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Use of frozen-hydrated axonemes to assess imaging parameters and resolution limits in cryoelectron tomography
Journal of
Structural Biology Journal of Structural Biology 138 (2002) 47–57 www.academicpress.com
Use of frozen-hydrated axonemes to assess imaging parameters and resolution limits in cryoelectron tomography Bruce F. McEwen,a,b,* Michael Marko,a Chyong-Ere Hsieh,a and Carmen Mannellaa,b a
Wadsworth Center, New York State Department of Health, P.O. Box 509, Empire State Plaza, Albany, NY 12201-0509, USA b Department of Biomedical Sciences, State University of New York at Albany, Albany, NY 12201-0509, USA Received 24 January 2002; and in revised form 11 April 2002
Abstract Using a 400-kV cryoelectron microscope, we have obtained tomographic reconstructions of frozen-hydrated sea urchin axonemes with 8–10-nm resolution, as assessed by detection of characteristic components including doublet microtubules, radial spokes, central sheath projections, and outer dynein arms. We did not detect the inner dynein arms or the microtubule lattice. The 1/(8 nm) and 1/(16 nm) layer lines are consistently present in power spectra of both projection images and tomographic reconstructions. Strength and detection of the layer lines are dependent upon total electron dose and defocus. Both layer lines are surprisingly resistant to electron doses of up to 11 000 electrons/nm2 . We present a summary of resolution considerations in cryoelectron tomography and conclude that the fundamental limitation is the total electron dose required for statistical significance. The electron dose can be fractionated among the numerous angular views in a tomographic data set, but there is an unavoidable fourth-power dependence of total dose on target resolution. Since higher-resolution features are more beam-sensitive, this dose requirement places an ultimate limit on the resolution of individual tomographic reconstructions. Instrumental and computational strategies to circumvent this limitation are discussed. Ó 2002 Elsevier Science (USA). All rights reserved. Keywords: Axoneme; Cryoelectron tomography; Electron tomography; Frozen-hydrated specimen
1. Introduction Electron tomography is a versatile three-dimensional (3D) reconstruction technique for transmission electron microscopy because it does not require the specimen to have symmetry or to occur as identical unit structures (reviewed in Baumeister et al., 1999; McEwen and Marko, 1999, 2001; McEwen and Frank, 2001). However, this versatility comes with the requirement that all projection images used for the reconstruction be recorded from a single copy of the object. Consequently, the susceptibility of biological specimens to radiation damage in the electron beam is a more severe limitation for electron tomography than it is for other 3D reconstruction methods. Despite this limitation, electron tomography has been applied to a wide variety of
*
Corresponding author. Fax: +1-518-486-4901. E-mail address: [email protected] (B.F. McEwen).
plastic-embedded and negatively stained specimens (see McEwen and Marko, 2001). Cryoelectron microscopy has been a landmark development in modern electron microscopy, because it enables imaging of macromolecular assemblies in a nearnative state (Dubochet et al., 1987, 1988). Initially, the susceptibility of frozen-hydrated specimens to electron beam damage precluded the recording of a complete tomographic tilt series on unique objects. The situation changed with the development of automated data collection methods that enabled efficient recording of tilt series with a relatively low electron dose (Koster et al., 1997; Fung et al., 1996). It has also become apparent that frozen-hydrated specimens imaged in thick ice at higher voltages are more dose-tolerant than previously thought (e.g., Grimm et al., 1998). As a result, there have been an increasing number of applications of electron tomography of frozen-hydrated specimens (e.g., Bullitt et al., 1997; Grimm et al., 1998; Nicastro et al., 2000; Mannella et al., 1999, 2001; Hsieh et al., 2001; and contributions by Frank et al., 2002 and Hsieh et al., 2002).
1047-8477/02/$ - see front matter Ó 2002 Elsevier Science (USA). All rights reserved. PII: S 1 0 4 7 - 8 4 7 7 ( 0 2 ) 0 0 0 2 0 - 5
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Despite the growing enthusiasm for electron tomography of frozen-hydrated specimens, there has yet to be a systematic evaluation of optimal imaging parameters or the ultimate resolution potential of the method. Predictions have been made for 2 to 3-nm resolution (Baumeister et al., 1999). If this level of resolution is attained, it would allow docking of atomic models of macromolecules into tomographic reconstructions and thereby determine their in situ interactions in the cellular context (see B€ ohm et al., 2000). However, the only example where that level of resolution has been obtained by cryoelectron tomography was a study that employed tomography in combination with single-particle averaging (Nitsch et al., 1998). At present, none of the reported tomographic reconstructions of frozen-hydrated specimens convincingly show resolution beyond 6–8 nm unless some form of particle averaging was invoked. Nevertheless, studies on insect flight muscle demonstrate that for favorable specimens 5- to 8-nm resolution is sufficient to achieve reasonably accurate docking of macromolecules such as actin and myosin (Taylor et al., 1999). Axonemes are the structural cores of eukaryotic cilia and flagella and an excellent test specimen for assessing the potential of electron tomography of frozen-hydrated specimens. The most common axoneme structural motif comprises nine doublet microtubules arranged cylindrically about a central pair of singlet microtubules (Gibbons, 1981; Goodenough and Heuser, 1985; Sugrue et al., 1991). The central pair of microtubules is surrounded by a sheath and is connected to each of the outer doublet microtubules via an array of radial spokes. The radial spokes and elements of the central sheath are arranged with a characteristic, and speciesdependent, periodicity along the cylindrical axis (Gibbons, 1981; Goodenough and Heuser, 1985; Sugrue et al., 1991). Dynein molecules are arranged in two radially separated rows along one side of each of the outer doublet microtubules. Dynein axial periodicity is 24 nm for the outer row (the outer dynein arms) and 96 nm for the inner row (inner dynein arms) (Porter, 1996). Inner dynein arms have a complex structure consisting of eight distinct heavy chains within the unit repeat (reviewed in Porter, 1996). Axonemes are good test specimens for establishing imaging and reconstruction parameters in tomography because their size is typical of tomographic specimens (diameter ¼ 250 nm), it is easy to isolate sufficient quantities of intact and functionally active organelles, and the regular arrays of distinct, well-studied structural components provide a convenient benchmark for evaluating structural preservation of the specimen and the quality of both individual projection images and reconstructions at several different resolution levels. The sizes of these components span a useful range: 25–30 nm for the outer doublet and central pair microtubules,
15–25 nm for the radial spokes, 10–20 nm for the outer dynein arms and the central sheath elements, 5–10 nm for inner dynein arm components, and 3–6 nm for tubulin subunits. Because of the periodic and partially helical arrangement of these components, the power spectra of projection images (and slices from the reconstruction) contain layer lines that lend themselves to easy detection and intensity measurement. Thus, the overall resolution of the reconstruction can be estimated from structural features that are detectable in the unprocessed 3D volume, whereas structural preservation in the specimen can be monitored by inspection of power spectra layer lines in either the input projection images or single slices from the reconstructions. Since the signal in layer lines of the power spectra is inherently averaged over multiple copies of a unit structure, power spectra cannot be used to assess the resolution obtained for unique structures in the 3D reconstruction. In the current study, we use the axoneme as a tool with which to investigate the relationship between electron dose, defocus, and resolution attained in electron tomography of frozen-hydrated specimens. We use these data, and the relationship between resolution and the electron dose required for statistical significance, to assess the limitations of electron tomography of frozenhydrated specimens. Finally, we suggest strategies to circumvent such limitations. Preliminary reports of these data have been published (McEwen et al., 1998, 1999; Marko et al., 1999, 2000).
2. Materials and methods 2.1. Specimen preparation Axonemes from sea urchin flagella were prepared from Strongylocentrotus purpuratus sperm by osmotic shock and differential centrifugation (Bell et al., 1982). Half of the sample was prepared with the outer membrane intact; in the other half, the outer membrane was removed with 1% Nonidet-P40 detergent. Axonemal pellets were stored in liquid nitrogen until use. Pellets were thawed and resuspended in low-salt Hepes buffer. Ten-nanometer colloidal gold was spun and resuspended in low-salt Hepes buffer and then mixed 50:50 with the axoneme suspension to serve as fiducial markers for tilt-series alignment. Immediately, 5-ll aliquots of sample were deposited on 200-mesh grids having a lacy carbon support film. The grids were double-blotted and plunged in liquid ethane cooled by liquid nitrogen (Dubochet et al., 1988). 2.2. Microscopy Routine cryoelectron microscopy was carried out using a JEOL JEM4000FX at an accelerating voltage of
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400 kV. A Gatan Model 626 cryo-transfer specimen holder was used, and the temperature was maintained at )176 °C during imaging. Images were recorded on a Tietz (TVIPS, Gauting, Germany) 1024 1024-pixel slow-scan CCD camera binned to 512 512 pixels. The scintillator consisted of a 15-lm-thick layer of P40 phosphor. With binning, the effective CCD element size was 48 lm, and the final pixel size on all images and reconstructions was 1.0 nm. Low-dose imaging and tomographic data collection were carried out using a modification of the Tietz EM automation system (Rath et al., 1997). The electron dose was determined from the mean pixel value of the CCD image, by means of calibration data using a Faraday cage. All images were recorded from axonemes lying over holes in the lacy carbon support film. For electron tomography, tilt series were recorded from )60 to +60° with a 2° tilt increment and an underfocus value of 15 lm. The total electron dose was 6100 e =nm2 . The dose was increased with the tilt angle so as to keep the mean pixel value of the image constant. The sample was exposed to an additional dose of approximately 20% during initial setup and search operations. For some experiments, a series of images was recorded from the same field of the specimen. In this case, the electron dose per image and the exposure time (1 s) remained the same, and the images were recorded at intervals of 20 s with the beam blanked between exposures. Energy-filtered microscopy was done at the National Institute of Standards and Technology (Gaithersburg, MD) using an FEI CM300FEG with a Gatan GIF200 postcolumn energy filter. The accelerating voltage was 300 kV, and a Gatan Model 626 cryotransfer specimen holder was used at )176 °C. The GIF CCD camera had an effective CCD element size of 48 lm for 512 512pixel images and used a YAG crystal scintillator. The underfocus value was 10 lm, at which a CTF first minimum was observed at about 1/(6 nm). Images of the same field were recorded in pairs: one with and one without energy filtration. The zero-loss images were recorded with a 10-eV slit width. An incident dose of 1000 e =nm2 was used for both filtered and unfiltered images. This dose was about 10 times higher than that used with the JEM4000 system and was required because of the lower sensitivity of the YAG scintillator. Nevertheless, the results did not change when the order of recording filtered and non filtered images was reversed. 2.3. Image analysis Tilt-series alignment was determined from the locations of gold fiducial markers as described in Penczek et al. (1995) and tomographic reconstructions were computed using SPIDER (Frank et al., 1996). Power spec-
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trum plots were obtained as follows: axoneme images were rotated so that the cylindrical axis of the axoneme was horizontal. An area free of gold or other background particles was then windowed out and padded back to the original image size of 512 512 pixels. The Fourier transform was computed, and the power spectrum was projected in the direction parallel to the layer lines for plotting. These operations were performed in the same way for each experiment, and no normalization or rescaling of the images took place at any step. Peak heights of layer lines over background were measured from the plots. For analyses in which individual images of an exposure series were summed, images of the series were first aligned using cross-correlation.
3. Results 3.1. Tomographic reconstructions Before tomographic data collection, we screened specimens using on-line Fourier transformation of image fields approximately 256 256 nm. We recorded a tilt series only if the 1/(8 nm) and 1/(16 nm) layer lines were clearly visible in the power spectrum. Figs. 1a and b show an example of an image of an untilted frozenhydrated sea urchin axoneme and the corresponding power spectrum with visible 1/(8 nm) and 1/(16 nm) layer lines. Fig. 1c shows a single slice from the tomographic reconstruction of the same axoneme. The reconstructed volume has been rotated so that the cylindrical axis of the axoneme is horizontal. A number of structural features are evident. The power spectrum of this slice is shown in Fig. 1d with 1/(8 nm) and 1/(16 nm) layer lines indicated. The diagonal dark band indicates the direction of the ‘‘missing wedge’’ artifact caused by the limited tilt range of the specimen stage, 60°. Longitudinal and axial slices from a typical axoneme reconstruction illustrating a row of radial spokes, central sheath projections, and outer dynein arms are presented in Fig. 2. The black arrows in Figs. 2a, b, and e indicate a point on the tip of a radial spoke viewed from the y–z, x–y, and x–z planes. Similarly, the black arrowheads in Figs. 2c and d indicate the same dynein outer arm from longitudinal and axial views, while white arrows point out two different central sheath projections in Fig. 2b. The radial spokes and central sheath projections are readily apparent in Fig. 2, while the outer dynein arms are less clear but still distinct. We did not detect tubulin subunits in the microtubule lattice, and we were not able to resolve inner dynein arms from the adjoining radial spoke heads. The size of detectable features in the reconstruction—i.e., outer dynein arms with a head domain diameter of approximately 10 nm (Mastronarde et al., 1992), but not tubulin subunits (4–5 nm), or inner dynein arms (5–8 nm in diameter;
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Fig. 1. Cryoelectron tomography of the axoneme. (a) Projection image of a frozen-hydrated axoneme. Horizontal striations are primarily due to the outer doublet microtubules. (b) Power spectrum from a window of (a). The 1/(8 nm) and 1/(16 nm) layer lines are indicated. (c) A single 1.2-nm-thick slice from the tomographic reconstruction of (a). (d) Power spectrum from a window of (c). The 1/(8 nm) and 1/(16 nm) layer lines are indicated. The dark streak in the diffraction pattern is due to the wedge of missing Fourier information that arises from the limited angular tilt range.
Porter, 1996)—is consistent with a resolution of 8– 10 nm. The need for more quantitative resolution measures for electron tomography is discussed below (Section 4) and in Porter (1996). From the axial views of Figs. 2d and e, it is evident that this particular axoneme is severely flattened. Although the origin of this flattening is unclear, it is likely to involve surface tension from the thinning film of water formed as the specimen is blotted shortly before plunging (Kellenberger, 1991). This explanation predicts that axonemes in thicker ice would be less flattened.
Fig. 2. Selected components from an axoneme reconstruction as shown in 1.2-nm-thick slices from the tomographic reconstruction. (a) A row of radial spokes. A single spoke is indicated by the black arrow. (b) A row of central sheath projections with two of the projections indicated by white arrows. The black arrow points to the same location as in (a) and marks the head of that spoke. (c) A row of outer dynein arms, with a single dynein indicated by the black arrowhead. (d) Cross-sectional view of the axoneme. Black arrowhead indicates the same coordinates as in (c). (e) Another cross-sectional view. The black arrow indicates the same radial spoke as in (a) and (b) viewed from the third orthogonal direction. From cross-sectional views, it is evident that the axoneme is flattened.
However, image contrast will be lower in such regions of the grid because of increased multiple scattering. We believe that is the reason that we detected the 1/(16 nm) and 1/(8 nm) layer lines in regions of thin ice in which
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tempted, the author argued that the structures were not flattened based upon the width of the axonemes. The images were collected from intact cells using a 120-keV TEM with an energy filter. The strong layer lines observed in the power spectra from these images may be attributable to the use of energy filtration. 3.2. Underfocus optimization
Fig. 3. The effect of energy filtering. Images and power spectra are compared for unfiltered and zero-loss filtered microscopy, using the same axoneme field and the same electron dose. (a) Unfiltered image. (b) Power spectrum of the unfiltered image. (c) Filtered image. (d) Power spectrum for the filtered imaged. Energy filtration both improves the contrast of the specimen and renders minima of the contrast transfer function more visible in the power spectrum of the filtered image (at symbol 0). Acceleration voltage 300 keV, underfocus 10 lm, inelastic mean-free path 0:45 lm.
the axoneme tends to be collapsed. Energy filtering is an obvious approach for recovering contrast lost due to thicker ice. In Fig. 3 we present preliminary data that show significant improvement in image contrast from the use of energy filtering. There is an earlier report of detection of the 1/(4 nm) layer line of frozen-hydrated sea urchin axonemes (Murray, 1986). Although 3D imaging was not at-
The need to assess imaging parameters for electron tomography of frozen-hydrated specimens arises because, until recently, frozen-hydrated specimens most frequently consisted of suspensions of relatively small macromolecular assemblies occurring in multiple copies that can be averaged for enhancement of the signal-tonoise ratio. For a growing number of such specimens, structural analysis has reached or surpassed 1.0-nm resolution. Consequently, images are generally recorded with relatively small underfocus values in order to minimize the effect of the contrast transfer function on high-resolution features. However, imaging close to focus reduces the contrast of low-frequency components, especially for microscopes that are not equipped with a field emission gun (e.g., see Dubochet et al., 1987, 1988; Downing and Jontes, 1992). This is demonstrated for axonemes in Fig. 4, where the power in the 1/(8 nm) and 1/(16 nm) layer lines is plotted against defocus values. The strength of both layer lines is greatly diminished at underfocus values of less than 10 lm, with the optimal underfocus value for the 1/(8 nm) layer line being 10–20 lm at 400 kV on the JEM4000. At 25-lm underfocus the intensity of the 1/(8 nm) layer line falls off, because it approaches the minimum of the contrast transfer function. Given the inherent resolution limits discussed below, the data in Fig. 4 suggest that optimal imaging of tomographic specimens will generally be at relatively high underfocus values.
Fig. 4. Variation of layer-line intensity with defocus. The relative intensities of the 1/(8 nm) and 1/(16 nm) layerlines were measured from power spectrum plots (see Section 2 and Fig. 5) as the peak height above background. The spatial frequencies of the first minimum and first maximum of the contrast-transfer function are indicated below the abscissa for each defocus setting. This information is useful for ‘‘tuning’’ the underfocus to maximize the contrast at the expected tomographic resolution. Acceleration voltage 400 keV.
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Next, we investigated the extent to which loss of contrast from recording the image closer to focus could be compensated for by effectively increasing the electron dose. Figs. 5a and b illustrate the loss in layer line intensity for an axoneme image when recorded at 4- rather than 15-lm underfocus, at an equivalent dose of 80 e =nm2 . In Fig. 5c we sum 20 low-underfocus images to demonstrate that this lost layer line intensity can be retrieved by increased electron dose. Each image was recorded at 4-lm underfocus and 80 e =nm2 . This plot shows the presence of a 1/(5.3) nm layer line that is not
visible at higher underfocus values. There is, however, no indication of the 1/(4 nm) layer line, even though it should be visible at this underfocus value. 3.3. Effects of cumulative electron dose The images summed to produce the plot in Fig. 5c were images 1–20 of a series of 61 images taken successively at 4-lm defocus and 80 e =nm2 to assess the cumulative effect of electron dose on the specimen. Fig. 5d shows the power spectrum plot from the sum of
Fig. 5. Variation of layer-line intensity with defocus and accumulated electron dose. Power spectrum plots were constructed by summing rows in the power spectrum (see Section 2). (a and b) Plots from power spectra of images recorded at 80 e =nm2 and 15- (a) or 4-lm (b) defocus. (c and d) Plots from power spectra of the sum of 20 images from a 61-image exposure series of the same axoneme. Note that the image in (b) is from the first image in the series. Each image of the series was recorded at 4-lm defocus and 80 e =nm2 . (c) Power spectrum plot derived from the sum of images 1–21 of the exposure series. (d) Power spectrum plot derived from the sum of images 41–61 in the series. Note that a trace of the 1/(5.3 nm) layer line remains even after a total accumulated dose of 4900 e =nm2 . The dose required to record strong 1/(8 nm) or 1/(16 nm) layer lines is nearly 20-fold greater at the lower underfocus values. Acceleration voltage 400 keV.
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Fig. 6. Effect of cumulative electron dose on layer-line intensity. Layer-line intensities were measured from power spectra (Figs. 3 and 5) for an exposure series in which the individual images were recorded at 15-lm defocus and 180 e =nm2 at 400 keV. In contrast to Figs. 5c and d, measurements were taken from every third image, and images were not summed. Intensity of the 1/(16 nm) layer line remains steady throughout the series, while the 1/(8 nm) layer line shows an initial sharp drop, followed by a more gradual decline throughout the exposure series. Some structural information at 8 nm is detectable in single images even after 11 000 e =nm2 .
images 41–61 in the same series, corresponding to an average cumulative dose of 4000 e =nm2 . Comparison of Figs. 5c and d indicates that the 1/(8 nm) and 1/ (16 nm) layer lines are remarkably resistant to a total dose of 4000 e =nm2 . Even the 1/(5.3 nm) layer line is still detectable. A second exposure series taken under the same conditions yielded similar results (data not shown). Fig. 6 shows a more detailed analysis of the variation in intensities of layer lines for individual axoneme images in a similar exposure series, recorded at 15-lm underfocus. The intensity of the 1/(8 nm) layer line dropped by 30–40% after an electron dose of less than 1800 e =nm2 and by 80% at the end of the series, corresponding to a total accumulated dose of 11 000 e =nm2 . Similar results were obtained in three repetitions of this experiment (data not shown). The slower drop-off in intensity of the 1/(8 nm) layer line with irradiation for the experiment in Figs. 5c and d than that in the experiment shown in Fig. 6 is explained, at least in part, by the different defocus values employed in the two image series. Due to the lower image contrast at 4-lm defocus (Fig. 5), a higher dose threshold is needed to detect the high-frequency layer lines. In fact, at the dose represented in Fig. 5c (1800 e =nm2 ), the intensity of the 1/(8 nm) layer in the experiment of Fig. 6 had already dropped by almost 45% and decreased only another 20% after the cumulative dose corresponding to that in Fig. 5d. It is also possible that loss of intensity of the high-frequency layer lines with electron exposure is not entirely due to structural degradation, but may also be due to effects such as condensation of vitreous ice (e.g., Heide, 1984). However, in contrast to the 1/(8 nm) layer line, the 1/(16 nm) layer line loses very little of its original intensity with an accumulated electron dose of 11 000 e =nm2 (Fig. 6). This suggests that contrast loss due to ice condensation is not the primary mechanism
for dose-dependent loss of high-resolution information. Instead, there appear to be fundamental differences in response to electron exposure between high- and lowfrequency image components.
4. Discussion In this study, we used the axoneme to assess the current capability of electron tomography to reconstruct frozen-hydrated specimens in the absence of energy filtering. The axoneme is well suited as a test object because of its regular array of well-characterized components that span a size range that is suitable for testing the resolving power of electron tomography. In addition, the prominent layer lines provide a convenient measure for assessing the effects of imaging parameters and irradiation damage. In our tomographic reconstructions, we obtained a resolution of about 8 nm, as judged by our ability to resolve microtubules, radial spokes, central sheath projections, and outer dynein arms (Figs. 2 and 3). From layer line analysis of single images, we were able to quantitate the variation of layerline intensity with defocus and electron dose used for imaging (Figs. 4 and 5). Finally, we characterized specimen damage with irradiation and found a surprising resistance of the 1/(8 nm) and 1/(16 nm) layer lines to electron dose (Figs. 5 and 6). Figs. 5 and 6 also highlight the central dilemma in electron tomography: higher resolution requires higher electron doses, but higher electron doses preferentially degrade high-resolution features. Consequently, while it is relatively straightforward to obtain 8- to 10-nm resolution in cryoelectron tomography, our data indicate that pushing the resolution to 5 nm or better could be a formidable task. Therefore, it is instructive to take a
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closer look at the factors that determine resolution in cryoelectron tomography. In contrast to light microscopy, resolution in biological electron microscopy is not diffraction limited. Rather, resolution is limited by low S/N caused by under-sampling or by specimen damage caused by irradiation or specimen preparation procedures. Most previous descriptions of resolution in electron tomography have only considered limitations due to angular sampling. This was initially formulated by Crowther et al. (1970) as d ¼ pD=N ;
ð1Þ
where d is resolution, D is the diameter of the object, and N is the number of projection images collected. This formulation assumes a cylindrical specimen, single-axis tilt geometry, and full 180° angular coverage. Since the Crowther formulation is based upon maintaining adequate sampling for high-frequency components in the 3D Fourier transform, it is actually the angular interval rather the total number of projections that determines resolution. This distinction is important because full 180° angular coverage is generally not obtained in electron microscopy. Hence, for a given angular interval, the total number of projections collected in tomographic tilt series is variable and fewer than what would have been collected if there were full angular coverage. Therefore, resolution in the region of the 3D Fourier transform where data have been collected is given by d ¼ aDðp=180Þ;
ð2Þ
where a is the tilt angle interval. For quick resolution estimates we can use d aD=60:
ð3Þ
Since the diameter of the axoneme shown in Fig. 1 was about 250 nm (before flattening) and the tilt angle interval 2°, resolution of our reconstructions should be about 8.3 nm, which roughly corresponds to the features we see in the reconstruction (Fig. 2). For plastic sections, the specimen geometry is a slab, not a cylinder (Barnard et al., 1992; McEwen and Heagle, 1997; McEwen and Marko, 1999). Since it is now feasible to cut reasonable-quality frozen-hydrated sections suitable for tomographic reconstruction (Sitte, 1996; Dubochet and Sartori Blanc, 2001; Hsieh et al., this volume), slab geometry is also relevant to cryoelectron tomography. Radermacher (1992) pointed out that when a specimen has slab geometry, and when the tilt series is collected with a constant tilt angle interval, the diameter of the object should be replaced by the slab thickness (i.e., section thickness) divided by the cosine of the maximum tilt angle. Although this formulation addresses undersampling of high-tilt data, it disregards the potential for higher resolution sampling at low tilt an-
gles. Improved results can be obtained by making the angular tilt angle interval progressively finer in proportion to the cosine of the tilt angle as suggested by Saxton et al. (1984). If this cosine tilt scheme is followed, then Eqs. (2) and (3) can be used to determine resolution if D is taken as the slab thickness and a the tilt angle interval at 0°. Although angular sampling is important for experimental design, it is not the fundamental limitation to resolution in electron tomography, because a given electron dose can be fractionated over any number of projection images without loss of statistical significance to the whole reconstruction (Hegerl and Hoppe, 1976; McEwen et al., 1995). This is strictly true if the only noise in the system is electron shot noise, i.e., if a perfect detector is used. Modern slow-scan CCD cameras come close to this requirement. Until recently, the large number of tilt images required for adequate angular sampling of large specimens had discouraged investigators from making full use of dose fractionation. However, improvements in tilt stage design and the speed of automated data collection have made it routine to collect tilt series with a 1° angular interval, and feasible to collect with even finer increments (Ziese et al., 2002). Thus, now is an opportune time to reassess the factors that limit resolution in electron tomography. Grimm et al. (1998) considered resolution limits imposed by the fact that dose fractionation can be carried out only to the extent that each projection is recorded with a dose that provides an adequate signal-to-noise ratio for image alignment. Since smaller specimens require less angular sampling (i.e., smaller value of D in Eq. (2)), the electron dose does not have to be spread over as many images to achieve adequate sampling. Grimm et al. (1998) predicted that it is feasible to achieve a resolution of 2–3 nm for specimens 50–100 nm in diameter with reasonable electron doses of 1000–5000 e =nm2 . For specimens 400 nm in diameter, 10 000 e =nm2 would be required to achieve 5- to 8-nm resolution. These results suggest that a resolution of 2–3 nm will be feasible with specimens that are relatively small and embedded in thin ice layers. Although it makes use of dose fractionation, analysis based upon sufficient electrons for imaging still ignores the more fundamental requirement that the total electron dose be sufficient to achieve statistical significance in the tomographic reconstruction. From the early analysis of Saxberg and Saxton (1981), it is clear that the electron dose required for significance is strongly resolution-dependent and ‘‘disappointingly high’’ for even moderate levels of resolution. According to their formulation Dq ¼ m0 =p1=2 d 2 ;
ð4Þ
where Dq is the standard error of mass density in the 3D reconstruction, p is the total electron dose per unit
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area, d is the pixel size of the reconstruction (1/2 of the resolution limit), and m0 is a constant relating mass density to image contrast. The value for m0 given by Saxberg and Saxton (1981) is 2 1022 kg=nm2 . Note that this formula assumes perfect imaging, which in practice is never achieved. In order to put this formulation into the more familiar terms of resolution and required electron dose, we have defined a contrast factor, Cr , as the difference (from the background) in mass density that must be resolved in order to detect a feature. Since three times the standard error is taken as the smallest mass density that can be reliably detected (see Saxberg and Saxton, 1981), Cr is defined relative to the density of water as Cr ¼ 3 Dq=qH2 O ;
ð5Þ
where the density of water, qH2 O , is taken to be 1024 kg=nm3 . Substituting Eq. (5) and the value for m0 into Eq. (4), we arrive at a form that expresses the required electron dose in terms of desired spatial resolution and the specimen contrast factor P ¼ 5:76 106 =Cr2 r4 ;
ð6Þ
where P is the required electron dose and r is the desired spatial resolution (2 d). In Fig. 7, the relationship in Eq. (6) is plotted for Cr values of 0.3, 0.4, and 0.8. The first two values are based upon estimates by Saxberg and Saxton (1981) that mass density resolution needs to be about 1/3 the density of water for detection of proteins in frozen-hydrated specimens. The fourth-power dependence of electron dose on spatial resolution (Eq. (6)) results in curves slightly steeper than those presented by Grimm et al. (1998), which postulate a third-power dependence of dose on spatial resolution. Comparison of the curves in
Fig. 7. Electron dose required for statistical significance, plotted as a function of desired spatial resolution for contrast factors (i.e., mass density that must be resolved; see text) of 0.3, 0.4, and 0.8 times the density of water.
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Fig. 7 with those in Grimm et al. reveal that for smaller specimens the limiting factor is the electron dose required for statistical significance of the reconstruction, as per Eq. (6), while for larger specimens the limiting factor is the electron dose required for statistical significance in the individual projections, as per the analysis of Grimm et al. (1998). Predictions of Eq. (6) and the curves in Fig. 7 are consistent with a study by Nitsch et al. (1998) in which 227 thermosome particles from cryotomographic reconstructions were averaged to obtain a structural map with an approximate resolution of 2.8 nm. Since the tomography step used a total dose of 2000 e =nm2 , the final reconstruction was made from the equivalent of 2000 227 ¼ 454 000 e =nm2 , indicating a Cr value of 0.45. Thus, a required contrast factor of 1/3 the density of water might be slightly pessimistic and these results indicate that the curves in Fig. 7 are in the right range. The steep dependence of dose on spatial resolution is also indicated by the fact that pushing the resolution of the ribosome to 1.1 nm required approximately 70 000 particles recorded at 1000 e =nm2 (Gabashvili et al., 2000). Actually the dose required was higher than predicted by Eq. (6), due to alignment difficulties and particle inhomogeneities that can limit single-particle reconstructions at higher resolutions. One way to circumvent the dose requirement for statistical significance is to make use of the fact that many tomographic specimens, including the axoneme, contain ordered arrangements of unit components that can be averaged to enhance resolution (e.g., Taylor et al., 1999; Chen et al., 2002). When working with such specimens it is important to note that analysis of power spectra (Figs. 4–6) inherently makes use of averaging information. Therefore, detection of a particular reflection in a power spectra is not evidence that level of resolution is present in the full reconstruction. Since there are several factors that can influence resolution in electron tomography, it will be important to incorporate objective measures for the resolution, rather than relying on estimates from angular sampling or visible details in the reconstructions (Penczek, 2002). From the above considerations, it is evident that, in the absence of averaging, electron tomography of frozen-hydrated specimens will be limited in spatial resolution by the electron dose required for statistical significance. Furthermore, since Eq. (6) assumes perfect imaging, it is important to employ strategies to optimize imaging parameters such as the choice of defocus and, when feasible, use of energy filtration to reduce background due to inelastically scattered electrons. Likewise, the total electron dose should be as high as can be tolerated by the specimen without causing structural damage in the resolution range of interest. This may require some trial and error for each individual specimen, but the data in Figs. 5 and 6 indicate that
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structural information is preserved in frozen-hydrated specimens out to 5.3 nm at doses approaching 5000 e =nm2 at 400 kV (doses will be lower at lower accelerating voltages). It is possible that some specimens can tolerate even higher electron doses when cooled to liquid helium temperature (Chiu et al., 1986). This may extend resolution beyond 5 nm. There are several other promising approaches to circumvent the fundamental resolution limit of biological electron tomography. These include identification of the common structural elements in irregular specimens through use of neural network classification schemes (see the contribution of Pascual-Montano et al., 2002). Such methods have the potential to act as a form of pseudo-averaging that could improve interpretability of low-resolution structural maps. Interpretability of the reconstruction can also be enhanced by noise suppression techniques (Frangakis and Hegerl, 2001). For some specimens, it might be possible to obtain greater interpretability by comparing reconstructions of frozen-hydrated samples with reconstructions of samples prepared by rapid freezing and freeze substitution (e.g., Cheng et al., 2001). The latter are embedded and stained preparations that have higher contrast and are more resistant to damage from the electron beam. When considering estimations of resolution limits for electron tomography of frozen-hydrated specimens, it is also important to keep in mind that an important motivation for attaining higher resolution in cryoelectron tomography is to be able to describe subcellular structures in sufficient detail to recognize and determine the organization of components whose structures may have already been determined at high resolution. The atomic structural maps of such components can then be ‘‘docked’’ into the lower-resolution tomographic reconstruction to deduce how molecular components interact in the cellular context (e.g., Volkmann, 2002). Although the resolution required to achieve this analysis may be specimen-dependent, 5- to 8-nm resolution in reconstructions of insect flight muscle is sufficient to fit atomic maps of myosin into the different myosin conformations found during the power stroke cycle (Taylor et al., 1999; Chen et al., 2002). Furthermore, cryotomography will certainly provide useful information on the conformations of cellular organelles even at resolutions that are too low to enable docking. In summary, although the requirement for statistical significance will set the ultimate limitation on achievable spatial resolution, it is clear that electron tomography of frozen-hydrated specimens has tremendous potential for elucidating subcellular structure, both alone and in combination with other methods. Optimizing this methodology will require continued improvement in our understanding of the factors that limit resolution and corresponding advances in instrumentation, computation, and specimen preparation.
Acknowledgments We thank Dr. Michael Koonce for preparation of the sea urchin sperm and Dr. John Henry Scott of NIST for access to and assistance with energy-filtered microscopy. We also thank Dr. Joachim Frank for helpful comments on the manuscript and stimulating conversations during the analysis of the data. This work was supported by NIH-NCRR Grant P41 RR01219 that supports the Wadsworth Center’s Resource for Visualization of Biological Complexity as a National Biotechnology Resource and by the Wadsworth Center’s core facility for electron microscopy.
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McEwen, B.F., Marko, M., 1999. Three-dimensional electron microscopy and its application to mitosis research. Methods Cell Biol. 61, 81–111. McEwen, B.F., Marko, M., 2001. The emergence of electron tomography as an important tool for investigating cellular ultrastructure. J. Histochem. Cytochem. 49, 553–563. McEwen, B.F., Downing, K.H., Glaeser, R.M., 1995. The relevance of dose-fractionation in tomography of radiation-sensitive specimens. Ultramicroscopy 60, 357–373. McEwen, B.F., Hsieh, C.-E., Marko, M., Buttle, K., Frank, J., 1998. Cryo-electron tomography applied to sperm flagella. In: Benavides, H.A.C., Jienez, L.F. (Eds.), Proceedings of the 14th International Congress on Electron Microscopy, Cancun, vol. IV. Inst. Physics Publishing, Philadelphia, pp. 459–460. McEwen, B.F., Marko, M., Hsieh, C.-E., Frank, J., 1999. The potential of cryo-electron tomography as assessed by reconstruction of sea urchin axonemes. Microsc. Microanal. 5 (Suppl. 2: Proceedings), 410–411. Murray, J.M., 1986. Electron microscopy of frozen hydrated eukaryotic flagella. J. Ultrastruct. Mol. Struct. Res. 95, 196–209. Nicastro, D., Frangakis, A.S., Typke, D., Baumeister, W., 2000. Cryoelectron tomography of neurospora mitochondria. J. Struct. Biol. 129, 48–56. Nitsch, M., Walz, J., Typke, D., Klumpp, M., Essen, L.-O., Baumeister, W., 1998. Group II chaperonin in an open conformation examined by electron tomography. Nat. Struct. Biol. 5, 855–857. Pascual-Montano, A., Taylor, K.A., Winkler, H., Pascual-Marqui, R.D., Carazo, J.-M., 2002. Quantitative self-organizing maps for clustering electron tomograms. J. Struct. Biol. 138, 114–122. Penczek, P.A., 2002. Three-dimensional spectral signal-to-noise ratio for a class of reconstruction algorithms. J. Struct. Biol. 138, 34–46. Penczek, P., Marko, M., Buttle, K., Frank, J., 1995. Double-tilt electron tomography. Ultramicroscopy 60, 393–410. Porter, M.E., 1996. Axonemal dyneins: assembly, organization, regulation. Curr. Opin. Cell Biol. 8, 10–17. Radermacher, M., 1992. Weighted back-projection methods. In: Frank, J. (Ed.), Electron Tomography. Plenum, New York, pp. 91–115. Rath, B.K., Marko, M., Radermacher, M., Frank, J., 1997. Low-dose automated electron tomography: a recent implementation. J. Struct. Biol. 120, 210–218. Saxberg, B.E.H., Saxton, W.O., 1981. Quantum noise in 2D projections and 3D reconstructions. Ultramicroscopy 6, 85–90. Saxton, W.O., Baumeister, W., Hahn, M., 1984. Three-dimensional reconstruction of imperfect two-dimensional crystals. Ultramicroscopy 13, 57–70. Sugrue, P., Avolio, J., Satir, P., Holwill, M.E.J., 1991. Computer modeling of Tetrahymena axonemes at macromolecular resolution: interpretation of electron micrographs. J. Cell Sci. 98, 5–16. Taylor, K.A., Schmitz, H., Reedy, M.C., Goldman, Y.E., FranziniArmstrong, C., Sasaki, H., Tregear, R.T., Poole, K., Lucaveche, C., Edwards, R.J., Chen, L.F., Winkler, H., Reedy, M.K., 1999. Tomographic 3D reconstruction of quick-frozen, Ca2þ -activated contracting insect flight muscle. Cell 99, 421–431. Volkmann, N., 2002. A novel three-dimensional variant of the watershed transform for segmentation of electron density maps. J. Struct. Biol. 138, 123–129. Ziese, U., Janssen, A.H., Murk, J.L., Geerts, W.J.C., Krift, T., Verkleij, A.J., Koster, A.J., 2002. Automated high-throughput electron tomography by pre-calibration of image shifts. J. Microsc. 205, 187–200.
Structural Biology Journal of Structural Biology 138 (2002) 47–57 www.academicpress.com
Use of frozen-hydrated axonemes to assess imaging parameters and resolution limits in cryoelectron tomography Bruce F. McEwen,a,b,* Michael Marko,a Chyong-Ere Hsieh,a and Carmen Mannellaa,b a
Wadsworth Center, New York State Department of Health, P.O. Box 509, Empire State Plaza, Albany, NY 12201-0509, USA b Department of Biomedical Sciences, State University of New York at Albany, Albany, NY 12201-0509, USA Received 24 January 2002; and in revised form 11 April 2002
Abstract Using a 400-kV cryoelectron microscope, we have obtained tomographic reconstructions of frozen-hydrated sea urchin axonemes with 8–10-nm resolution, as assessed by detection of characteristic components including doublet microtubules, radial spokes, central sheath projections, and outer dynein arms. We did not detect the inner dynein arms or the microtubule lattice. The 1/(8 nm) and 1/(16 nm) layer lines are consistently present in power spectra of both projection images and tomographic reconstructions. Strength and detection of the layer lines are dependent upon total electron dose and defocus. Both layer lines are surprisingly resistant to electron doses of up to 11 000 electrons/nm2 . We present a summary of resolution considerations in cryoelectron tomography and conclude that the fundamental limitation is the total electron dose required for statistical significance. The electron dose can be fractionated among the numerous angular views in a tomographic data set, but there is an unavoidable fourth-power dependence of total dose on target resolution. Since higher-resolution features are more beam-sensitive, this dose requirement places an ultimate limit on the resolution of individual tomographic reconstructions. Instrumental and computational strategies to circumvent this limitation are discussed. Ó 2002 Elsevier Science (USA). All rights reserved. Keywords: Axoneme; Cryoelectron tomography; Electron tomography; Frozen-hydrated specimen
1. Introduction Electron tomography is a versatile three-dimensional (3D) reconstruction technique for transmission electron microscopy because it does not require the specimen to have symmetry or to occur as identical unit structures (reviewed in Baumeister et al., 1999; McEwen and Marko, 1999, 2001; McEwen and Frank, 2001). However, this versatility comes with the requirement that all projection images used for the reconstruction be recorded from a single copy of the object. Consequently, the susceptibility of biological specimens to radiation damage in the electron beam is a more severe limitation for electron tomography than it is for other 3D reconstruction methods. Despite this limitation, electron tomography has been applied to a wide variety of
*
Corresponding author. Fax: +1-518-486-4901. E-mail address: [email protected] (B.F. McEwen).
plastic-embedded and negatively stained specimens (see McEwen and Marko, 2001). Cryoelectron microscopy has been a landmark development in modern electron microscopy, because it enables imaging of macromolecular assemblies in a nearnative state (Dubochet et al., 1987, 1988). Initially, the susceptibility of frozen-hydrated specimens to electron beam damage precluded the recording of a complete tomographic tilt series on unique objects. The situation changed with the development of automated data collection methods that enabled efficient recording of tilt series with a relatively low electron dose (Koster et al., 1997; Fung et al., 1996). It has also become apparent that frozen-hydrated specimens imaged in thick ice at higher voltages are more dose-tolerant than previously thought (e.g., Grimm et al., 1998). As a result, there have been an increasing number of applications of electron tomography of frozen-hydrated specimens (e.g., Bullitt et al., 1997; Grimm et al., 1998; Nicastro et al., 2000; Mannella et al., 1999, 2001; Hsieh et al., 2001; and contributions by Frank et al., 2002 and Hsieh et al., 2002).
1047-8477/02/$ - see front matter Ó 2002 Elsevier Science (USA). All rights reserved. PII: S 1 0 4 7 - 8 4 7 7 ( 0 2 ) 0 0 0 2 0 - 5
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Despite the growing enthusiasm for electron tomography of frozen-hydrated specimens, there has yet to be a systematic evaluation of optimal imaging parameters or the ultimate resolution potential of the method. Predictions have been made for 2 to 3-nm resolution (Baumeister et al., 1999). If this level of resolution is attained, it would allow docking of atomic models of macromolecules into tomographic reconstructions and thereby determine their in situ interactions in the cellular context (see B€ ohm et al., 2000). However, the only example where that level of resolution has been obtained by cryoelectron tomography was a study that employed tomography in combination with single-particle averaging (Nitsch et al., 1998). At present, none of the reported tomographic reconstructions of frozen-hydrated specimens convincingly show resolution beyond 6–8 nm unless some form of particle averaging was invoked. Nevertheless, studies on insect flight muscle demonstrate that for favorable specimens 5- to 8-nm resolution is sufficient to achieve reasonably accurate docking of macromolecules such as actin and myosin (Taylor et al., 1999). Axonemes are the structural cores of eukaryotic cilia and flagella and an excellent test specimen for assessing the potential of electron tomography of frozen-hydrated specimens. The most common axoneme structural motif comprises nine doublet microtubules arranged cylindrically about a central pair of singlet microtubules (Gibbons, 1981; Goodenough and Heuser, 1985; Sugrue et al., 1991). The central pair of microtubules is surrounded by a sheath and is connected to each of the outer doublet microtubules via an array of radial spokes. The radial spokes and elements of the central sheath are arranged with a characteristic, and speciesdependent, periodicity along the cylindrical axis (Gibbons, 1981; Goodenough and Heuser, 1985; Sugrue et al., 1991). Dynein molecules are arranged in two radially separated rows along one side of each of the outer doublet microtubules. Dynein axial periodicity is 24 nm for the outer row (the outer dynein arms) and 96 nm for the inner row (inner dynein arms) (Porter, 1996). Inner dynein arms have a complex structure consisting of eight distinct heavy chains within the unit repeat (reviewed in Porter, 1996). Axonemes are good test specimens for establishing imaging and reconstruction parameters in tomography because their size is typical of tomographic specimens (diameter ¼ 250 nm), it is easy to isolate sufficient quantities of intact and functionally active organelles, and the regular arrays of distinct, well-studied structural components provide a convenient benchmark for evaluating structural preservation of the specimen and the quality of both individual projection images and reconstructions at several different resolution levels. The sizes of these components span a useful range: 25–30 nm for the outer doublet and central pair microtubules,
15–25 nm for the radial spokes, 10–20 nm for the outer dynein arms and the central sheath elements, 5–10 nm for inner dynein arm components, and 3–6 nm for tubulin subunits. Because of the periodic and partially helical arrangement of these components, the power spectra of projection images (and slices from the reconstruction) contain layer lines that lend themselves to easy detection and intensity measurement. Thus, the overall resolution of the reconstruction can be estimated from structural features that are detectable in the unprocessed 3D volume, whereas structural preservation in the specimen can be monitored by inspection of power spectra layer lines in either the input projection images or single slices from the reconstructions. Since the signal in layer lines of the power spectra is inherently averaged over multiple copies of a unit structure, power spectra cannot be used to assess the resolution obtained for unique structures in the 3D reconstruction. In the current study, we use the axoneme as a tool with which to investigate the relationship between electron dose, defocus, and resolution attained in electron tomography of frozen-hydrated specimens. We use these data, and the relationship between resolution and the electron dose required for statistical significance, to assess the limitations of electron tomography of frozenhydrated specimens. Finally, we suggest strategies to circumvent such limitations. Preliminary reports of these data have been published (McEwen et al., 1998, 1999; Marko et al., 1999, 2000).
2. Materials and methods 2.1. Specimen preparation Axonemes from sea urchin flagella were prepared from Strongylocentrotus purpuratus sperm by osmotic shock and differential centrifugation (Bell et al., 1982). Half of the sample was prepared with the outer membrane intact; in the other half, the outer membrane was removed with 1% Nonidet-P40 detergent. Axonemal pellets were stored in liquid nitrogen until use. Pellets were thawed and resuspended in low-salt Hepes buffer. Ten-nanometer colloidal gold was spun and resuspended in low-salt Hepes buffer and then mixed 50:50 with the axoneme suspension to serve as fiducial markers for tilt-series alignment. Immediately, 5-ll aliquots of sample were deposited on 200-mesh grids having a lacy carbon support film. The grids were double-blotted and plunged in liquid ethane cooled by liquid nitrogen (Dubochet et al., 1988). 2.2. Microscopy Routine cryoelectron microscopy was carried out using a JEOL JEM4000FX at an accelerating voltage of
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400 kV. A Gatan Model 626 cryo-transfer specimen holder was used, and the temperature was maintained at )176 °C during imaging. Images were recorded on a Tietz (TVIPS, Gauting, Germany) 1024 1024-pixel slow-scan CCD camera binned to 512 512 pixels. The scintillator consisted of a 15-lm-thick layer of P40 phosphor. With binning, the effective CCD element size was 48 lm, and the final pixel size on all images and reconstructions was 1.0 nm. Low-dose imaging and tomographic data collection were carried out using a modification of the Tietz EM automation system (Rath et al., 1997). The electron dose was determined from the mean pixel value of the CCD image, by means of calibration data using a Faraday cage. All images were recorded from axonemes lying over holes in the lacy carbon support film. For electron tomography, tilt series were recorded from )60 to +60° with a 2° tilt increment and an underfocus value of 15 lm. The total electron dose was 6100 e =nm2 . The dose was increased with the tilt angle so as to keep the mean pixel value of the image constant. The sample was exposed to an additional dose of approximately 20% during initial setup and search operations. For some experiments, a series of images was recorded from the same field of the specimen. In this case, the electron dose per image and the exposure time (1 s) remained the same, and the images were recorded at intervals of 20 s with the beam blanked between exposures. Energy-filtered microscopy was done at the National Institute of Standards and Technology (Gaithersburg, MD) using an FEI CM300FEG with a Gatan GIF200 postcolumn energy filter. The accelerating voltage was 300 kV, and a Gatan Model 626 cryotransfer specimen holder was used at )176 °C. The GIF CCD camera had an effective CCD element size of 48 lm for 512 512pixel images and used a YAG crystal scintillator. The underfocus value was 10 lm, at which a CTF first minimum was observed at about 1/(6 nm). Images of the same field were recorded in pairs: one with and one without energy filtration. The zero-loss images were recorded with a 10-eV slit width. An incident dose of 1000 e =nm2 was used for both filtered and unfiltered images. This dose was about 10 times higher than that used with the JEM4000 system and was required because of the lower sensitivity of the YAG scintillator. Nevertheless, the results did not change when the order of recording filtered and non filtered images was reversed. 2.3. Image analysis Tilt-series alignment was determined from the locations of gold fiducial markers as described in Penczek et al. (1995) and tomographic reconstructions were computed using SPIDER (Frank et al., 1996). Power spec-
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trum plots were obtained as follows: axoneme images were rotated so that the cylindrical axis of the axoneme was horizontal. An area free of gold or other background particles was then windowed out and padded back to the original image size of 512 512 pixels. The Fourier transform was computed, and the power spectrum was projected in the direction parallel to the layer lines for plotting. These operations were performed in the same way for each experiment, and no normalization or rescaling of the images took place at any step. Peak heights of layer lines over background were measured from the plots. For analyses in which individual images of an exposure series were summed, images of the series were first aligned using cross-correlation.
3. Results 3.1. Tomographic reconstructions Before tomographic data collection, we screened specimens using on-line Fourier transformation of image fields approximately 256 256 nm. We recorded a tilt series only if the 1/(8 nm) and 1/(16 nm) layer lines were clearly visible in the power spectrum. Figs. 1a and b show an example of an image of an untilted frozenhydrated sea urchin axoneme and the corresponding power spectrum with visible 1/(8 nm) and 1/(16 nm) layer lines. Fig. 1c shows a single slice from the tomographic reconstruction of the same axoneme. The reconstructed volume has been rotated so that the cylindrical axis of the axoneme is horizontal. A number of structural features are evident. The power spectrum of this slice is shown in Fig. 1d with 1/(8 nm) and 1/(16 nm) layer lines indicated. The diagonal dark band indicates the direction of the ‘‘missing wedge’’ artifact caused by the limited tilt range of the specimen stage, 60°. Longitudinal and axial slices from a typical axoneme reconstruction illustrating a row of radial spokes, central sheath projections, and outer dynein arms are presented in Fig. 2. The black arrows in Figs. 2a, b, and e indicate a point on the tip of a radial spoke viewed from the y–z, x–y, and x–z planes. Similarly, the black arrowheads in Figs. 2c and d indicate the same dynein outer arm from longitudinal and axial views, while white arrows point out two different central sheath projections in Fig. 2b. The radial spokes and central sheath projections are readily apparent in Fig. 2, while the outer dynein arms are less clear but still distinct. We did not detect tubulin subunits in the microtubule lattice, and we were not able to resolve inner dynein arms from the adjoining radial spoke heads. The size of detectable features in the reconstruction—i.e., outer dynein arms with a head domain diameter of approximately 10 nm (Mastronarde et al., 1992), but not tubulin subunits (4–5 nm), or inner dynein arms (5–8 nm in diameter;
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Fig. 1. Cryoelectron tomography of the axoneme. (a) Projection image of a frozen-hydrated axoneme. Horizontal striations are primarily due to the outer doublet microtubules. (b) Power spectrum from a window of (a). The 1/(8 nm) and 1/(16 nm) layer lines are indicated. (c) A single 1.2-nm-thick slice from the tomographic reconstruction of (a). (d) Power spectrum from a window of (c). The 1/(8 nm) and 1/(16 nm) layer lines are indicated. The dark streak in the diffraction pattern is due to the wedge of missing Fourier information that arises from the limited angular tilt range.
Porter, 1996)—is consistent with a resolution of 8– 10 nm. The need for more quantitative resolution measures for electron tomography is discussed below (Section 4) and in Porter (1996). From the axial views of Figs. 2d and e, it is evident that this particular axoneme is severely flattened. Although the origin of this flattening is unclear, it is likely to involve surface tension from the thinning film of water formed as the specimen is blotted shortly before plunging (Kellenberger, 1991). This explanation predicts that axonemes in thicker ice would be less flattened.
Fig. 2. Selected components from an axoneme reconstruction as shown in 1.2-nm-thick slices from the tomographic reconstruction. (a) A row of radial spokes. A single spoke is indicated by the black arrow. (b) A row of central sheath projections with two of the projections indicated by white arrows. The black arrow points to the same location as in (a) and marks the head of that spoke. (c) A row of outer dynein arms, with a single dynein indicated by the black arrowhead. (d) Cross-sectional view of the axoneme. Black arrowhead indicates the same coordinates as in (c). (e) Another cross-sectional view. The black arrow indicates the same radial spoke as in (a) and (b) viewed from the third orthogonal direction. From cross-sectional views, it is evident that the axoneme is flattened.
However, image contrast will be lower in such regions of the grid because of increased multiple scattering. We believe that is the reason that we detected the 1/(16 nm) and 1/(8 nm) layer lines in regions of thin ice in which
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tempted, the author argued that the structures were not flattened based upon the width of the axonemes. The images were collected from intact cells using a 120-keV TEM with an energy filter. The strong layer lines observed in the power spectra from these images may be attributable to the use of energy filtration. 3.2. Underfocus optimization
Fig. 3. The effect of energy filtering. Images and power spectra are compared for unfiltered and zero-loss filtered microscopy, using the same axoneme field and the same electron dose. (a) Unfiltered image. (b) Power spectrum of the unfiltered image. (c) Filtered image. (d) Power spectrum for the filtered imaged. Energy filtration both improves the contrast of the specimen and renders minima of the contrast transfer function more visible in the power spectrum of the filtered image (at symbol 0). Acceleration voltage 300 keV, underfocus 10 lm, inelastic mean-free path 0:45 lm.
the axoneme tends to be collapsed. Energy filtering is an obvious approach for recovering contrast lost due to thicker ice. In Fig. 3 we present preliminary data that show significant improvement in image contrast from the use of energy filtering. There is an earlier report of detection of the 1/(4 nm) layer line of frozen-hydrated sea urchin axonemes (Murray, 1986). Although 3D imaging was not at-
The need to assess imaging parameters for electron tomography of frozen-hydrated specimens arises because, until recently, frozen-hydrated specimens most frequently consisted of suspensions of relatively small macromolecular assemblies occurring in multiple copies that can be averaged for enhancement of the signal-tonoise ratio. For a growing number of such specimens, structural analysis has reached or surpassed 1.0-nm resolution. Consequently, images are generally recorded with relatively small underfocus values in order to minimize the effect of the contrast transfer function on high-resolution features. However, imaging close to focus reduces the contrast of low-frequency components, especially for microscopes that are not equipped with a field emission gun (e.g., see Dubochet et al., 1987, 1988; Downing and Jontes, 1992). This is demonstrated for axonemes in Fig. 4, where the power in the 1/(8 nm) and 1/(16 nm) layer lines is plotted against defocus values. The strength of both layer lines is greatly diminished at underfocus values of less than 10 lm, with the optimal underfocus value for the 1/(8 nm) layer line being 10–20 lm at 400 kV on the JEM4000. At 25-lm underfocus the intensity of the 1/(8 nm) layer line falls off, because it approaches the minimum of the contrast transfer function. Given the inherent resolution limits discussed below, the data in Fig. 4 suggest that optimal imaging of tomographic specimens will generally be at relatively high underfocus values.
Fig. 4. Variation of layer-line intensity with defocus. The relative intensities of the 1/(8 nm) and 1/(16 nm) layerlines were measured from power spectrum plots (see Section 2 and Fig. 5) as the peak height above background. The spatial frequencies of the first minimum and first maximum of the contrast-transfer function are indicated below the abscissa for each defocus setting. This information is useful for ‘‘tuning’’ the underfocus to maximize the contrast at the expected tomographic resolution. Acceleration voltage 400 keV.
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Next, we investigated the extent to which loss of contrast from recording the image closer to focus could be compensated for by effectively increasing the electron dose. Figs. 5a and b illustrate the loss in layer line intensity for an axoneme image when recorded at 4- rather than 15-lm underfocus, at an equivalent dose of 80 e =nm2 . In Fig. 5c we sum 20 low-underfocus images to demonstrate that this lost layer line intensity can be retrieved by increased electron dose. Each image was recorded at 4-lm underfocus and 80 e =nm2 . This plot shows the presence of a 1/(5.3) nm layer line that is not
visible at higher underfocus values. There is, however, no indication of the 1/(4 nm) layer line, even though it should be visible at this underfocus value. 3.3. Effects of cumulative electron dose The images summed to produce the plot in Fig. 5c were images 1–20 of a series of 61 images taken successively at 4-lm defocus and 80 e =nm2 to assess the cumulative effect of electron dose on the specimen. Fig. 5d shows the power spectrum plot from the sum of
Fig. 5. Variation of layer-line intensity with defocus and accumulated electron dose. Power spectrum plots were constructed by summing rows in the power spectrum (see Section 2). (a and b) Plots from power spectra of images recorded at 80 e =nm2 and 15- (a) or 4-lm (b) defocus. (c and d) Plots from power spectra of the sum of 20 images from a 61-image exposure series of the same axoneme. Note that the image in (b) is from the first image in the series. Each image of the series was recorded at 4-lm defocus and 80 e =nm2 . (c) Power spectrum plot derived from the sum of images 1–21 of the exposure series. (d) Power spectrum plot derived from the sum of images 41–61 in the series. Note that a trace of the 1/(5.3 nm) layer line remains even after a total accumulated dose of 4900 e =nm2 . The dose required to record strong 1/(8 nm) or 1/(16 nm) layer lines is nearly 20-fold greater at the lower underfocus values. Acceleration voltage 400 keV.
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Fig. 6. Effect of cumulative electron dose on layer-line intensity. Layer-line intensities were measured from power spectra (Figs. 3 and 5) for an exposure series in which the individual images were recorded at 15-lm defocus and 180 e =nm2 at 400 keV. In contrast to Figs. 5c and d, measurements were taken from every third image, and images were not summed. Intensity of the 1/(16 nm) layer line remains steady throughout the series, while the 1/(8 nm) layer line shows an initial sharp drop, followed by a more gradual decline throughout the exposure series. Some structural information at 8 nm is detectable in single images even after 11 000 e =nm2 .
images 41–61 in the same series, corresponding to an average cumulative dose of 4000 e =nm2 . Comparison of Figs. 5c and d indicates that the 1/(8 nm) and 1/ (16 nm) layer lines are remarkably resistant to a total dose of 4000 e =nm2 . Even the 1/(5.3 nm) layer line is still detectable. A second exposure series taken under the same conditions yielded similar results (data not shown). Fig. 6 shows a more detailed analysis of the variation in intensities of layer lines for individual axoneme images in a similar exposure series, recorded at 15-lm underfocus. The intensity of the 1/(8 nm) layer line dropped by 30–40% after an electron dose of less than 1800 e =nm2 and by 80% at the end of the series, corresponding to a total accumulated dose of 11 000 e =nm2 . Similar results were obtained in three repetitions of this experiment (data not shown). The slower drop-off in intensity of the 1/(8 nm) layer line with irradiation for the experiment in Figs. 5c and d than that in the experiment shown in Fig. 6 is explained, at least in part, by the different defocus values employed in the two image series. Due to the lower image contrast at 4-lm defocus (Fig. 5), a higher dose threshold is needed to detect the high-frequency layer lines. In fact, at the dose represented in Fig. 5c (1800 e =nm2 ), the intensity of the 1/(8 nm) layer in the experiment of Fig. 6 had already dropped by almost 45% and decreased only another 20% after the cumulative dose corresponding to that in Fig. 5d. It is also possible that loss of intensity of the high-frequency layer lines with electron exposure is not entirely due to structural degradation, but may also be due to effects such as condensation of vitreous ice (e.g., Heide, 1984). However, in contrast to the 1/(8 nm) layer line, the 1/(16 nm) layer line loses very little of its original intensity with an accumulated electron dose of 11 000 e =nm2 (Fig. 6). This suggests that contrast loss due to ice condensation is not the primary mechanism
for dose-dependent loss of high-resolution information. Instead, there appear to be fundamental differences in response to electron exposure between high- and lowfrequency image components.
4. Discussion In this study, we used the axoneme to assess the current capability of electron tomography to reconstruct frozen-hydrated specimens in the absence of energy filtering. The axoneme is well suited as a test object because of its regular array of well-characterized components that span a size range that is suitable for testing the resolving power of electron tomography. In addition, the prominent layer lines provide a convenient measure for assessing the effects of imaging parameters and irradiation damage. In our tomographic reconstructions, we obtained a resolution of about 8 nm, as judged by our ability to resolve microtubules, radial spokes, central sheath projections, and outer dynein arms (Figs. 2 and 3). From layer line analysis of single images, we were able to quantitate the variation of layerline intensity with defocus and electron dose used for imaging (Figs. 4 and 5). Finally, we characterized specimen damage with irradiation and found a surprising resistance of the 1/(8 nm) and 1/(16 nm) layer lines to electron dose (Figs. 5 and 6). Figs. 5 and 6 also highlight the central dilemma in electron tomography: higher resolution requires higher electron doses, but higher electron doses preferentially degrade high-resolution features. Consequently, while it is relatively straightforward to obtain 8- to 10-nm resolution in cryoelectron tomography, our data indicate that pushing the resolution to 5 nm or better could be a formidable task. Therefore, it is instructive to take a
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closer look at the factors that determine resolution in cryoelectron tomography. In contrast to light microscopy, resolution in biological electron microscopy is not diffraction limited. Rather, resolution is limited by low S/N caused by under-sampling or by specimen damage caused by irradiation or specimen preparation procedures. Most previous descriptions of resolution in electron tomography have only considered limitations due to angular sampling. This was initially formulated by Crowther et al. (1970) as d ¼ pD=N ;
ð1Þ
where d is resolution, D is the diameter of the object, and N is the number of projection images collected. This formulation assumes a cylindrical specimen, single-axis tilt geometry, and full 180° angular coverage. Since the Crowther formulation is based upon maintaining adequate sampling for high-frequency components in the 3D Fourier transform, it is actually the angular interval rather the total number of projections that determines resolution. This distinction is important because full 180° angular coverage is generally not obtained in electron microscopy. Hence, for a given angular interval, the total number of projections collected in tomographic tilt series is variable and fewer than what would have been collected if there were full angular coverage. Therefore, resolution in the region of the 3D Fourier transform where data have been collected is given by d ¼ aDðp=180Þ;
ð2Þ
where a is the tilt angle interval. For quick resolution estimates we can use d aD=60:
ð3Þ
Since the diameter of the axoneme shown in Fig. 1 was about 250 nm (before flattening) and the tilt angle interval 2°, resolution of our reconstructions should be about 8.3 nm, which roughly corresponds to the features we see in the reconstruction (Fig. 2). For plastic sections, the specimen geometry is a slab, not a cylinder (Barnard et al., 1992; McEwen and Heagle, 1997; McEwen and Marko, 1999). Since it is now feasible to cut reasonable-quality frozen-hydrated sections suitable for tomographic reconstruction (Sitte, 1996; Dubochet and Sartori Blanc, 2001; Hsieh et al., this volume), slab geometry is also relevant to cryoelectron tomography. Radermacher (1992) pointed out that when a specimen has slab geometry, and when the tilt series is collected with a constant tilt angle interval, the diameter of the object should be replaced by the slab thickness (i.e., section thickness) divided by the cosine of the maximum tilt angle. Although this formulation addresses undersampling of high-tilt data, it disregards the potential for higher resolution sampling at low tilt an-
gles. Improved results can be obtained by making the angular tilt angle interval progressively finer in proportion to the cosine of the tilt angle as suggested by Saxton et al. (1984). If this cosine tilt scheme is followed, then Eqs. (2) and (3) can be used to determine resolution if D is taken as the slab thickness and a the tilt angle interval at 0°. Although angular sampling is important for experimental design, it is not the fundamental limitation to resolution in electron tomography, because a given electron dose can be fractionated over any number of projection images without loss of statistical significance to the whole reconstruction (Hegerl and Hoppe, 1976; McEwen et al., 1995). This is strictly true if the only noise in the system is electron shot noise, i.e., if a perfect detector is used. Modern slow-scan CCD cameras come close to this requirement. Until recently, the large number of tilt images required for adequate angular sampling of large specimens had discouraged investigators from making full use of dose fractionation. However, improvements in tilt stage design and the speed of automated data collection have made it routine to collect tilt series with a 1° angular interval, and feasible to collect with even finer increments (Ziese et al., 2002). Thus, now is an opportune time to reassess the factors that limit resolution in electron tomography. Grimm et al. (1998) considered resolution limits imposed by the fact that dose fractionation can be carried out only to the extent that each projection is recorded with a dose that provides an adequate signal-to-noise ratio for image alignment. Since smaller specimens require less angular sampling (i.e., smaller value of D in Eq. (2)), the electron dose does not have to be spread over as many images to achieve adequate sampling. Grimm et al. (1998) predicted that it is feasible to achieve a resolution of 2–3 nm for specimens 50–100 nm in diameter with reasonable electron doses of 1000–5000 e =nm2 . For specimens 400 nm in diameter, 10 000 e =nm2 would be required to achieve 5- to 8-nm resolution. These results suggest that a resolution of 2–3 nm will be feasible with specimens that are relatively small and embedded in thin ice layers. Although it makes use of dose fractionation, analysis based upon sufficient electrons for imaging still ignores the more fundamental requirement that the total electron dose be sufficient to achieve statistical significance in the tomographic reconstruction. From the early analysis of Saxberg and Saxton (1981), it is clear that the electron dose required for significance is strongly resolution-dependent and ‘‘disappointingly high’’ for even moderate levels of resolution. According to their formulation Dq ¼ m0 =p1=2 d 2 ;
ð4Þ
where Dq is the standard error of mass density in the 3D reconstruction, p is the total electron dose per unit
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area, d is the pixel size of the reconstruction (1/2 of the resolution limit), and m0 is a constant relating mass density to image contrast. The value for m0 given by Saxberg and Saxton (1981) is 2 1022 kg=nm2 . Note that this formula assumes perfect imaging, which in practice is never achieved. In order to put this formulation into the more familiar terms of resolution and required electron dose, we have defined a contrast factor, Cr , as the difference (from the background) in mass density that must be resolved in order to detect a feature. Since three times the standard error is taken as the smallest mass density that can be reliably detected (see Saxberg and Saxton, 1981), Cr is defined relative to the density of water as Cr ¼ 3 Dq=qH2 O ;
ð5Þ
where the density of water, qH2 O , is taken to be 1024 kg=nm3 . Substituting Eq. (5) and the value for m0 into Eq. (4), we arrive at a form that expresses the required electron dose in terms of desired spatial resolution and the specimen contrast factor P ¼ 5:76 106 =Cr2 r4 ;
ð6Þ
where P is the required electron dose and r is the desired spatial resolution (2 d). In Fig. 7, the relationship in Eq. (6) is plotted for Cr values of 0.3, 0.4, and 0.8. The first two values are based upon estimates by Saxberg and Saxton (1981) that mass density resolution needs to be about 1/3 the density of water for detection of proteins in frozen-hydrated specimens. The fourth-power dependence of electron dose on spatial resolution (Eq. (6)) results in curves slightly steeper than those presented by Grimm et al. (1998), which postulate a third-power dependence of dose on spatial resolution. Comparison of the curves in
Fig. 7. Electron dose required for statistical significance, plotted as a function of desired spatial resolution for contrast factors (i.e., mass density that must be resolved; see text) of 0.3, 0.4, and 0.8 times the density of water.
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Fig. 7 with those in Grimm et al. reveal that for smaller specimens the limiting factor is the electron dose required for statistical significance of the reconstruction, as per Eq. (6), while for larger specimens the limiting factor is the electron dose required for statistical significance in the individual projections, as per the analysis of Grimm et al. (1998). Predictions of Eq. (6) and the curves in Fig. 7 are consistent with a study by Nitsch et al. (1998) in which 227 thermosome particles from cryotomographic reconstructions were averaged to obtain a structural map with an approximate resolution of 2.8 nm. Since the tomography step used a total dose of 2000 e =nm2 , the final reconstruction was made from the equivalent of 2000 227 ¼ 454 000 e =nm2 , indicating a Cr value of 0.45. Thus, a required contrast factor of 1/3 the density of water might be slightly pessimistic and these results indicate that the curves in Fig. 7 are in the right range. The steep dependence of dose on spatial resolution is also indicated by the fact that pushing the resolution of the ribosome to 1.1 nm required approximately 70 000 particles recorded at 1000 e =nm2 (Gabashvili et al., 2000). Actually the dose required was higher than predicted by Eq. (6), due to alignment difficulties and particle inhomogeneities that can limit single-particle reconstructions at higher resolutions. One way to circumvent the dose requirement for statistical significance is to make use of the fact that many tomographic specimens, including the axoneme, contain ordered arrangements of unit components that can be averaged to enhance resolution (e.g., Taylor et al., 1999; Chen et al., 2002). When working with such specimens it is important to note that analysis of power spectra (Figs. 4–6) inherently makes use of averaging information. Therefore, detection of a particular reflection in a power spectra is not evidence that level of resolution is present in the full reconstruction. Since there are several factors that can influence resolution in electron tomography, it will be important to incorporate objective measures for the resolution, rather than relying on estimates from angular sampling or visible details in the reconstructions (Penczek, 2002). From the above considerations, it is evident that, in the absence of averaging, electron tomography of frozen-hydrated specimens will be limited in spatial resolution by the electron dose required for statistical significance. Furthermore, since Eq. (6) assumes perfect imaging, it is important to employ strategies to optimize imaging parameters such as the choice of defocus and, when feasible, use of energy filtration to reduce background due to inelastically scattered electrons. Likewise, the total electron dose should be as high as can be tolerated by the specimen without causing structural damage in the resolution range of interest. This may require some trial and error for each individual specimen, but the data in Figs. 5 and 6 indicate that
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structural information is preserved in frozen-hydrated specimens out to 5.3 nm at doses approaching 5000 e =nm2 at 400 kV (doses will be lower at lower accelerating voltages). It is possible that some specimens can tolerate even higher electron doses when cooled to liquid helium temperature (Chiu et al., 1986). This may extend resolution beyond 5 nm. There are several other promising approaches to circumvent the fundamental resolution limit of biological electron tomography. These include identification of the common structural elements in irregular specimens through use of neural network classification schemes (see the contribution of Pascual-Montano et al., 2002). Such methods have the potential to act as a form of pseudo-averaging that could improve interpretability of low-resolution structural maps. Interpretability of the reconstruction can also be enhanced by noise suppression techniques (Frangakis and Hegerl, 2001). For some specimens, it might be possible to obtain greater interpretability by comparing reconstructions of frozen-hydrated samples with reconstructions of samples prepared by rapid freezing and freeze substitution (e.g., Cheng et al., 2001). The latter are embedded and stained preparations that have higher contrast and are more resistant to damage from the electron beam. When considering estimations of resolution limits for electron tomography of frozen-hydrated specimens, it is also important to keep in mind that an important motivation for attaining higher resolution in cryoelectron tomography is to be able to describe subcellular structures in sufficient detail to recognize and determine the organization of components whose structures may have already been determined at high resolution. The atomic structural maps of such components can then be ‘‘docked’’ into the lower-resolution tomographic reconstruction to deduce how molecular components interact in the cellular context (e.g., Volkmann, 2002). Although the resolution required to achieve this analysis may be specimen-dependent, 5- to 8-nm resolution in reconstructions of insect flight muscle is sufficient to fit atomic maps of myosin into the different myosin conformations found during the power stroke cycle (Taylor et al., 1999; Chen et al., 2002). Furthermore, cryotomography will certainly provide useful information on the conformations of cellular organelles even at resolutions that are too low to enable docking. In summary, although the requirement for statistical significance will set the ultimate limitation on achievable spatial resolution, it is clear that electron tomography of frozen-hydrated specimens has tremendous potential for elucidating subcellular structure, both alone and in combination with other methods. Optimizing this methodology will require continued improvement in our understanding of the factors that limit resolution and corresponding advances in instrumentation, computation, and specimen preparation.
Acknowledgments We thank Dr. Michael Koonce for preparation of the sea urchin sperm and Dr. John Henry Scott of NIST for access to and assistance with energy-filtered microscopy. We also thank Dr. Joachim Frank for helpful comments on the manuscript and stimulating conversations during the analysis of the data. This work was supported by NIH-NCRR Grant P41 RR01219 that supports the Wadsworth Center’s Resource for Visualization of Biological Complexity as a National Biotechnology Resource and by the Wadsworth Center’s core facility for electron microscopy.
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