Multivariate statistical analysis of ribosome electron micrographs

J. Mol. Rio/. (1982) 161, 107-137

Multivariate Ribosome

Statistical Analysis of Electron Micrographs

L and R Lateral Views of the 40 S Subunit

from HeLa Cells

The morphology

of the small (40 S) suhurrit of the wkaryotic rihsorne from HrJ,a cells has hren examined hy single-particlr averaging and multivariatr image analysis applied to electron micrographs of negatively stained specimens. Thtx use of multivariate image analysis allo\vs diffcwnt. indepcxndent, components of the, structural variation within the particles to he idtmtified and separatrly studied. Thtb largest, component of variance for both lateral views (termed I, and R) was the variation in the peripheral stain intensity. The second largest component of intrrpartic~le variation is due to changw in the parti& appearance most likeI> associated with a change of oric~ntat,ion o11 thr spwimen film. Arrragrs formed from particles falling within a small range of peripheral a&in int’ensity allowed the changes in thtx projrcted structure to be studied as a fbnrtion of local st,ain level. Visual observations of st,ain variation could Iw cotlfirmed quantitativrly. Significant differences were found bct,wecn avrragcs of particlrs ill the I, vi,,, and those in the R view. Multivariattl image analysis of a mixed population of 1, and mirrored R particles showed that the diffbrencrs collsistrntly affect all particlrs. Howver, the R virw incwasingly rcsrml)lrs thtl I, view as the ovc,rall Iclvel of stain is increawd, in agreemc~nt with a model of partial st,ain immrrsiotl.

1. Introduction The problem of sorting out significant informat,ion from electron microscopic images of ribosomal particles has been evident in the attempts to model ribosomal subunits. notably for Escherichia coli (e.g. Tischendorf‘et al.. 1971: Vasiliev, 1974: Lake. 1976; Koublik et al., 1976). Models for the tnore cwmplex eukaryotic: 10 S and 105

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60 H subunits are at an earlier stage of development (Nonomura et al.. 197 1 ; Lutsch rt al.. 1972; Kiseler et ILZ., 1974: Boublik & Hellmann, 1978). In each case, the models were derived from a visual. correlative evaluation of large numbers of elwtrori microscopic images showing the ribosomal particle in different charac%eristic views. However. visual extraction of a “typical” appearance of a particular view may be very subject’ivc. A higher deprec> of objectivity can be gained through the use of single-particlr~ a,veraging (Lutsch rt ~1.. 1977; Frank rt al.. 1978,198lb; Boublik et nl.. 1981(l), \vhich allows the averaged projection to be computed from a set of images displaying tht> sarnc view of the particle. However, analysis of a diverse set, of particles I;y this method may give rise to a problem. which has been addressed by Moore (1980) in a simila,r context. discussing t,hr significance of averaged struct,ural dat’a obtained bg nrut’ron scattering. If the populat’ion is known to be heterog;eneous in composition (Kurland rt 01.. 1969) or in conformation (Lam et ml., 1979). what, is t’hc significance of an average structure I Is the average truly representativ(l of the t,ypical struc~t~ure. or is it “merely a mathematical curiosit’g which no individual particle ever closely resembles at any time”? (Moore. 1980). Ewn if randomly formed averages can be shown to be highly reproducible (Frank it ~1.. 39816). this must, not be taken as an indication of negligible structural variability. The situation is further complicated when negat’ive st,aining is used to enhance the elect’ron microscopic contrast. This may introduce a variation in the visualized structurt and bring out’ different features depending on the local stain concentration (Moody, 1967). It becomes apparent that we need an objective means of sorting and classifying images on the basis of their overall similarit,y. In other words, since the goal of this elassificat’ion is the description of the noise-free projection, what is required is a quantitative technique of extracting st,ructural informat’ion that takes the diversity of the images into account (see also Wade et al.. 1980). The ability t,o isolate more or less homogeneous subsets of a population will allow formation of subaverages much closer in appearance to the individual particles over which they were formed. As a consequence. struct’urally significant detail will be presclrved to a, higher resolution. Correspondence analysis (Benzecri. 1969). a multivariate statistical method of analysis. allows such subset,s to be discriminated and the most significant, t’rrnds of variation present in the data to be identified. The potential of this technique in image analysis and in elect)ron microscopic structure analysis becaame cridcnt from study of thr hemocyanin molecule (van Heel 8~ Frank. 19XOa ,h, I 981). WC have analyzed a set’ of electron micrographs of t*he two lateral views of the 40 s ribosornal subunit frorn HeLa cells (Fig. I ) using single-particle averaging and correspotrdenc~t~ analysis. One of these views, t)he left or L view (Fig. l(b)). was previously studied using single-particle averaging without prior discrimination (Prank et ~1.. 1981b). This study suggested a variation in the density of the peripheral stain layer relative to the particle density to be a major source of possible source of interimage hcterogeneit’y of the particle images. Another \rariat,ion is the variability in the orientation of the particle on the support film.

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FIG:. 1. (a) Electron micrograph showing 40 8 ribosomal subunits in the 2 characteristic lateral views. labrlled L and R. Electron microscopic magnification, 70.000 x (b) Representative particles in the I, lateral view. after 3 cycles of alignment. (c) Particles in the R latrral view after alignment. The particle images in (b) and (c) have been low-pass filtered (see the text) with a limiting resolution (l/e falloff of Gaussian) of l/28 A-‘. In this form. and after application of a mask (see Fig. 2). t,he images entrr the statisticsal analysis.

which gives rise to a multitude of closely related views. The particle outline and the positions of stain minima were found to be reproducible in independent averages with an overall resolution of l/32 A-‘. Thus, the purpose of the multivariate statistical anaIysis was to investigat’e these phenomena quantitatively, and to separate particle images according to their

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similarities and to inherent trends in their statistical distribution. In the course of this investigation, we came to appreciate some features of correspondence analysis that promise to offer unique advantages in the investigation of macromolecules with the electron microscope. Our analysis has allowed earlier observations of the variability of the stain in close contact with the protein (Valentine, 1961; Moody, 1967) to be verified quantitatively. Systematic studies of this kind may ultimately lead to a more refined model of the mechanism of negative staining than hitherto possible. One of the significant findings of the present study is a strong difference in highresolution appearance between averaged projections of ribosome particles lying in “flip/flop” related positions on the specimen grid. Since this difference is closely linked to the distribution of stain in the two positions of the ribosomal particle, we defer a comparison of the two averaged projections until after the method of analysis and a description of the stain variability have been presented.

2. Principle of multivariate

image analysis

To characterize the diversity among the images, we consider them as represented by an array of M density readings. Since two images may differ in any combination of the M readings, the appropriate space for the representation of the image information is the M-dimensional space R‘s, where each co-ordinate axis represents the density reading at a particular point of the grid on which the image is sampled Any image represented by M density readings can thus be represented by a point in R“‘. If comparable features in different images are aligned with one another, then the distance between two points in R’” takes on a special meaning : it can be interpreted in terms of the similarity of the corresponding images (see e.g. Frank, 1974). Points representing similar images lie in close proximity to one another. In this representation, a set of N images showing a particle in the same view reflects the becomes a “cloud” of N data points in R” whose internal structure diversity, and the existence of divisions (discontinuous variations) and trends (continuous variations) among the images. If; for example, the particle existed in two different conformations, the data cloud would appear divided into two separate subclouds. A two-dimensional projection of the data cloud, if done in a direction perpendicular to the direction of the data separation, would show the existence of the two separate clouds, and would allow the corresponding subsets of is the purpose of applying multivariate images to be identified. This, briefly, statistical methods of analysis to the image data: the description of the most significant separations of the data cloud in a suitably chosen. low-dimensional subspace. Correspondence analysis (see the Appendix) is distinguished from other methods of data analysis by a distance measure t’hat is scale-invariant. and by the fact that it allows image profiles (the sets formed by the density readings for each image) and image-element profiles (the sets formed by the N realizations of each image element in the X images) to be represented simultaneously in the same subspace. In correspondence analysis of images (van Heel bi Frank, 1980a,6,1981) the

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images are represented as an expansion by a series of orthogonal eigenvectors representing the most important features associated with interimage variation. These eigenvectors are found by diagonalizing a symmetric matrix containing all interimage distances in R“‘. The decomposition of the images into a series of orthogonal eigenvectors is equivalent to a separation and ordination of the information into portions that are statistically independent with respect to their interimage variation. The mathematical analysis of the image set leads to a scatter diagram that shows the positions of the images in a co-ordinate system formed by two selected eigenvectors. The relative importance of the eigenvectors in representing the interimage variation can be assessed from a histogram of the associated eigenvalues. Frequently, the major part of the total information is concentrated in versus the second is two or three eigenvectors. A map of the first eigenvector generally sufficient to allow major trends and separations present in the image set to be detected.

3. Methods The 40 S rihosomal subunits of HeLa cells were prepared

according to Schreier & Staehelin (1973). The sample was stained with OG& (u ,/ v ) uranyl acetate and examined in a JEM 1OOH electron microscope at 80 kV. Lateral views termed L and R. which correspond to flip/flop related positions of the particle on the support film, were selected from the electron micrographs and digitized with a Perkin Elmer PDS 1OlOA flatbed microdensitometer. The sampling distance corresponded to 7.14 A on the object scale. Orientational and translational correlation techniques (Frank et crl.. 1978) implemented as part of the SPIDER software system (Frank et al., 1981~~) were used to align the images in the computer. In the version of the alignment procedure described by Frank et al. (19816). the alignment is done in 3 cycles, and combines autocorrelation alignment (Frank et al.. 1978) with direct alignment of the images (Steinkilberg & Schramm. 1980) in the orientation search. In previous studies (Frank et al.. 1978.1981h; Zingsheim rt al.. 1980), all aligned images were simply summed to form the total average. which could in some cases be further enhanced by using symmetry operations (Frank et al.. 1978). However, in the present stud?, we extended the averaging only over subsets of images that were found to be sufficient,l> homogeneous (van Heel & Frank, 1980a,h,1981). To prepare the image data for the statistical analysis, we used 2 procedures designed to reduce the influence of noise. (1) Low-pass filtration eliminated part of the noise at high spatial frequencies by smoothing the images. The Fourier transform of the image is multiplied with a rotationally symmetric filter function having a Gaussian profile. From this filtered transform,.the smoothed image is obtained by inverse Fourier transformation. (2) A mask eliminated the support-film structure surrounding the particle. The same mask wa,s used for all particles, and was produced from the low-pass filtered average L image b> thresholding “from the outside”. This procedure assigns zero values to the output arra! forming the mask in the region outside the particle where all image elements are above a certain threshold. This threshold is chosen so as to define the outer boundarv of the stain layer surrounding the particle. The computer algorithm is very simple for a s&in layer with convex outside boundary. First, all elements of the mask array are set equal to 1. Each row is scanned from left to right, and mask elements are set at 0. However, the scanning of a ran’ stops when an image element with a density value lower than the threshold is encountered. This procedure is repeated first for a right-to-left scanning movement, and then for both directions of each column of the sampling raster. The resulting mask (Fig. 2) was used to

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FIG. 3. Mask applied to all aligned images for the statistical analysis. This rcduoes the contribution of noise by restricting the analysis to the 1020 image &ments of the parti&= and its surrounding stain layrr. The mask approximates the outer boundary of thr stain lays of the averaged 1, image and only “passes” t,he elements within this awa of interest.

define the M image elements in each of the A’ images that were subjected to the multivariate statistical analysis. As a preparation for correspondence analysis, the image data were brought into the form of an M x N matrix. Since image profiles entering the analysis are invariant to changes of scaling (see the hppendix). bright-field images, for which the optical density variations are proportional to the background density (e.g. Hawkes. 1980). need no scaling or “floating”. However. we adjusted all images to the same mean density level in order to avoid influences due to variation in support film thickness. Therefore. the image profiles being analyzed reflect the r&&up dist’ribution of stain density in the area of the particle and its

surroundings.

4. Stain Variation In our initial study of the L lateral view of the 40 S subunit (Frank et al., 1981b), we found a high interparticle variability in the relative st’rength of the stain layer surrounding the particle. What we therefore expected to find in the statistical analysis was that the variation in the outer stain density would be a prominent factor in the eigenvector expansion. This is indeed the case, as shown in the histogram of eigenvalues (Fig. 3) and the map of the first factor verBus the second (Fig. 4) for a population of 7’7 L particles. The factor with highest significance claims 25% of the total interimage variance, while the factor immediately following accounts for only 5%. The fact that the first factor is associated with the varying ratio between outer stain density and density of the inner, stain-excluding region becomes evident from inspection of individual images appearing at different positions along the first axis. For clarity, we will initially restrict the presentation to the first factor. The second factor, which relates to the orientation of the particle on the support film, is considered in section 6, below.

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OF RIROSOMES

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PI<:. 3. Correspondence analysis of 77 aligned 1, images of the 40 S subunit: histogram of eigenvalues. The first and second factors account for 245’3,b and 51% of the total interimage variance. respectively.

The position of a point representing an image profile on this map in the direction of the first axis (vertical in Fig. 4) is determined by the contribution of the first eigenvector to the eigenvector expansion of this image. In other words, images in extreme (top and bottom) positions on the map have a high relative contribution, positive or negative, from the first eigenvector. These extreme images can be said to “explain” the features associated with the ordering of the data in the direction of the first factorial axis : comparison of two images lying at opposite ends of the scale will show most clearly the complementary features that correspond to the separation along the first axis. Such a pair of complementary features might be the presence or absence of additional density in a particular region of the image. Comparison of particle images having extreme and opposite positions on the map shows the amount of staining outside of the particles to vary strongly (Fig. 5, particles 6 and 59). As a gallery of representative images shows (Fig. 5), intermediate positions between the two extremes on the map correspond to intermediate positions on a subjective scale of “peripheral stain strength”. As quantitative support for this observation, we plotted central, horizontal density profiles of the particles selected for the gallery. From top to bottom, the systematic increase in width and depth of the stain “valleys” (representing low optical densities) relative to the central particle “peak” is clearly visible (Fig. 5). The particles do not cluster on the map according to which micrograph they were chosen from. Particles from any one micrograph scatter to the same extent as the entire population. Thus, in the statistical analysis, the variability of the local staining around individual particles far outweighs the possible effect of different ranges of stain variation for different micrographs. Another means of characterizing the varying trait of the images is by forming part’ial averages over images falling into horizontal strips of the map that each

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FIG. 4. Correspondence analysis of the 77 1, particle images. map of the first twsus the second factor. The images. represented by numbers. scatter widely on the map. suggestive of a continuous variation with respect, to the 2 factors being examined. The ratio between the extents of this distribution (apart from outliers) in the vertical/horizontal directions reflects thr ratio in interimage variances of the first to the second axis (see Fig. 3). Images inset along thv sidr reprcscnt partial averages formed over 4 horizontal strips of thP map (subdivisions of the vertical axis. factor-l). The variation in the ratio of densities of the stain-excluding particle region wwux t,hr surrounding stain layer is apparent. Averages

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contain approximately the same number of particles. The averages (insets on right of Fig. 4) obtained by summing images falling into four successive horizontal strips of the map show the pronounced change in the ratio of stain density to density of stain-excluding region from top to bottom. We now must pose the following question. Apart from this demonstration that particles have been ordered according to their peripheral stain density, do the partial averages in Figure 4 have a physical interpretation 1 As the stain variation is completely random, it may seem pointless to look for additional information. Yet the ordering on the map implies that the particles have been sorted solely on the basis of a physical parameter that is not normally a free variable of the experiment. Averaging over images falling into a horizontal strip on the map combines all of those particles that underwent similar stain&y within a narrow range of stain variation. The use of such strip averages virtually eliminates the resolution-limiting effects of the stain variation and the associated variability of the apparent structure. At the same time, this method of analysis may provide additional information on the mechanism of stain penetration. In a comparison of the four horizontal strip averages in Figure 4, the similarity in the positions of the strong stain minima is remarkable, considering the strong increase of outside density evident from the images and profiles in Figure 5. Nevertheless. certain changes in the outline and the fine structure of the stainexcluding region may be discerned. As the amount of stain increases, some structural details defined by stain incursions or inclusions become less prominent OI disappear. An example is the behavior of the stain inclusion marked with an arrow in the top average of Figure 4. As we move down the map, this inclusion merges with the peripheral stain layer to form a continuous lobe of invasive stain. The existence of apparent structural variations dependent on the amount of peripheral stain favors adoption of a model of incomplete stain immersion (Valentine. 1961) to characterize the population of particles in our study. The marked differences between L and R averages (see section 7, below) also strongly support this hypothesis. A more precise understanding of negative staining behavior may be gained by several approaches. As we have seen, assessment of images ranked by amount of stain can be made by determining trends in the density profiles of individual particles (Fig. 5), or by comparing subaverages of similarly staining particles. However, a more direct evaluation of the statistical behavior of the particles in relation to this factor may be made through an analysis of the so-called importance masks and images that relate to the stain-strength axis of the factor map.

5. Importance

Masks and Images

The theorem of simultaneous representation (Lebart et al., 1977; and see the Appendix) implies that image element profiles may be projected on the same factor map as the image profiles. The particular distinguishing propert’ies of images inset at the bottom. formed over 2 vertical slices of the map (subdivisions of the horizontal axis. factor2). display high-resolution differences that prohahly relate to a variabiKt,v in thp angle of view. Thtx averages arp displayed with a contour increment of Ad (optical densit,y) = 091 and with slight Ion-pass filtration to a limiting resolution of l/14 A-‘.

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forming a cluster can thus be characterized by the set of image elements falling into the same area of the map. The simultaneous representation leads to a very sensitive means of identifying those image features that are responsible for separations on the factor map (van Heel & Frank, 1980a,b). The positions of the 1020 image elements passed by the mask on the factor map 1 verRw,B 2 are shown in Figure 6, together with the positions of the images. The circular inset focuses on the vicinity of an individual image (marked as *40*). Each four-digit number represents a pair of two-digit co-ordinates of an image element; e.g. 3022 denotes element 30 in the 22nd row of the image. It is convenient in an analysis of any subset of image elements relating to a domain on the map to make a pictorial representation using the original image grid. In our example, for each of the image elements lying within a circular domain around image *40* (Fig. 6), we have set the corresponding element in the sampling grid to the value d = 1 (which will be represented as black in the output image), while leaving all other elements at d = 0. We call the resulting pictorial mask (van Heel & Frank, 198Oa,6), since it has the representation an importance of “pass” elements indicate the properties of a mask, where the positions importance of t,he image region in explaining the data separation and the unique features of the images lying nearby on the map. The importance mask (inset in upper right corner, Fig. 6) relating to the area circled on the map shows that the elements in this region belong to the image region lying outside the particle proper. From inspection of the particle images, we know that the upper halfplane of the map is characterized by low peripheral stain density. Any image elemenm projecting into this plane will originate from image areas where the stain is relatively searet‘. In our example, the occurrence of image elements on the map in the vicinity of image *40* indicates that this image is characterized by relatively weak staining in the particular areas shown by the importance mask, a result that can be verified by a visual comparison of image *40* with the total average image. Since the simultaneous representation is actually an approximate one, caution must be exercised in the interpretation of proximities between image elements and images within a small region of the map. Thus, the finding in our example is no more than a qualitative stat,ement. Another technique of representation, developed by van Heel & Frank (198OuJ). allows all image elements projected onto a halfplane of the map to be assessed for t’heir relative importance in defining or explaining the associated data separation Here, a weight is attached to each image element according to its position along the associated axis (Fig. 6). The resulting importance image highlights those elements that, fall in extreme positions. The importance images obtained for two complementary halfplanes show complementary aspects of the data separation. In the case of the stain variation, the two complementary aspects (Fig. 6, insets at top FIN:. 5. (a) (:allery of representative L par-tick images that fall near the vertical axis of the map in Fig. 1. The particlrs to stain layer ratio shows a progressive change from the top of the map (particle no. 6) to the bottom (particle no. 59). (b) Central density profiles across the particles in (a). The profiles have been smoothed by local averaging over 7 image points to show the progressive variation in densit? behavior mow clearly. The vertical broken lines mark the limits of thp masked region within which the analysis was applird

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FIG:. 6. Same factorial map as Pig. 4, but with thtl IWO irnagr donrwts (rrprescrrteti as dots) projcct,cd ont,o it. Elrments in the upper cluster belong to the ring-xhaprd periphrral rrgion on thr, image grid : thaw in the Iow-c~r vlustcr Iwlong to the ~wmpl~~mentary ww rcy$on. ‘I’hr circular inset is itu cnlargrmrnt of the map arca around a selected image (no. 40). shwring thr locat.icms of thr image rlrments. which RW repwsented hy thrir c-o-ordinat,cs. The rectangular inset al~ovr the circlt~ is the importanw mask for this circular region of the map. It highlight,s thr partiwlsr imagt~ elements. those falling in thr periphrd region along thr right sidr of thv partic,lr. that aw wsponsible for cic+wnining the position of imagt~ no. 40 on the map The I pairs of importance imagrs (wrtangular insets adjacent to the map) for t,hrx 4 halfplanrs show complemtwtary aspwts of thcs 2 data wpwations (along fador-I and factor-Z)

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and bottom of map) are the increase of stain around the outside and the decrease of stain (i.e. increase of stain-exclusion) in the central region. It should be noted in the following that, because of the bias adjustment applied in the preprocessing step (section 3, above), both “increase” and “decrease” are measured with reference to the adjusted mean density level of each image. The image-element map (Fig. 6) indicates a strong clustering into two clouds along the axis associated with stain variation. While a clustering of images on the map (e.g. van Heel & Frank, 1980a,1981) is easy to understand, namely, as an indication of strong similarity of images within a cluster with respect to the data separations on the map, the meaning of image-element clusters is more difficult to conceptualize. Elements belonging to a cluster behave very similarly over part of the image set; that is, their values are, on the average, highly correlated. The presence of two distinct clusters on the positive and negative sides of eigenvector 1 indicates the existence of regions in image space with opposite behaviors. Image elements belonging to a cluster on the map do not necessarily form a continuous region in image space. However. analysis by means of the importance images tells us that the lower cluster (in the halfplane identified with high peripheral stain density) corresponds to a contiguous region somewhat larger than the area of the image grid occupied by the particle (lower inset, Fig. 6), indicating a stain decrease relative to the mean level in this region. The upper cluster (in the halfplane identified wit,h low peripheral stain density) corresponds to a ring-shaped region of relative stain

FIN:. 7. Superposition of the bottom importance image from Fig. 6 (relating to the core region) upon a contour plot of the total I, average, in order to show the areas of coincidence and of disagreement in their outlines. The total average has been low-pass filtered in this display with a limiting resolution of l/28 A-‘.

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decrease (upper inset) surrounding the inner region, plus a small, disconnected inlier. (The outer boundary of this ring is defined by the thresholding mask, shown in Fig. 2, that was applied to limit the analysis to the particle and its surrounding stain ring.) The continuous scattering of images on the map is thus a reflection of a continuous statistical distribution of the ratio between the densities of two sharply defined image regions with opposite interparticle variance behaviors, From this analysis we learn that we must distinguish a “core” region and a “peripheral” region in the image. The interparticle variations of these regions are anticorrelated ; i.e. relatively high peripheral stain density correlates with relatively low stain density in the core region. Surprisingly, as noted above, the core region does not exactly coincide (Fig. 7) with the stain-excluding “particle” region that we see sharply demarcated in the average. Rather, it includes a narrow. discontinuous rim of stain in which the major stain maxima are situated, but it also truncates the tip of the “beak” (Boublik S: Hellmann. 1978) and other margins of the particle that extend out into the stain. The analysis thus reveals a very complex patt,ern of stain behavior, which comprises three different phenomena requiring explanation. As the peripheral stain density increases: (I ) the stain density in most of the particle area decreases in relative terms ; (2) certain small regions of the particle inmwzsr in stain density ; and (3) certain regions of strong stain concentration outside of. but in immediate contact wit,h. the particle decrease relatively in stain density. The first phenomenon, the relative stain decrease within the particle area, is consistent wit,h a negative staining model that assumes increased levels of stain surrounding the particle : an interpretation immediately suggested by the trend in the optical density profiles (Fig. 5). As to the second phenomenon. the small regions of the particle showing an increasr in the amount of staining are most likely to be areas that, due to their low elevation above the specimen grid, become increasingly “flooded” by t’he rising level of stain. Such areas include the outer tip of the beak region, as well as the recognized to be highly region around the stain inlier, which was previously variable (arrow in top inset, Fig. 4). Finally, the finding of a stain region whose density is anticorrelated with the depth of the outside stain is in remarkable agreement with observations reported by Moody (1967) on the staining of bacteriophage T4 sheaths. He found that “the shallowness of the stain is correlated with the intensity of the dark ring of stain in contact with the sheath: this ring is very prominent in shallowly embedded when the stain is sufficiently deep. .” specimens . but is scarcely perceptible The rim of stain accumulation immediately adjacent to the particle appears as the minimum expression of the negative staining ; it probably represents the portions of t,he stain meniscus that are drawn up to the highest elevations along the steep portions of the particle surface exposed to the stain. As the general stain level rises. t,he appearance of these areas and the particle itself will not vary to a great extent, but the outer stain ring will widen and deepen. Clearly, much more information is contained in the importance images and the pattern of stain variation t,han we are able to present here. We expect that, with appropriat,e supporting experiments. a more detailed model of negative staining

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can be derived than has been possible using conventional methods of image analysis. It is important for interpretation of the averaged L and R views in terms of the subunit structure that the particles occur in a wide range of stain immersion states. The immersion of the particle to greater depth in part’ of the population implies that, since the stain is outlining a greater portion of the particle surface, the corresponding partial average image should give us more faithful information on the mean topography of the particle than in the lightly stained case.

6. Variation

in the Direction

of View

In the previous study of the 40 S particle in L view (Frank et al., 1981b), we found the total interparticle variance to be high along the right-hand portion of the particle boundary (see Fig. l(b)), parallel to the long axis of the subunit. This variation could be caused by a variation in the effective angle of view due to different positions of the particle on the support grid, related by rotation around its long axis. The resulting variation in the appearance of the side view would be too subtle to be recognized visually, but could conceivably be detected by the statistical analysis. We believe that the existence of a small range of views for the L population is reflected in the data separation along the second axis (horizontal in Fig. 4) of the 1 verms 2 factorial map that we have already examined in relation to its first axis. Irrespective of the peripheral stain concentration, the particle projections show a difference in averaged structure along the second axis, evidenced by a comparison of averages over two vertical slices of the map (Fig. 4). The most conspicuous differences occur along the right-hand side of the particle, precisely where the total interparticle variance assumes its highest value (Frank et al., 1981b). The principal determinant of these changes appears to be the striking differences in intensity of staining along the upper right-hand portion of the particle. The average for the left half of the map shows disproportionately heavy staining in this region, and the outline of the averaged particle along its top and middle segments resembles that in the most heavily stained horizontal strip average. The small protrusion at the back of the “head” (Korn, 1980) has been inundated, and the two side protrusions in the middle segment have the same shapes and relative positions as in the heavy-stain horizontal strip average. Analogously, the average for the right half of the map agrees in these image regions with the most lightly stained horizontal strip average. The magnitude of the changes in the position of the protrusions ( - 10 8) is well above the distances ( 16 A) by which the positions of stain minima were found to vary from one average to another in a test of reproducibility (Frank et al., 1981h). Although the similarity of the progressive changes among the horizontal strip averages might suggest that the differences described above are directly related to the overall amount of surrounding stain, we do not see a true dependence of factor2 variability on factor-l variability. Such a dependency would be suggested by a skewed distribution of images on the map (cf. section 7, below), but here the distribut,ion is essentially vertically trending.

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What we do see is a local, anisotropic variation (imbalance) in the stain pattern surrounding the particle. One possible explanation is that the position of the particle on the support film changes over a small angular range. For example, if we assumed a pivoting of the particle about an axis roughly normal to the long dimension of the particle, the apparent x-y movement of the two side protrusions could be explained as the result of differential incomplete stain immersion of two morphological features having different positions in t’he z direction. According to this interpretation, the left-hand strip average shows the upper right portion of the particle deeply immersed in stain, while the lower left portion is oriented so as to stain only lightly. This stain pattern gives rise to a feature that finds no counterpart among the factor-l averages : a slanted appearance of the lefthand edge of the particle (cf. section 7, below). The right-hand strip average shows the reverse situation: shallow stain along the upper right, deep immersion of the bottom left portion of the particle. The importance images for the second factor (side insets, Fig. 6) show precisely the lateral/diagonal pattern evident from the two strip averages. The left-inset image shows particularly clearly the continuity of variance behavior from outer stain layer (top right dark region) to particle interior (dark region corresponding to the lower of the two side protrusions of the particle). The direct correlation of the appearance and variance behavior of the latter morphological feature with the local stain behavior is unequivocal. The distribution of the images in the direction of the horizontal axis indicates that the change in the appearance of the particle view is continuous, suggesting a continuous change in the angle of view. Due to flattening of the particle in the course of dehydration, however, it may be difficult to obtain supporting evidence for a link between the factor-2 changes and the effective tilt of the stained particle. Tilting of a flattened particle is not likely to reveal additional views; rather, it may merely render perspective views of an essentially flat layer of stain having the characteristic shape of one particular projection (see Wabl ef al. (1973). where this behavior was observed for E. coli 50 S subunits). shape, then If the particle were preserved in its true three-dimensional correspondence analysis would allow us to verify the link between the second axis? and the tilting changes in a very simple way: controlled tilting of a particle by tilting the specimen stage by a small angle would move the particle projection on the map along a path parallel to this axis. If this interpretation of the second axis were confirmed, the tilting experiment would also serve to calibrate the scale of this axis in terms of the absolute tilt angle of the particle. An attempt to confirm this link between tilt and the distinctions shown by the second axis by studying a tilt series with correspondence analysis failed, because the particles appeared strongly flattened. It is interesting to note that the analysis technique was, nevertheless, able to distinguish tilt angles by the different degrees of perspective shortening of the “flat” particles in the direction normal to the tilt axis. Thus, for a mixture of different projections of several different particles, t Depending on the data analyzed, the shape changes due to tilting the first axis. or in an axis of higher than second order.

could of course be expressed in

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correspondence analysis distinguished both tilt angle and particle identity in the first two factorial axes. We anticipate that preparation of the ribosomal particles by freeze-drying, particle shrinkage and without staining (Boublik et al.; 1981b), will minimize deformation, and ultimately allow corroboration in this manner.

7. R Lateral View In an extension

of our studies on the L lateral view of 40 S subunits (Frank the right or R projection with the same method of computer averaging. Fifty particles were aligned in three cycles and an average was formed as before. The R average appears distinctly different from the average of the L views in the positions and sizes of the stain minima as well as in the overall shape of the stain-excluding particle region (Fig. 8). The stain minima (represented by white) in the R average are less distinct at. the bottom of the particle than in the beak segment. In contrast. the averaged L projection shows clear minima equally defined in top, middle and bottom segments of the particle. Differences in the overall shape of the averaged projections are most notable in the beak region, in the two protrusions on the side of the particle, and to a lesser extent along the bottom edges of the particle. The R average shows the beak

et al., 1981b), we investigated

IQ:. 8. Total L and R averages (obtained from 77 and 50 images, respectively) displayed at l/14 A-’ resolution and with identical contour increment, (dd = 0.01). The diff erences in the particle outlines as ~11 as in the sizes and relative intensities of the stain minima (white areas in this representation) are Ggnifioant to a resolution limit of l/32 A-‘. This has been verified by forming and comparing 2 ndrpendent averages for both the L (38/39 images. random1.v drawn) and N (25/25 images) views.

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FIN:. 9. (~orrespondrnw anitlysis of .iO aligned. mirrorrd R views of thv 40 R subunit: map of the tirst w~.ws the second factor. Insets represent partial averages formed over strips of the map analogously to the I, strip a~verages in Pig. 4. and displayed with the same limiting resolution. The clustering of thr majority of the particles oblique to the 2 axes of the map leads to a relationship between thv averages of the upper and right,-hand halfplanes. and brtwvrn thosr of the lower and left-hand halfplanps. The small

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slightly less “pinched off” from the rest of the top segment, due largely to the lighter staining along this portion of the R view. Further, the upward stain invasion into the underside of the top segment is less pronounced for the R view : the small stain inlier characteristic of the L view is absent. The two side protrusions not only appear different in size, shape and positions of their stain minima, but they also demarcate distinctly different stain distributions for L and R projections. Roughly speaking, the L average shows the major stain accumulation above the smaller, upper protrusion ; the R average shows it below the smaller, lower protrusion. In either case, the larger protrusion defines a break in the stain ring. The large concentration of stain below the lower protrusion in the R average also appears to invade and dissect the stain-susceptible region beneath the lower protrusion of the particle. Since the R views were selected from the same micrographs from which the L views were taken, factors of experimental preparation and electron microscopy can be excluded as causes for the difference in appearance. Such a difference would not be expected if the particles were completely embedded in negative stain, as in the model used by Steven & Navia (1980). The observed structural differences between the two side-views of the 40 S subunit (cf. Kiselev, 1980) must be interpreted as a result of incomplete immersion of the particle in the stain, and must be related to differences in topology between the two sides facing the support grid. Evidence for incomplete stain immersion has been found for glutamine synthetase (Kessel et al., 1980) and Limulus hemocyanin half-molecules (van Heel & Frank, 1981): in both cases the projections attributed to flip and flop positions of the molecules were not related by mirror inversion. Correspondence analysis of the 50 R projections (in mirrored form, and using the same mask as in the L analysis (Fig. 2), to enable direct comparison with the L results) revealed. as expected, that the first factor was again the varying ratio of the outer stain ring veraus the inner, particle or core region (19.7o/o of the variance). Four strip averages corresponding to the L averages in Figure 4 show the same trend of increasing relative width and density of the peripheral stain ring from top to bottom of the map, although the overall range of variation is not as great (side insets, Fig. 9). Although each horizontal R strip includes only 12 or 13 particles, large-scale features such as the apparent widths of the segments comprising the subunit and their relative locations or orientations, to be discussed in the following, are highly significant in these averages. Two vertical strip averages were also formed from this map (bottom insets, Fig. 9). The relationship between the four horizontal strip averages (axis 1) and the two vertical (axis 2) in Figure 9 reflects the uneven particle distribution on the map. The majority of the particles fall in a diagonally trending cluster through the origin, although the outliers scatter widely. This distribution contrasts with the more even overall scattering of the L particles (Fig. 4). For the R view, the lowest horizontal vertical (factor-l) extent of this main cluster suggests particles is not as gRat as for L particles. Although the the largest individual portion of the total variability of second (slant) factor (6.7%) is proportionately greater Fig. 3).

that, in general, the staining variability of K first (stain variation) factor again accounts for the population (19.7%). the contribution of the than that of the factor-2 in the L analysis (cf.

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strip average is quite similar in detail to the left-halfplane vertical strip average, notably in the straight (vertical) lateral edge of the particle. The top horizontal strip average and the right-halfplane vertical strip average are even more obviously similar, with t,heir dissected and backwards-slanting appearance. Of the vertical strip averages, that of the right-halfplane shows a somewhat narrower and more sharply defined stain ring, illustrating the fact that, it includes a greater proportion of the more lightly stained particles. Initial visual examination of images falling in extreme positions along the second axis suggested the existence of a gradation in apparent width and in slant of the lower segment of the particle. Since the distribution of the images on the map has an oblique trend, as stated before, these changes in appearance of the particle are correlated with the stain variation. Half-averages formed for the two sides of the map (bottom insets, Fig. 9) confirm the existence of the change in slant. The particle appears to have different overall width because of the different angular relationship between upper and lower segments. The R average formed for the left halfplane, which contains a large fraction of particles with high stain density, shows the left-hand edge of the lower segment to be nearly vertically oriented and the upper segment to form almost a 90” angle to it. Tn these features, it closely resembles any L average. However, the other R halfaverage, associated with a small amount of stain, shows what resembles a flexure of the particle, giving rise to a more acute angle between the segments. The difference is. at least partially, a consequence of different degrees of stain invasion below the beak: the absolute length of the slanting lateral boundary of the stain-excluding particle region (right-hand average) is less than that’ of the straight edge in the lefthand average. Following our model of partial stain immersion, the darker (and presumably deeper) the stain, the more an R particle resembles an L particle, or a projection of the entire stain-excluding nucleoprotein mass resulting from total stain immersion. We have seen that the statistical analysis confirms this prediction. Lighter staining mark” at a height around the particle where apparently results in a “high-water the topography of the side facing the support is considerably different from the mean topography of a heavily stained particle in either view. The apparent lateral extension of the upper side protrusion of an R particle is far greater with lighter staining but, paradoxically, the stain invasion is much greater into the other lateral margin of the particle. While it might be tempting to make direct morphological interpretations from this pattern of variation, the fact that these images are merely projections of the actual particle structure must be borne in mind. Also, no attempt has been made in the model to account for possible preferential binding of the uranyl ions to sites of exposed RNA (Korn, 1980), which could result in positive staining effects overlying or modifying the basic negative-stain pattern.

8. Discrimination

Between L and R Views of the 40 S Subunit

It is important to note that the difference observed in the total result of a consistent difference between any L and any R projection

averages is the and is not due

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FIG. 10. Correspondence analysis of a mixed population of 31 L (0) and 31 mirrored R (A) particles taken from the same micrographs: map of the first 2 factors. The 2 populations are almost completely differentiated by a steeply diagonal dividing line. While axis 2 performs the major L ver.w~ R discrimination on the basis of differences in certain specific regions of the particle (see Fig. 1 l), the slight inclination of the L/R boundary line implies that axis-l stain variations also contribute to a small degree to the distinction. The relative importance of the axis-2 distinction relative to that of axis 1 has increased to 1: 2 (105 versus 21.2% of the total variance) in this analysis. This may be compared to ratios of 1 : 5 (Fig. 3) and 1 : 3 (see the legend to Fig. 9), respectively, for the analyses of the individual I, and R populations.

to the deviation of just a fraction of the mirrored R views from the L views. We made this observation by subjecting a mixed population of L and mirrored R views to correspondence analysis (Fig. 10). To exclude the influence of the selection of particles in the two views from different micrographs, L and R particles were chosen from the same six micrographs, and identical numbers of particles in each

Id8

,J. FRANK.

A.

VERSCHOOR

AND

M.

BOUBLIK

view were taken from any one micrograph. L and mirrored R views were aligned with respect to each other. While the first factorial axis remains the axis of stain variation (cf. section 4, above), the second axis now separates the L from the mirrored R views. The map of these first two factors (Fig. 10) shows the existence of two clear domains separated ,by a steep diagonal, almost coincident with the vertical axis, from upper left to lower right. To the left of it fall all of the L particles (0’7 to 70, denoted by circles) ; to the right fall the mirrored R particles (81 to 132, denoted by triangles). Only one R particle (111) falls on the wrong side of the boundary and would thus have been misclassified by this analysis as an L particle. Another particle (105) falls along the dividing line, but otherwise the distinction is unambiguous. The importance images for the L + R 1 versus 2 map show by what criteria the analysis distinguishes the particles. As in the analyses of L and R populations alone, the two images relating to axis 1 reveal the outer stain ring : inner core region distinction (data not shown). The importance images for the left and right halfplanes (Fig. 11) show which features vary between the L and R populations, since the boundary between the two clusters almost coincides with the first axis. The main areas of the image grid highlighted by these importance images relating to axis 2 are those regions in which I, particles differ from R particles. However, the boundaries of these regions do not coincide with the particle boundaries found in the two averages. This indicates that not only the stain distribution within the particle area, but also some portion of the outer stain wall in contact with the nucleoprotein mass, is characteristically different in the two positions of the subunit on the specimen grid.

FIG:. 11. Comparison of the importance images (bottom row) relating to the second axis in Fig. 10 with the L and mirrored R total averages (top row). The centers of the regions of high variance (black) depicted in the importance images correspond precisely to the locations of stain minima in the averages that change in position, size or intensity between the 2 views.

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The most obvious visual difference between L and averaged R particle images is in the relative sizes and positions of the two side protrusions in the middle segment of the particle. The corresponding regions of the importance images should show how the two views are distinguished in the statistical analysis, In the left-halfplane importance image of Figure 11, one major concentration of variance forms an annulus precisely centered on the stain minimum of the upper protrusion in the L average. A similar comparison can be made for the right-halfplane importance image and the lower protrusion in the mirrored R average. In essence, the complementary importance images are describing inversely correlated expansions of the two particle protrusions. The central light spot within the dark region of high variance can be envisaged as the minimum expression of the particle protrusion, and the nearly encircling dark area corresponds to the area on the image grid into which the protrusion expands (and the stain area thus contracts).

9. Stain Variability

in R and L Views

In all populations of the 40 S particles investigated (L, R, and L+R), the stain variation was the predominant distinguishing feature of interparticle variation. That the extent of this variation is different in the L and R populations can be inferred from a comparison of the clusters on the L+ R map, from a visual comparison of horizontal strip averages for both populations, and from a quantitative comparison of the Fourier transforms of independent averages within each view. On the L + R map (Fig. lo), the main cluster of the R particles (right-hand side) extends over less of the vertical extent of the map than does the L distribution (lefthand side). Investigation of the entire population of R particles (section 7, above) showed that the virtual absence of particles with strong staining (lowermost quarter of the map) is significant. The same observation can be made from a comparison of the four horizontal strip averages for L and R particles from the maps of Figures 4 and 9. The range of stain variation is significantly smaller for the R population than for the L population. A heavy, wide ring of stain such as observed in the lowest horizontal strip average of L particles (Fig. 4) is not observed for R particles. A further indication for a difference in the statistics of L and R views is found by applying criteria from X-ray crystallography to the Fourier transforms of independent averages. We used the differential phase residual A8 (Frank et al., 1981b) as a measure of agreement between averages formed from two independent, randomly selected sets of particles within each population. The numbers of particles taken from any one electron micrograph were exactly matched for each average to exclude bias. The phase residual is defined as:

where F, and F, are the two Fourier transforms, SC$is their phase difference, and the summation extends over an annulus of the Fourier plane. A plot of AtI versus the

130

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. : 0

. 0

0

2

0 JO-0 -

20-0 0

. 0

.

. 0

cl 0 . o-01 l/l50

0.02

0.031 l/32 5, (x-1)

0.04

FIN:. 12. Plot of the differential phase residual A0 between the Fourier transforms of matched pairs of independent averages (each formed over 13 particles) from the L (0) and the R (0) populations analyzed in Fig. 10, as a function of a resolution si. A low value indicates good agreement between the transforms, but with increasing resolution the deviation between them increases. The notable difference in behavior at low resolution (
median radius of the annulus (Fig. 12) shows a large discrepancy at very low spatial frequencies ( < l/150 A-‘) between averages in the L view (Frank et aZ., 19816) but not between the R averages. Fourier coefficients in this low-resolution range represent mainly the shape and relative strength of the outer stain layer. A high phase residual indicates a relatively large initial fluctuation of these coefficients, which is not sufficiently suppressed by averaging over a limited number of particles. The larger stain variation observed for the L population might indicate that particles in the L view present a surface to the stain that is somehow less uniform or smooth. The difference may be attributed to differences in the paths of stain migration into cavities and channels formed by the irregular particle surface in contact with the support film. Stain has been found to contract under electron irradiation (Unwin, 1974), and the variability of the residual stain pattern will depend upon the sizes, shapes and connectivity of these crevices in a complicated way. Another possible factor affecting the variability of the stain is the range of orientations that the particle can assume in either position under the geometric constraints imposed by the respective topography (see van Heel & Frank, 1981).

10. Discussion This statistical analysis of two populations of 40 S subunits appearing in different lateral views has led us to conclude that not only do L and R particles but their populations also have have different characteristic appearances, distinctive statistical behaviors. In addition to the morphological differences immediately clear from averages for

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the two views, differences in the patterns of negative stain surrounding the particles indicate an asymmetry between the two sides of the particle. Differing topographies could further result in differing preferred orientations on the support film, leading to variations in the angle of view of the projected structure. While the overall pattern of stain maxima around the particles is different between the two lateral views, the two populations also each display a continuous range of staining behavior, which differs between the two populations. The immersion of particles in stain is evidently partial. Successive subaverages of sets of particles in either L or R view that have a similar degree of staining show a consistent pattern of changes in the outline of the stain-excluding region. Our finding for the R strip averages relating to relative stain strength, that the lighter the outside stain concentration the more “atypical” the outline of the stainet al. (1971) that excluding particle region, agrees with the finding of Nonomura “one-sided” (Horne & Wildy, 1963) images were more frequent in regions of thin stain. In these images, the details from the side of the particle facing the support will be imaged predominantly or even exclusively. In the present study, we have only discussed the first two factors of variance for each of the three populations (L, R, L+ R), but this is sufficient to show that different interpretations must be placed on the variations that are distinguished. In each case, the first factor was the stain variation. Determination of whether the second factor bears a direct relationship to the first, as indicated by skewedness of the map distribution, should enable us to distinguish “structurally significant” variations of the particle projections (e.g. differences in orientation related to the topography of the particle in contact with the support film) from variations due only to different degrees of immersion of otherwise “identical” particles. It appears that in a situation of partial, and necessarily variable, negative stain immersion, the differences between particles will be considerable. In fact, these will predominate to the extent that subtler differences that would be of more direct value for structural interpretation may be completely masked. Detailed statistical analysis may be the only way to separate, or at least recognize, the role of stain behavior in determining the appearance of the particle projection. Other sources of variation not within experimental control include specimen distortion due to air-drying, electron beam damage, and fluctuations in the composition and conformation of the ribosomal particles due to variability in their state of biological activity; in a standard preparation, only about 20 to 40o/o of ribosomal particles are active. In principle, each of these effects can be investigated and accounted for similarly to the variation of negative staining in the present study. However, both the random stain variation and the distortion associated with air-drying can be eliminated through investigation of unstained, freeze-dried specimens with the scanning transmission electron microscope (Boublik et al., 1981h).

11. Conclusions The results presented here point to the potential of a new methodology, singleparticle averaging combined with multivariate statistical analysis, in the electron


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microscopic investigation of macromolecular assemblies. Re-examination and quantitative confirmation of many visual interpretations made in the study of ribosomal structure are now possible. However, the most important aspect of the method is that it allows averages of a well-characterized set of images relating to a particle projection to be obtained, which is a necessary step toward threedimensional reconstruction. The multivariate statistical analysis, when applied to images of a particle population, characterizes and quantifies the different trends of interparticle variance. Its value in assessing the validity of the single-particle averaging procedure is clear: an understanding of how the particle images vary tells us whether it is legitimate to sum all images, or whether only images within certain subsets should be summed to attain an average that is truly representative for the population. Not only is the resolution higher if only particles within a map cluster are averaged, but also this average will characterize one particular form of the particles comprising the population. Several such distinct and independent subaverages are obviously more informative than a total average that blurs what the analysis has shown to be significant distinctions. The general potential of the technique is as a new analytical tool that could help us to recognize subtle differences in molecular structure, existing or introduced by chemical modifications, and to monitor experimental procedures. The way in which images are distributed on the map, in distinct clusters or in a continuous manner, is in itself informative. The form of the distribution will determine how the population should be treated subsequently, and how results of averaging are to be interpreted. Clustering implies the existence of as many major forms of the particle projection as there are clusters. A separation into two clusters on the basis of size or position of some morphological feature may arise from many causes: two stable positions of the particle on the grid, giving rise to two different projections ; the existence within the population of two groups of particles differing in protein composition, producing subtle differences in the morphology of the nucleoprotein mass, etc. Continuous trends observed in the statistical analysis, on the other hand, may suggest a continuous variation of the morphology, or a continuous variation in produce viewing angle. Many random factors, such as the density of staining, continuous variations. Here, the value of the analysis lies in the fact that, it allows images to be selected that fall into a narrow range of variation of a factor that cannot be directly controlled in the experiment. We thank discussions.

Drs

Marin

van

Heel.

David

DeRosier

and

Jean-Pierre

Bretaudiere

for

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Korn. A. P. (1980). Fltramicroscopy. 5, 513%520. Kurland, C. G.. Voynow, P., Hardy, S. J. S.. Randall, L. 8 Lutter, L. (1969). Cold Spri,tg Hurbor Symp. Quant. Biol. 34, 17-24. Lake. tJ. A. (1976). J. Mol. Biol. 105, 131P159. Lam, M, K. T., Changchien, L.-M. & Craven. G. R. (1979). J. Mol. Biol. 128, 561-575. Dunod. Lebart, L.. Morineau, A. & Tabard. N. (1977). Techniques de la description statistique. Paris. Lutsch. G., Bielka. H., Wahn, K. 8: Stahl. J. (1972). Actn Biol. Med. Germ. 29. 851-876. Lutsch. (G., Pleissner. K.-P.. Wangermann. G. & Noll, F. (1977). =1ctn Biol. Med. Germ. 36. K59-K62. Moody, M. F. (1967). J. ilfol. Biol. 25, 167%200. Moore. P. B. (1980). In Ribosomrs (Chambliss, G.. Craven, G. R.. Davies. J.. Davis. K.. Kahan, I,. & Nomura, M.. eds). pp. 11 I-133, University Park Press, Baltimore. Nonomura, IT., Blobel, G. & Sabatini. D. (1971). J. MoZ. Biol. 60. 303-323. Schreier, M. H. & Staehelin, T. (1973). J. Mol. Biol. 73. 329-349. Steinkilberg. M. & Schramm, H. J. (1980). Hoppe-fkyler’s Z. Physiol. Chum. 361. 1363-1369. Steven. A. C. $ Navia. M. A. (1980). Proc. AVat. Acad. ~S”ci.. L7.N.A 77, 4721-4725. Tischendorf, G. n::., Zeichardt. H. & Stoffler, G. (1974). IWO/. 0~~~. Gent. 134. 209-223. I:nwin. I’. N. T. (1974). J. ,noZ. Biol. 87, 657-670. Valent’ine. R. C. (1961). Advan. Virus RPS. 8. 287-318. van Heel; M. & Frank, J. (1980a). In Pattern Recognitio?l in Practice (Gelsema. E. S. & Kanal. L. R’., eds). pp. 235-243, North-Holland, Amsterdam. van Heel. M. & Frank, J. (1980b). In Proc. 7th Eur. Congr. Elec. Microsc. (Brederoo. P. & de Priester. W., eds), vol. 2. pp. 692-693. the Seventh European Congress on Electron Microsropy Foundation, Leiden. van Heel. M. & Frank, J. (1981). Ultramicroscopy. 6, 187-194. Vasilier. V. D. (1974). Acta Biol. Med. Germ. 33. 779-793. Wabl. M. R.. Barends, P. J. & Nanninga. 1\‘. (1973). Cytobiologie. 7. I-9. Wade, R. H.. Brisson, A. & Tranqui, L. (1980). J. Microsc. Spectrosc. Electron. 5. 69&‘jl2. Zingsheim, H. P.. Seugebauer, D.-Ch.. Barrantes. F. cJ. 8r Frank. J. (1980). Proc. Sat. Acad. Sci.. r-.S.d 77, 952-956. Edited

by A. Klug