Open Access

3D reconstruction of biological structures: automated procedures for alignment and reconstruction of multiple tilt series in electron tomography

  • Sébastien Phan1,
  • Daniela Boassa1,
  • Phuong Nguyen1,
  • Xiaohua Wan1,
  • Jason Lanman2, 3,
  • Albert Lawrence1 and
  • Mark H. Ellisman1, 2, 3Email author
Contributed equally
Advanced Structural and Chemical Imaging20162:8

DOI: 10.1186/s40679-016-0021-2

Received: 1 February 2016

Accepted: 1 June 2016

Published: 28 June 2016

Abstract

Transmission electron microscopy allows the collection of multiple views of specimens and their computerized three-dimensional reconstruction and analysis with electron tomography. Here we describe development of methods for automated multi-tilt data acquisition, tilt-series processing, and alignment which allow assembly of electron tomographic data from a greater number of tilt series, yielding enhanced data quality and increasing contrast associated with weakly stained structures. This scheme facilitates visualization of nanometer scale details of fine structure in volumes taken from plastic-embedded samples of biological specimens in all dimensions. As heavy metal-contrasted plastic-embedded samples are less sensitive to the overall dose rather than the electron dose rate, an optimal resampling of the reconstruction space can be achieved by accumulating lower dose electron micrographs of the same area over a wider range of specimen orientations. The computerized multiple tilt series collection scheme is implemented together with automated advanced procedures making collection, image alignment, and processing of multi-tilt tomography data a seamless process. We demonstrate high-quality reconstructions from samples of well-described biological structures. These include the giant Mimivirus and clathrin-coated vesicles, imaged in situ in their normal intracellular contexts. Examples are provided from samples of cultured cells prepared by high-pressure freezing and freeze-substitution as well as by chemical fixation before epoxy resin embedding.

Keywords

Electron tomography 3D reconstruction TxBR Tomogram averaging Iterative methods

Background

High-resolution localization and visualization of proteins and assemblies of macromolecular complexes in three dimensions (3D) within cells and tissues remain a difficult goal to achieve. With the advent of many new genetic probe-based or click chemistry-based correlated light and electron microscopy (CLEM) labeling strategies [13], it is desirable to facilitate production of higher quality 3D electron microscopic tomography (EMT) data sets from plastic-embedded specimens [4, 5]. In contrast to fluorescent label-based light microscopy, which provides a more limited view of the distribution of only the fluorescently labeled constituents, EMT allows the simultaneous visualization of all the intricate complexity of biological structures around the cellular or subcellular domain under investigation. However, compared to procedures for high-resolution light microscopy, EMT remains a relatively complicated method. For example, to image tissues or thicker regions of epoxy-embedded cells, semi-thin sections must generally be produced by ultramicrotomy and then imaged from many different sample orientations, yielding a set of digital electron micrographs. These micrographs must be processed through several steps to deliver the 3D volume for further analysis.

Aside from the imperfection in the optical performance of transmission electron microscopes (TEMs), such as optical aberrations [6, 7], the quality of an electron tomogram depends on additional factors. These arise from the interaction between a sample and the electron beam, the data acquisition scheme and the reconstruction process. While the electron beam damage in a plastic-embedded material mostly depends on the dose rate and not the accumulated dose [8], the overall quality of EMT data would clearly be improved from collecting more micrographs of a sample, if the micrographs alignment could be effectively optimized to handle the sample warping and other optical distortions.

In order to improve the electron tomogram quality of dose tolerant specimens, we developed a multiple-tilt series data acquisition scheme for the EMT. In contrast to the traditional single/double tilt series acquisition protocol [9, 10], this approach involves recording of a very large number of low dose or low-dose rate micrographs distributed across a wider range of specimen rotations. By sampling the specimen of interest through more orientations, the data folding into the reconstructed volume become more evenly distributed, further reducing sampling artifacts and producing higher quality tomograms. The visibility of weakly contrasted structures and thus overall specimen contrast is also enhanced by the additional summing of feature densities which accrues from the convergence of the greater multiplicity of views of the same weakly stained objects. To reduce the additional complexity of this extreme sampling and multiple tilt series reconstruction strategy, we have developed automated procedures for alignment and volume generation processes, reducing (or eliminating) the requirement for user input.

We demonstrate the utility of this method using two different test cases: the giant amoeba-infecting DNA virus Mimivirus [1113] and a clathrin-coated vesicle in a human embryonic kidney HEK293T cell in culture. For each example, we employed both filtered back-projection and non-linear iterative reconstruction routines to generate the 3D EMT volumes. Mimivirus and the clathrin lattice assembly have been extensively studied by other methods, establishing details of their structure and thus providing useful reference data with which to compare the quality of the results obtained using our multi-tilt EMT approach.

Methods

Specimen preparation

Two types of specimens were used to develop and evaluate our multiple tilt EMT methodology.

To reduce preservation-associated artifacts, we examined samples of Mimivirus-infected amoebae preserved by rapid freezing, vitrified directly from the living state and processed by freeze-substitution to epoxy resin embedding. Since the structure of this virus has been studied in detail by cryoEM methods, following extraction from cells and vitrification [11, 12], we reasoned that these published findings would provide us with useful reference data to facilitate assessment of the quality of data from the multi-tilt strategy applied to stained and plastic-embedded samples described here.

Similarly, to assess our method on a well-studied ubiquitous intracellular structure following more typical mixed aldehyde fixation and plastic embedding, we examined clathrin-coated vesicles in a mammalian cell in culture (HEK293T cells). These cells were grown at 37 °C, and 10 % CO\(_{2}\) in Dulbecco’s Modified Eagles Medium (DMEM) containing 10 % fetal bovine serum (Invitrogen). Adherent HEK293T cells were grown on poly-d-lysine-coated glass bottom dishes (MatTek Corporation, MA, USA), and fixed for 30 min in 2 % glutaraldehyde in 0.1M sodium cacodylate buffer (pH 7.4) on ice for EM processing. After washes in cacodylate buffer, cells were post-fixed with 1 % osmium tetraoxide for 30 min, stained with 0.2 % tannic acid and 2 % uranyl acetate, and then dehydrated and embedded in Durcupan epoxy resin.

Sections from both sample types were cut using a diamond knife (Diatome) at a thickness between 200 and 300 nm. To improve stability of specimens under the beam of the EM, these sections were coated with carbon on both sides. Colloidal gold particles (5 and 10 nm diameter) were deposited on each side of the sections to serve as fiducial markers.

Data acquisition protocol

EM data were obtained using an FEI Titan high base microscope operated at 300 kV; micrographs were produced using a 4k × 4k Gatan CCD camera (US4000). Both microscope and detector were controlled by the SerialEM software package [14] which managed the automated tilt series acquisition.

With recent advances in instrument automation, collection of a large number of tilt series is straightforward, and parameters to acquire all images with a relatively low-dose rate were used for this project.

The n-fold tilt series scheme we have refined and applied is a straightforward generalization of the popular double tilt series that can provide useful improvement to information in tomograms when compared to more standard single tilt series [9, 10]. In a double tilt series acquisition, the specimen is rotated \(\sim\)90° to obtain a combination of two tilt series, one orthogonal to the other. This is most effective in reducing reconstruction artifacts arising from the “missing wedge” problem. This two tilt series acquisition is easily achieved with a manual rotation holder such as the one offered by Fischione Instruments (Model 2040) and used in this study.

As shown below, this strategy can be extended to add additional information to the reconstruction from just two series with orthogonal tilt axes. As shown in Fig. 1, we carried out azimuthal rotations for 8-tilt series acquisitions. The specimen angles (represented by letters in Fig. 1) are arranged according to a sequence similar to the multilevel access scheme (MAS) described in [15]. By using a multilevel access scheme, the artifacts would in principle be attenuated more rapidly than alternative orders of azimuthal rotations as the number of tilt series added to the reconstruction increases.
Fig. 1

Protocol for acquiring multiple tilt series. A Between each series, the sample is rotated within the goniometer holder (left side) following an orientational multilevel access scheme (MAS) that optimizes the reconstruction space sampling. The tilt axis is displayed schematically for the 8-tilt series case (right side); series are labeled with letters from ‘a’ to ‘h’. The first and last series ‘a’ and ‘h’ correspond to a 0°–157.5° sample orientation, respectively. B 3D illustration representing the increase in accessible volume information as the number of tilt series augments

Series up to 16-fold rotation axis and 1° tilt increments between −60° and +60° were acquired for this study; in this extreme scenario (with around 2000 projection views), the data acquisition step was completed within a single day. Each micrograph can be indexed by \(i_\omega\) following the order of acquisition process (here \(1 \le i_\omega \le 16\times 121\)).

For the work described here, all but the specimen rotation step was automated using the serial EM scripting tools. However, full automation of such a multi-tilt strategy would only require adding in a sample holder with motorized control (and readout) for rotation. The only additional step between tilt series is to determine and adjust the stage position for the specimen to be at its eucentric height for each tilt series. Routines for automating this eucentricity adjustment are already in place in openly available automation packages such as SerialEM [14]. Projection micrographs were binned by 2 to overcome the detector limitations.

Reconstruction procedure

To produce a high-quality reconstruction, the projection images must be aligned accurately. In TxBR [16], a reconstruction package developed at NCMIR, this is done with a non-linear bundle adjustment scheme that optimizes the micrograph registration to the final volume with the 3D distribution of markers. This registration is parametrized by means of polynomial maps [16, 17]. TxBR is able to account for a sizable amount of sample warping, optical distortion, and non-linear trajectories [18], which makes it a good candidate to align and reconstruct multiple tilt series [17].

In TxBR, the optimization procedure handles all series simultaneously. This has proved to be more accurate and efficient [10] than aligning individual reconstructions after they are generated [19, 20]. The bundle adjustment routine minimizes a gold bead marker-based reprojection error, simultaneously calculating projection maps and marker positions in 3D. In order to accomplish this, gold markers or equivalent point-like features are required. We have developed an automatic solution for both the marker tracking and projection alignment procedure that allows easy reconstruction of any n-fold tilt series. In summary, our method takes advantage of (i) second-order Gaussian derivatives detectors for localizing the markers [21], (ii) a cluster analysis to identify them throughout a series and (iii) iterative procedures to refine the alignment process. Details are provided in  "Appendix 1”.

Once the alignment step is completed, micrograph densities can be backprojected in the final 3D reconstruction. We have investigated two options: a regular filtered back-projection (FBP) routine and an iterative procedure requiring more complicated steps. The first approach has been described in [16] and consists of a modified Shepp-Logan filtered back-projection scheme adapted to the case of curvilinear trajectories. Our second approach, wSIRT, is a SIRT-type iterative method with an adaptive weighting scheme along trajectory paths. Compared to regular FBP, it requires multiple iterations of projection/back-projection sequences, but yields better results. It is a modified version of the so called ASART procedure introduced in [22] and recently extended to accomodate non-linear alignment [23]. In the case of incomplete phantom data, ASART was proved to generate high-quality reconstructions in comparison to other approaches [22]. In fact, the adaptive relaxation parameter used in ASART to accelerate the convergence process is responsible for attenuating some missing data artifacts.

This method can be regarded as an iterative version of cross-validation and as such can be assigned a physical meaning in the context of cross-validation [10]. It is related statistically to multiplicative-type algorithm which maximizes expectation in emission tomography [24]. A more comprehensive discussion is available in "Appendix 3."

Results

Sampling refinement

Traditionally in EMT, the data acquisition scheme consists in single or double tilt series [9, 10], with rather large angle increments (2°) in order to reduce the specimen full exposure to the electron beam radiations. In particular, assuming a full pixel resolution can be achieved, we note that the basic sampling requirement arising from a 2D analysis, \(\Delta \theta = (2/L)*180^{\circ }/\pi\) [25], would not be fulfilled with the latest detector size—with for instance \(L=4k\) pixels, \(\Delta \theta \simeq 0.03^{\circ }\). Refined sampling schemes have been developed within the context of Fourier slice theorem to optimize the resolution of the obtained reconstructions [26, 27]. Nevertheless, the reconstruction artifacts caused by (i) the missing data issue (this is the missing wedge/pyramid problem) and (ii) the discretization problem, can only be attenuated through more sampling, and in some extent by computationally intensive iterative reconstruction methods.

Although the sampling of the reconstruction space is improved with this n-fold tilt series protocol, there is still a missing pyramid issue. Following  [27], it is easy to show that the fraction q of the missing Fourier space information is given by the following expression:
$$\begin{aligned} q(n) = \frac{n}{6} \tan \left( \frac{\pi }{2 n} \right) \left( \frac{L_z}{L} \frac{1}{ \tan \theta _\text{max} } \right) ^2, \end{aligned}$$
(1)
where \(L_z\) and L are, respectively, the sample thickness and its lateral dimension, while \(\theta _\text{max}\) is the maximum tilt angle within a series—usually \(\theta _\text{max} \simeq 60^{\circ }\). Here, Eq. (1) is only valid when n is a power of 2, \(L>L_z\) and \(\theta _\text{max}>45^\circ\). When the number of tilt series equals 2 or becomes infinite, q(n) coincides well with the double tilt and conical series cases, respectively [27]. It is clear from above that accumulating the number of tilt series does not bring a large decrease in the fraction of missing Fourier information; q(2) = 11.1 %, q(4) = 9.2 %, q(8) = 8.84 %, q(16) = 8.75 %, and q() = 8.73 % with taking \(L=L_z\) and \(\theta _\text{max}=60^\circ\). In contrast, a n-tilt series scheme allows averaging data that belong to the same Fourier space region multiple times with different sampling procedures.

The giant Mimivirus in situ

The double-stranded DNA Mimivirus, prototypic member of the Mimiviridae family, is the primary focus of our first reconstruction example. With a genome size of about 1.1 megabases, it is one of the largest known virus. When first discovered in 1992, this virus was indeed wrongly recognized as a bacterium because of its unusual dimension and its affinity to Gram-staining [28]. Its capsid envelope is an icosahedron-like structure with a vertex-to-vertex diameter about 500 nm. The capsid presents a starfish opening on one of its fivefold vertices. Additionally, the capsid envelope is surrounded by a dense layer of fibers, bringing the overall virion size within the 750 nm range. The fine structure of the capsid envelope, which has been well characterized both with atomic force microscopy and single particle analysis on virions whose fiber coatings were removed, suggests a p3 symmetry of depressions with the capsomers being arranged in a p6 symmetry [11, 12]. This level of detail has only been reported when the external layer of fibers is enzymatically digested with lysozyme and proteases, thus drastically improving the imaging conditions of an otherwise chemically modified virus. A goal of our work was to determine if we could see these structures for virus imaged in situ (and without digestion) and if so, to determine if the multiple tilt series acquisition and processing schemes help visualize features otherwise seen only in higher resolution studies of these fiber-free isolated capsids.

We applied the EMT methodology described above to generate a 3D representation of a Mimivirus virion in situ, from a semi-thick (\(\sim\)150 nm) plastic section of amoebae. For reference, a projection snapshot of the area under examination is displayed in figure  when the specimen has no tilt. In this example, we used a 16-tilt series scheme at a magnification of 29 k; this corresponds to a 0.32 nm pixel size in the raw electron micrographs. For each tilt series, a 1° angular increment was used from −60° to +60°.

Tomogram slices close to a Mimivirus capsid layer (corresponding to the boxed area in Fig. 2) built from specified numbers N of tilt series are compared in Fig. 3. Five images generated through FBP after having binned the original projection data by a factor of 2 are shown; the lower rightmost image corresponds to the wSIRT method on the N = 16 tilt series case. A gradual improvement with N is noticeable on this front view, which is theoretically the least impaired with missing information. As expected, the signal-to-noise ratio improvement is the most striking during the transition from single to double tilt, when the reconstruction artifacts are strongly reduced. Note that a p3 symmetry pattern of dense material (dark spots on the images) is clearly apparent, and consistent with the arrangement of depressions visualized in the previous studies [11, 12]. This stained material is likely to match the root of the external Mimivirus fibers connecting into the capsid depressions.
Fig. 2

TEM micrograph of a plastic section containing Mimivirus virions infecting a cell culture at 4h post infection. The sample is at zero tilt; 5-nm gold particles (G) are used as fiducial markers for aligning the tilt series. The enclosed area corresponds to the capsid envelope portion displayed in Fig. 3

Fig. 3

Mimivirus reconstruction: comparison of XY views of the capsid layer. Tomogram slices corresponding to the boxed area in Fig. 2 showing the progression in the reconstruction refinement as more tilt series (N = 1, 2, 3, 4, 5, 16) are included in the process, both with FBP and wSIRT. A p3 symmetry pattern of high density material in the capsid envelope (pointed by a red triangle in the bottom right image) becomes apparent, with a \({\sim}14\,\text{nm}\) peak to peak distance

In Fig. 4, the front (XY), top (XZ) and side (YZ) views of a Mimivirus reconstruction are displayed for a single tilt (N = 1, Fig. 4A top row) and a 16-tilt (N = 16, Fig. 4A bottom row) series; the uppercase letters X, Y, and Z are used to specify the coordinates of a point in the specimen, Z being in the normal direction to the specimen slab. Results are displayed using FBP (Fig. 4A left column) and the more compute-intensive wSIRT method (Fig. 4A right column). For each case, the organization of the inner membranes of a Mimivirus virion is quite visible, and consistent with details in previous reports [13]. Benefits of our finer resampling scheme in the reconstruction space (N = 16 versus N = 1) are the most apparent on the XZ and YZ views, for which the p3 symmetry pattern structure previously discussed in XY (Fig. 3) becomes recognizable for the 16-tilt series, while it is barely discernible on the side view of the single tilt series reconstruction.
Fig. 4

Mimivirus reconstruction obtained from different schemes. A Tomogram views (XY, YZ, and XZ) of a giant Mimivirus generated from the first tilt series (N = 1) and the whole set (N = 16), both with FBP and wSIRT. B Density profile of the various layers indicated by numbers along the blue line drawn in a as discussed in [13] obtained for each reconstruction case; 1 DNA core, 2 inner membrane, 3 outer membrane, 4 inner capsid shell, 5 outer capsid shell and 6 fibers

Density profiles along the blue line shown in Fig. 4A (top right image) were drawn for each reconstruction (Fig. 4B). It appears the signal amplitude of a single tilt (N = 1) reconstruction is higher compared to a 16-tilt reconstruction. This amplitude decrease with N should not be interpreted as a real effect: artifacts from the missing wedge induce a deceptive contrast into the reconstructions, with for instance white fringes around the darker features in the XY view (Fig. 4A, FBP N = 1). This explains the overall behavior of the coefficient of variation \(c_\text{v}\) of a simple tomogram slice when plotted versus the number N of tilt series (Fig. 5); \(c_\text{v}\) is defined as the ratio of the standard deviation to the mean of the pixel values.
Fig. 5

Assessment on the convergence process. We monitor the coefficient of variation \(c_\text{v}\) on the middle tomogram slice as the number N of tilt series increases; \(c_\text{v}\) is implemented both with FBP (red diamond points, left y-axis) and wSIRT (blue circular points, right y-axis). For the iterative approach, the total number of iterations is 50 with a mixing parameters \(\alpha\) of 2; the original data were binned by 4

As N increases, the coefficient of variation \(c_v\) is first lowered (this corresponds to a decrease in the contrast), a trend only triggered by the artifact attenuation. In Fig. 5, the reconstruction process for FBP appears to converge towards a nearly stable solution, roughly after \(N=8\) at which point the orientation space sampling appears fully effective.

Both FBP and wSIRT methods have been examined, and displayed a similar trend with more pronounced fluctuations for the iterative method. The total number of iteration cycles in the iterative approach was fixed to 50, and the relaxation parameter \(\alpha\) was set to 2 (see Eq. (15) in "Appendix 3"). With these parameters, the relative error in the projections ended up around 5.0×10−4. We note the contrast enhancement between FBP and wSIRT, with clearly less white fringes around the dark features in the latter case.

For completeness, the front (XY), top (XZ), and side (YZ) views of a 5-nm gold particle are displayed in Fig. 6. Despite the improved sampling (with N = 1,...,15), artifacts around gold particles from the missing pyramid (or cone) are still slightly visible in any FBP reconstruction. However, they are greatly attenuated in the wSIRT reconstruction (Fig. 6).
Fig. 6

Tomogram views (XY, YZ, and XZ) of a 5-nm gold particle with respect to the number of tilt series N. A FBP is used. B wSIRT is used. While the image quality improves as N increases, the reconstruction still remain impaired by artifacts caused by the missing pyramid problem (equivalent to a missing cone problem when \(N\rightarrow \infty\)). Note artifacts are attenuated for wSIRT (50 iterations and \(\alpha =2\)) compared to FBP

The electron dose rate applied onto the Mimivirus sample over the data acquisition course was maintained at a low level, within 2–3 electrons per Angstrom square per second. However, this is enough to induce some obvious specimen deformations, as previously reported [8]. As described above, the bundle adjustment procedure used here in conjunction with a general projection model for aligning the micrographs offers an effective solution to the problem as shown in Fig. 7. After analyzing the final projections maps, we found that the corrected sample deformation is quantitatively in line with [8], showing a compression factor up to 15 % along the normal axis to the section and half or less along the lateral directions. Correction of this sample deformation is provided during the alignment process ensuring a minimal re-projection error [1618]. To estimate the compression factors, we considered a simple deformation model with only three deformation coefficient rates along the X, Y, and Z sample directions, see "Appendix 2" for more details. With this model, we are able to capture the main variations of the final projection maps with a minimal set of adjustment parameters. As an illustration, we plot in Fig. 7 the quantity \(n_{3,\omega }\) defined in Eq. (10) versus the micrograph index \(i_\omega\), both for the projection maps computed from the bundle adjustment and the ones from the simple deformation model. In an ideal system with in particular no sample deformation, the quantity \(n_{3,\omega }\) should remain equal to 1 by design; deviations from 1 would indicate a possible specimen warping. Once the model is adjusted, the prediction for \(n_{3,\omega }\) roughly follows the computed map estimates as shown in Fig. 7, validating our choice of model. Note that the Z compression rate contribution to \(n_{3,\omega }\) is larger at high tilt angles compared to its in-plane (X and Y) counterparts, explaining the oscillatory behavior of \(n_{3,\omega }\) versus the micrograph index \(i_\omega\). One interesting feature of this analysis is the ability to monitor both the transient and stationary sample deformation while the specimen is irradiated, the stable state being reached after 3–4 tilt series in this experiment. It is worth noting that while some EMT practices for recording data from epoxy-embedded samples include a preliminary long exposure beam “cooking” step prior to the image acquisition protocol, this can certainly be viewed as contributing to the alteration of the sample dimensions (particularly its thickness) and potentially a loss of useful information. However, as long as the transient behavior can be accurately modeled through a low-dose rate strategy and a refined tomographic alignment scheme, it is possible to ensure the final reconstruction geometry to be close to that of the original sample when it was first inserted into the TEM.
Fig. 7

Sample warping caused by the electron beam radiation can be simultaneously monitored and corrected for in the multiple tilt process. A The variations of \(n_{3,\omega }\) (green lines), defined in Eq. (10) and based on the linear portion of the computed projection maps, are a good indicator of the sample deformation happening over the course of the data acquisition. Its main behavior can be reproduced (doted blue lines) by considering a simple model having three deformation rates (\(\gamma _X\), \(\gamma _Y\) and \(\gamma _Z\)) allowing their estimates after an adjustment procedure. \(n_{3,\omega }\) oscillates between two curves as the many different tilt series (a, b,…, p) are successively acquired between −60° and +60°. The lower bound curve, reached at high tilt angles (\(|\theta | =\pi /3\)), specifically depends on the sample compression along the normal axis, while the upper bound curve, reached at zero tilt, only depends on the lateral compressions. B Representation of the amount of compression along the three main sample directions versus the micrograph index. In the stationary region, the sample compression is estimated to be 2–4 % in the lateral directions and 15 % along the normal axis

Clathrin-coated vesicles

Clathrin-coated vesicles mediate the vesicular transport of cargo such as proteins between organelles in eukaryotic cells connecting the trans-Golgi network, endosomes, lysosomes, and the cell membrane. Clathrin is a large protein complex composed of three heavy chains and three light chains. This complex is referred to as a triskelion based on its three-legged appearance; it coassembles together with adaptor proteins to form the ‘coat’ around the vesicles. The spherical clathrin lattice structure appears as a polyhedron made of regular pentagons and hexagons. The adaptor proteins serve as links between the clathrin lattice and the membrane of the vesicle. The lattice structure of highly symmetrical forms of clathrin-coated vesicles assembled in vitro has already been studied in detail from single particle analysis [29]—for instance the mini-coat with its tetrahedral symmetry and the hexagonal barrel. Cryo-electron tomography reconstructions of lesser symmetrical clathrin-coated vesicles isolated from cells have also been reported [30]. We present here a sub-volume reconstruction of a cell in culture containing an individual coated vesicle (Figs. 8, 9). For this, we used a TEM magnification of 37 k and a 16 tilt-series scheme with 1° angle increment between −60° and +60°. Compared to the previously reported studies of isolated clathrin-coated vesicles, this in situ instance is a large assembly containing a 100 nm diameter inner vesicle; the outer coat diameter being measured at roughly 140 nm. Note that the overall shape is not perfectly spherical but slightly oblong. We counted 61 hexagons, 11 pentagons, and 1 heptagon on the cage surface, which includes a total of 143 triskelions and 214 edges. Those numbers are consistent with prior studies as we expect them to behave linearly with the overall vesicle surface (Fig. 8C). In Fig. 8A, a micrograph snapshot of the vesicle is displayed when the sample is not tilted; specimen features are then hardly discernible. This is not the case on a tomogram slice once the 16-tilt reconstruction is performed (Fig. 8B). The wSIRT reconstruction was generated after 50 iterations and a mixing parameter \(\alpha =2\); the original data were binned by 2. The clathrin cage structure imaged here is within the functional context of the cell, a major difference from previous studies which were also carried out using cryoEM utilizing different contrast mechanisms. As this is an in situ-coated vesicle, its relationship with other cellular elements such as free ribosomal units can be seen directly, as indicated in Figs. 8B and 9A; a portion of rough endoplasmic reticulum is also visible in Fig. 9D.
Fig. 8

Clathrin-coated vesicle reconstruction using a 16 tilt series scheme. A EM snapshot at zero tilt; gold markers (G) are indicated with arrows. B XY section in the middle of the reconstruction. Note the contrast increase between the projection in A and the tomogram slice. Free ribosomal units (R) are indicated with arrows. The diameter of this organelle inner vesicle averaged around 100 nm, making it significantly larger than previously reported similar structures [30]. C The number of triskelions should increase linearly with the vesicle surface; we counted 143 triskelions, which is consistent with the trend reported in [30]. Indeed, the square root of triskelions number versus inner vesicle diameter roughly follows a straight line.

Fig. 9

Clathrin-coated vesicle reconstruction using different schemes. A XY tomogram slices containing a partial view of the clathrin cage obtained with different reconstruction schemes (FBP, N = 1, 2 and 16; wSIRT, N = 16). Note the free ribosomal units (R) around the cage. B, C An isosurface of a portion of the cage reconstruction (orange wireframe) is compared to the corresponding theoretical protein model assembly (solid gray surface). No extra matching transformation other than simple translations/rotations is necessary. D A segmentation of the clathrin cage is displayed on a wider scale showing a rough endoplasmic reticulum (ER) as well

In Fig. 9B, C, we matched the theoretical model of a basic molecular assembly made of three consecutive triskelions to our EMT reconstruction. For a larger scale perspective, the clathrin cage vertices, which also correspond to triskelion center locations, are displayed in Fig. 9C.

Discussion

In this work, we established automatic procedures to facilitate the processing of EMT reconstructions. This enabled us to introduce an averaging-like strategy to increase contrast of weakly stained structures based on multiple tilt series acquisition, thereby enhancing visibility of fine structure in 3D. This strategy was applied on two distinct samples providing examples of its benefits and also demonstrating the use of two reconstruction procedures, a regular FBP and wSIRT, a weighted iterative procedure. High-quality reconstructions were obtained with both procedures.

Use of a specific variation of an EMT image acquisition and reconstruction strategy should be determined based on the requirements of the project and the characteristics of the specimen being studied.

With frozen hydrated samples, a weak signal to noise ratio and a low radiation tolerance are the key concerns. Cautions must be taken to decrease the damage from electron interaction with the objects of interest. Techniques to boost the contrast are used to enhance image information, either with a strong defocus, an imaging energy filter or a phase plate [31]; this, in return, requires additional corrections with for instance a phase flipping step [32].

In contrast, considering the case of plastic-embedded material, as the electron dose rate appears to be more limiting than total dose, more extensive data acquisitions are possible especially if the dose rate is low. This was applied in our work. Contrast and resolution of objects within the tomograms are improved by increasing the angular density of projections and processing the resulting set of images with software designed for this purpose. Efficiency and accuracy in aligning large sets of micrographs then become the critical practical challenge to overcome in 3D reconstruction. Our procedure can be viewed as a variant of averaging to improve signal to noise, combined with multiple tilt-based improvement on sampling from a greater number of perspectives.

Many other approaches in modern 3D EM rely on averaging. In single particle analysis [33], the reconstruction process involves a large collection of snapshots containing identical structures with random orientations. This technique offers the opportunity to obtain very high-resolution average-based reconstructions representing the features of small molecular assemblies. Averaging is also possible in 3D [34, 35]. Unfortunately, the quality of the products of this process can be hampered by the contributions of reconstruction artifacts which therefore need to be accounted for during the image processing.

Our approach focuses on a single specimen area within a rather large field of view, and seeks to redistribute the sample dose images taken over many orientations. It can be likened to some 3D tomogram averaging aspects, the difference being we are averaging data from exactly the same volume, the specimen only being rotated around the optical axis between each series, and it would be difficult to totally overcome the missing wedge issue.

With a large number of exposures/tilt series, marker-based registration for the EMT process remains very effective. The automatic alignment procedures developed in this work allow us to handle a high density of gold particles, with thousands of markers in the field of view. In the two examples we considered that the total number of gold particles used for alignment is 365 and 60 for the giant Mimivirus and clathrin-coated vesicle, respectively. We successfully tested our alignment routines on other reconstructions containing several thousands markers. While the presence of numerous markers might be detrimental to the reconstruction, with streak-type artifacts, it also allows for very accurate image registration especially when using polynomial map correspondences as in TxBR. Artifacts surrounding a gold particle—an electron dense material on a dim background—can be limited if its diameter is chosen small (a few pixels), or if the weighted iterative method is used (Fig. 6).

wSIRT brings significant improvements over FBP. It enables a clear contrast enhancement and a large artifact reduction (Figs. 5, 6). As a downside, this iterative approach is compute-intensive and requires hundred times more operations compared to FBP. Nevertheless, it is possible to make modifications in our current routine to accelerate the convergence process. For instance, one could gradually include the tilt series into the iterative computations, similarly to the approach we took taken in MAS data acquisition protocol, as shown in Fig. 1.

In a high throughput EMT production environment, implementing wSIRT with a very large number of tilt exposures might be difficult to carry out as a routine process. This leads to the practical dilemma of whether to acquire a small number of tilt series (typically ranging from 2 to 4) with the iterative approach, or to acquire a large number of tilt series and restrict the reconstruction process to filtered back-projections.

The answer to this question may reside in the properties of the specimen preparation itself. For a sample with a strong level of heavy metal staining, use of a large number of tilt series might not be as beneficial since the incoming signal to noise ratio can be comparatively high. More data averaging will not likely bring out the details of unstained or weakly contrasted biological features in the reconstruction, while the high-resolution features can be muddied by over-staining. In this case, implementing wSIRT on fewer tilt series may be judicious. A “multiple tilt and summed view averaging technique”—like the one presented here—may be more useful at lower magnification. For a sample with low staining level, this averaging technique would probably bring more reconstruction details than a regular tomographic process (with a single/double tilt series scheme), as our example on the clathrin-coated vesicle seems to indicate. Further investigations in this direction need to be done.

Conclusions

We believe that the developments described above provide a useful method to enhance resolution of fine detail in tomographic reconstructions from plastic-embedded and heavy metal stained samples, thereby progressing a general goal of revealing supramolecular details in situ. While this approach addresses the under-sampling and noise averaging issues, it does not overcome the ambiguity related to a missing cone in the raw data. The impact of this missing data nevertheless remains small, especially when a weighted iterative procedure is applied.

Acquiring many micrographs at a lower dose rate, as we demonstrate in this work, could be useful in a full 180° EMT process as well. In such a setup, the biological specimen should be more sensitive to the beam-associated mass loss given its geometry, a few hundred nanometers diameter cylinder with isolated supports (Fig. 10). Micrographs in this particular application should be distributed within a single series as an unequivocal mathematical solution to the problem is available.

Finally, additional refinements to this multiple tilt series reconstruction strategy are still possible. For instance, registration adjustments can be included at each iteration step i of the wSIRT approach. A small misalignment in the micrographs creates systematic patterns in the projection errors \(v-v_i\) [see "Appendix 3" Eq. (15)], which can be reused as a feedback to correct for the original projection maps. This would accelerate the convergence of this recursive approach, and also improves the quality of the completed reconstruction on the smaller scale.

Notes

Declarations

Authors' contributions

SP and DB designed and executed the experiments, and analyzed the data. SP designed and wrote the computational algorithms. PN assisted with image processing. XW and AL participated in the algorithm design. JL prepared the Mimivirus sample. SP, DB, and ME prepared the manuscript. All authors read and approved the final manuscript.

Acknowledgements

This work was supported by grants from the NIH National Institute of General Medical Sciences under award number P41GM103412 to Mark H. Ellisman, to operate the National Center for Microscopy and Imaging Research, and through award number P41 GM103426 to Rommie Amaro, supporting the National Biomedical Computation Resource, and also from the American Heart Association award 10SDG2610281 to Daniela Boassa.

Competing interests

The authors declare that they have no competing interests.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
National Center For Microscopy and Imaging Research, Center for Research in Biological Systems, University of California
(2)
Departments of Neurosciences and Bioengineering, University of California
(3)
Department of Biological Sciences, Purdue University

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