reconstruction. The degree of symmetry exhibited by the image also enables the preservation of the specimento be judged. If one wished to study a particle with no symmetry,such as a ribosome, none of these advantages would accrue. Three-dimensional reconstruction would require a complete range of about 25 evenly spaced views to reconstruct to about 20 &. Because of radiation damage, only a very few useful images can be obtained by tilting a single particle. It is difficult to be sure whetherthe particle is well preserved even initially, since observations suggest that isolated particles are generally distorted. Data that can be collected by sets of limited tilts then have to be combined, whichrequires that the relative positions and ~rientations of the various views be determined no easy matter when the particle does not contain a natural frame of reference such as is provided by symmetryaxes. Symmetrical arrays of ribosomes (45, 46) are likely to provide a morefruitful approach. The reconstructions presented above demonstrate how structural information can be reliably retrieved by processing electron micrographs and how the results can be interpreted. An important general point emerges. The assessment and selection of imagescan be quantitatively performedby using their diffraction patterns to see whichspecimenspossess the greatest degree of regularity. Similarly the range of averaging in the filtering process can be precisely controlled: it must be sufficiently great for noise to be reduced but not so great that patches of specimen that differ significantly in preservation or staining becomemerged. However,the final intepretation of the reconstructed imageis muchmore difficult to quantitate and is more akin to a pattern recognition problem in which prior chemical and biological information must play a part. NOTEADDED IN PROOFm very important advance in specimen preparation has recently been made by’ Unwin& Henderson(submitted to J. Mol. Biol.), who have used glucose to preserve otherwise unstained specimens of purple membraneand catalase crystals, whichwere then photographedwith extremely low electron doses to avoid specimen damage. The resulting micrographs exhibit very low contrast and high electron noise, and computeraveraging is crucial for extracting an image of the structure. The small amountof contrast present is producedby underfocusing, which is then compensatedfor in the computer reconstruction (1). The resolution so far obtained is better than 10 A and appears to be limited by the performance of the microscope. Literature Cited 1. Erickson, H. P., Klug, A. 1971. Phil. Trans. Roy. Soc. LondonB 261 : 10518 2. Reedy, M. K., Bahr, G. F., Fischman, D. A. 1972. Cold Spring HarborSymp.

Quant.Biol. 37:397-421 3. Branton,D., Klug,A. 1975.J. Mol.Biol. Submitted 4. Brenner,S., Horne,R. W.1959.Biochim.


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Biophys. Acta 34 : 103-10 5. Laemmli, U. K. 1970. Nature 227 : 68085 6. DeRosier, D. J., Klug, A. 1972. J. Mol. Biol. 65:469-88 7. Klug, A., Berger, J. E. 1964. J. Mol. Biol. 10:565-69 8. Klug, A., DeRosier, D. J. 1966. Nature 212:29-32 9. Amos, L. A., Klug, A. 1972. Proc. 5th Eur. Congr. Electron Microscopy. 580-81 10. Aebi, U., Smith, P. R., Dubochet, J., Henry, C., Kellenberger, E. 1973. 3’. Supramoleeular Struct. 1:498-522 11. King, J., Mykolajewycz,N. 1973, J. Mol. Biol. 75 : 339-58 12. King, J., Lae~nmli, U. K. 1973. J. Mol. Biol. 75 : 315-37 13. Crowther, R. A., Amos, L. A. 1971. J. Mol. Biol. 60:123-30 14. Markham,R., Frey, S., Hills, G. J. 1963. Virology 20 : 88-102 15. Markham,R., Hitchborn, J. H., Hills, G. J., Frey, S. 1964. Virolooy 22 : 342-59 16. DeRosier, D. J., Klug, A. 1968. Nature 217:130-34 17. Moody, M. F. 1971. Phil. Trans. Roy. Soc. London B 261 : 181 95 18. DeRosier, D. J., Moore, P. B. 1970. J. Mol. Biol. 52 : 355-69 19. Moody, M. F. 1973. J. Mol. Biol. 80: 613-35 20. Klug, A., Caspar, D. L. D. 1960. Advan. Virus Res. 7 : 225-325 21. Unwin, P. N. T. 1972. Proc. Roy, Soc. London A 329 : 327-59 22. Unwin,P. N. T., Klug, A. 11974. d. Mol. Biol. 87:641-56 23. Unwin, P. N. T. 1974. d. Mol. Biol. 87 : 657-70 24. Unwin, P. N. T. 1973. J. Microsc. 98: 299-312 25. Finch, J. T., Klug, A. 1974. d. Mol, Biol. 87 : 633-40

26. Gilbert, P., Klug, A. 1974. J. Mol. Biol. 86 : 193-207 27. Barrett, A. N. et al 1971. Cold Spring HarborSyrup. Quant. Biol. 36 : 433-48 28. Finch, J. T., Klug, A. 1971. Phil. Trans. Roy. Soc. London B 261:211-19 29. Williams, R. C., Fisher, H. W. 1970. J. Mol. Biol. 52! 121-23 30. Mellema, J. E., Klug, A. 1972. Nature 239 : 146-50 31. Huxley, H. E. 1969. Science 164: 135666 32. Huxley, H. E. 1972. Cold Spring Harbor Syrup. Quant. Biol. 37:361-76 33. Spudich, J. A., Huxley, H. E., Finch, J. T. 1972. J. Mol. Biol. 72:619 32 34. Moore, P. B., Huxley, H. E., DeRosier, D. J. 1970. J. Mol. Biol. 50:279-95 35. Caspar, D. L. D., Klug, A. 1962. Cold Sprin9 HarborSymp. Quant. Biol, 37 : 124 36. Klug, A., Finch, J. T. 1965. J. Mol. Biol. l 1 : 403-23 37. Finch, J. T., Klug, A. 1967. J. Mol. Biol. 24 : 289-302 38. Josephs, R. 1971. J. Mol. Biol. 55 : 147-53 39. Crowther, R. A., DeRosier, D. J., Klug, A. 1970. Proc. Roy. Soe. London A 317: 319-40 40. Crowther, R. A. 1971. Phil. Trans. Roy. Soc. LondonB 261 : 221-30 41. Crowther, R. A.,Amos, L. A. 1971. Cold Sprin9 Harbor Symp. Quant. Biol. 36: 489-94 42. Mellema, J.E., Amos,L. A. 1972. J. Mol. Biol. 72:819-22 43. Finch, J. T., Crowther, R. A., Hendry, D. A., Struthers, J. K. 1974. J. Gen. Virol. 24 : 191-200 44. Crowther, R. A., Geelen, J. L. M. C., Mellema, J. E. 1974. l/irolo~y 57:20-27 45. Byers, B. 1967. J. Mol. Biol. 26:155-67 46. Lake, J. A., Slayter, H. S. 1972. J. Mol. Biol. 66:271-82

Image reconstruction from cryo-electron micrographs reveals the morphopoietic mechanism in the P2-P4 bacteriophage system.

Three-dimensional measurements from scanning electron micrographs by electron scribing.

Analysis of optical diffraction patterns from electron micrographs of lattices.

A study of the pairing interaction between protein subunits in the tobacco mosaic virus family by image reconstruction from electron micrographs.

Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy.

The S-layer of Caulobacter crescentus: three-dimensional image reconstruction and structure analysis by electron microscopy.

The cellular anatomy of embryos of the nematode Caenorhabditis elegans. Analysis and reconstruction of serial section electron micrographs.

Analysis of freeze-fracture electron micrographs by a computer-based technique.

Evaluation and publication of scanning electron micrographs.

Quantitative analysis of micrographs by computer graphics.

Image reconstruction from projections.

Electron image analysis of ribosomal subunits from Thermus aquaticus.

3D image reconstruction of fiber systems using electron tomography.

Cryo-electron Microscopy Analysis of Structurally Heterogeneous Macromolecular Complexes.

Review of free software tools for image analysis of fluorescence cell micrographs.

Differences in alpha and beta polypeptide chains of tubulin resolved by electron microscopy with image reconstruction.

Invariant classification of molecular views in electron micrographs.

New method for localizing proteins in periodic structures: Fab fragment labeling combined with image processing of electron micrographs.

Image Reconstruction Using Analysis Model Prior.

Characterization of Influenza Vaccine Hemagglutinin Complexes by Cryo-Electron Microscopy and Image Analyses Reveals Structural Polymorphisms.

Polybivalency and disordered proteins in ordering macromolecular assemblies.

Automated structure refinement of macromolecular assemblies from cryo-EM maps using Rosetta.

An absolute method for the determination of the persistence length of native DNA from electron micrographs.

The dynamics of signal amplification by macromolecular assemblies for the control of chromosome segregation.