Biol. Cell (2006) 98, 415–425 (Printed in Great Britain)
doi:10.1042/BC20050097
Research article
Multiple-axis tomography: applications to basal bodies from Paramecium tetraurelia ´ Cedric Messaoudi*, Nicole Garreau de Loubresse†, Thomas Boudier*, Pascale Dupuis-Williams‡ and Sergio Marco*1 ´ INSERM U759, Imagerie integrative, 91405 Orsay, France, and Institut Curie, Centre de Recherche, Laboratoire Raymond Latarjet, Centre ˆ 112, 91405 Orsay CEDEX, France, †Centre de Gen ´ etique ´ ´ Universitaire d’Orsay, Bat Moleculaire, CNRS, 91198 Gif-sur-Yvette, France, and ˆ 444, Faculte´ des Sciences d’Orsay, 91400 Orsay, France, and ESPCI, 10 rue Vauquelin, 75005 Paris, ‡UMR 8080, CNRS/UPS, IBAIC, Bat France
Background information. Transmission electron tomography is becoming a powerful tool for studying subcellular components of cells. Classical approaches for electron tomography consist of recording images along a single-tilt ◦ axis. This approach is being improved by dual-axis reconstructions and/or high-tilt devices (tilt angle >+ −60 ) on microscopes to compensate part of the information loss due to the ‘missing wedge’ phenomena. Results. In the present work we have evaluated the extension of the dual-axis technique to a multiple-axis approach, and we demonstrate a freely available plug-in for the Java-based freeware image-analysis software ImageJ. Our results from phantom and experimental data sets from Paramecium tetraurelia epon-embedded sections have shown that multiple-axis tomography achieves results equivalent to those obtained by dual-axis approach without the requirement for high-tilt devices. Conclusions. This new approach allows performance of high-resolution tomography, avoiding the need for high-tilt devices, and therefore will increase the access of electron tomography to a larger community.
Introduction Electron microscopy associated with increasingly sophisticated computer-based image-analysis techniques (Frank, 1992) has the capability to resolve 3D (three-dimensional) structures from the atomic scale by electron crystallography (Li et al., 2002; Gibbons et al., 2003; Zou et al., 2003) up to the cellular level by electron tomography (Lucic et al., 2005; McIntosh et al., 2005). Electron tomography is based on the acquisition of a small number of projections (100–300), denoted as tilt series, from an individual object. Images from the tilt series are aligned and combined to produce a 3D reconstruction (Marco et al., 2004). To date, public software for electron tomography, 1 To
whom correspondence should be addressed (email
[email protected]). Key words: basal body, electron microscopy, Paramecium, tomography. Abbreviations used: 3D, three-dimensional; COD, coefficient of determination; PSPC, pyramidal system for pattern construction; RA, reference alignment; RFA, reference-free alignment.
such as IMOD (Kremer et al., 1996) and TOM (Nickell et al., 2005), are based on the use of tiltseries recorded by tilting the samples in the electron microscope around one tilt axis using a goniometer. This approach, denoted as single-axis tomography, has proven to be a useful tool to understand the 3D structure of several non-symmetric biological objects. However, single-axis tomography has the disadvantage that the tilt-series are not complete, because effective specimen thickness is function of 1/cos (tilt angle). Thus the effective thickness prevents electrons from crossing the sample at high-tilt angles, resulting in a lack of information known as the ‘missing wedge’ (Frank, 1992). To compensate for this loss of information, it has been proposed to record two tilt series of the same object by rotating it by 90◦ in the plane. The combination of these two tilt series partially completes the missing wedge by producing a ‘missing pyramid’ (Mastronarde, 1997). This approach, denoted as dual-axis tomography, has been
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implemented in IMOD (Kremer et al., 1996) and successfully applied to the study of the Golgi (Ladinsky et al., 1999; Marsh et al., 2004), syncytial-type cell plates (Otegui et al., 2001), post-meiotic cytokinesis (Otegui and Staehelin, 2004), higher-plant chloroplast thylakoid membranes (Shimoni et al., 2005) and Chlamydomonas reinhardtii basal bodies (O’Toole et al., 2003). In addition, new algorithms for reconstruction (SIRT; simultaneous iterative reconstruction tomography) have been recently adapted for this dual-axis approach (Tong et al., 2006). An alternative approach to the dual-axis approach to recover the maximum amount of information is to fix a tilt angle and then record images by rotating the sample on the horizontal plane (conical tomography), as proposed by Radermacher (1988) and Lanzavecchia et al. (2005). This approach has been successfully applied to the study of cellular organelles in thin sections (Zampighi et al., 2005). Another possible approach to compensate for the missing pyramid is to extend dual-axis to multiple-axis tomography, which consists of combining several tilt series of the same object that are recorded after multiple rotations on the plane. Multiple-axis tomography should ensure the recovery of the maximum amount of information. However, the theoretical information gained with multiple-axis tomography has not been evaluated. This evaluation is mainly limited by the absence of software for the combination of tomograms produced from several tilt series, although an approach has been developed to combine volumes produced from several 3D reconstructions of the ribosome (Ofverstedt et al., 1997). In addition, recording tilt series at several rotation angles presents technical difficulties when applied to material sensitive to radiation, such as biological samples. Thus, in the case of resin-embedded samples, their thickness could be significantly affected after image acquisition (Luther, 2001). Recently, it has been demonstrated that this phenomenon can be decreased by working at liquid nitrogen temperature (Boudier et al., 2005), making multiple-axis tomography theoretically applicable to biological samples. The present work presents a comparative study of dual-axis and multiple-axis tomographies, comparison of several algorithms for volume alignment and a practical application of multiple-axis tomography to biological samples. Theoretical evaluation of multiple-axis tomography and algorithms
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for volume alignment has been achieved by using phantom data sets. Practical application to biological samples has been performed using experimental data sets recorded from Paramecium tetraurelia basal bodies. P. tetraurelia is a ciliated protist whose cortex is covered with more than 4000 motile cilia and associated basal bodies, whose regular organization into parallel ciliary rows and co-ordinated duplication during cell division facilitates their structural analysis. This biological model has therefore made a large contribution to the early ultrastructural description of basal bodies by electron microscopy (Ringo, 1967; Dippell, 1968). Paramecium basal bodies present a canonical cylindrical organization (250 nm in diameter and approx. 450 nm in length), enclosed by nine microtubule triplets consisting of a complete inner microtubule of 13 protofilaments (called tubule A) and two opposed outer incomplete microtubules (tubules B and C) of 11 protofilaments. Tubules A and B are extended into the axoneme, whereas tubule C is interrupted at the distal end of the basal body in a region called the transition zone, which is between the basal body and the characteristic 9 + 2 microtubule configuration of the ciliary axoneme. This transition zone, which has been the object of a very precise analysis by transmission electron microscopy (Dute and Kung, 1978), is characterized by distinctive internal structures, including successive plates and a central globule, called the axosome, which seems to be the site of nucleation of the central pair of microtubules of the axoneme. However, the internal organization of the basal body itself remains elusive, apart from its most prominent structure in its proximal end, called the cartwheel, which consists of a central hub and nine spokes which radiate to the nine A-type tubules. Finally, in Paramecium, cortical basal bodies are inserted in a submembranous skeleton, called the epiplasm, and, similar to all ciliate species, are associated with an asymmetrical set of appendages, namely two microtubule rootlets and a kinetodesmal fibre, presumably involved in basal body anchoring and cohesion of the whole ciliature. On the basis of our present results of test phantom data sets (Figure 1) and experimental tomographic data from P. tetraurelia, we demonstrate the feasibility of electron tomography using multipleaxis approaches. The algorithms for volume alignment to perform multiple-axis tomography have
Multiple-axis tomography of basal bodies
Research article
Figure 1 Sections of the phantom volume Panels depict the sections from 1 to 128 of the initial phantom with a step increment of 4. Numbers at the bottom of each panel correspond to the section number in the total volume.
Figure 2 Visual comparison of initial phantom and single-, dual- and multiple-axis reconstructions (A–F) Axial central planes of the initial phantom (A) and the reconstructed volumes corresponding to single-axis (B), dual-axis ◦ ◦ ◦ (C) and multiple-axis using tilt angles of + −69 (D), + −46 (E) and + −23 (F). (G–L) Coronal plane number 89 corresponding to the height indicated by a line in the axial central plane of the initial phantom (A). The panels correspond to: (G) starting phantom, +69◦ , (K) − +46◦ and (L) − +23◦ . (H) single-axis, (I) dual-axis, multiple-axis using tilt angles of (J) −
been implemented in Java as plug-ins for ImageJ (http://rsb.info.nih.gov/ij/; Abramoff et al., 2004) and can be freely downloaded.
Results Evaluation of implemented algorithms and accuracy test for multiple-axis tomography
In order to evaluate the performance of single-, dualand multiple-axis tomographic approaches, the COD
(coefficient of determination) and visual comparison of the reconstructed volume sections (Figure 2) have been achieved using data set 1 and the initial phantom with the same number of images. The COD calculated between the initial phantom and the singleaxis reconstruction is 0.56, which is slightly lower than that computed from the initial phantom and the reconstruction obtained from dual-axis approach (0.58). In the case of the multiple-axis approach,
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the three conditions tested: (i) equivalent tilt range ◦ (+ −69 ) to the single- or dual-axis, which implies a tilt ◦ increment of 3◦ , (ii) tilt range varying + −46 and in◦ crement 2 (medium tilt), which correspond to acquisition conditions easily reached by most microscopes without a high-tilt angle device, and (iii) very ◦ ◦ low-tilt range (+ −23 each 1 ), have resulted in COD values of 0.85, 0.68 and 0.48 respectively. With regards to the visual comparison of the reconstructed volume sections (Figure 2), the missing wedge phenomena is shown by the elongation and the blur of borders in the reconstructed features. The elongation artefacts appear to be lower when the multipleaxis technique is used. Regarding the blurred borders, the best results are obtained with dual-axis ◦ ◦ (+ −70 ) and multiple-axis (+ −69 ) high tilt. COD and visual evaluation showed the advantage of multipleaxis to compute reconstructions using data sets recorded on to microscopes using medium-tilt angles ◦ (+ −45 ). However, the problem of automatic tomogram alignment in the 3D space to combine reconstructions remains unsolved. In this case, the geometrical relationships between the different volumes must be computed. To this purpose, three algorithms have been implemented to combine volumes produced from multiple-axis approaches as ImageJ plug-ins. The correct implementation of the algorithms has been validated by the CODs obtained between the original phantom (after moving it to the position calculated after alignment) and the merged volumes. These CODs are equivalent in the three tested algorithms corresponding to 0.8081, 0.8073 and 0.8104 for RA (reference alignment), RFA (reference-free alignment) and PSPC (pyramidal system for pattern construction) respectively. Nevertheless, RA and RFA are slightly faster than PSPC. In addition, RFA presents the advantage that noreference volume is used, making the result independent of the data set. Thus we have selected RFA as algorithm to perform multiple-axis reconstructions with our actual data set recorded without a high-tilt angle device. Multiple-axis tomographic reconstruction of P. tetraurelia basal bodies
Volumes merged by RFA procedure from six single tomograms of P. tetraurelia basal bodies preserves the main basal bodies structures, as described previ-
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ously by transmission electron microscopy (Dippell, 1968; Dute and Kung, 1978). Our present tomographic analysis, obtained using a Paramecium cell at interphase, refers to two cortical basal bodies, whose sizes are 240 nm × 532 nm and 240 nm × 504 nm. The tomograms also include the corresponding transition zones. Sections from each five planes of these merged volumes are shown in Figures 3 and 4. The microtubule sheath is clearly visible on tangential planes (black arrows in Figures 3A and 4A), allowing the opportunity to follow each microtubule triplet of the basal body over its entire length and to reveal the proximal extremities of microtubule triplets which are distinctly capped (black arrows in Figures 3D, 3E, 4C and 4D), as described previously (O’Toole et al., 2003). On the planes that cross the middle of the basal body lumen, the peripheral microtubules are clearly delimited, and the closure of the C-tubule is discernable above the terminal plate (black arrows in Figures 4E and 4F), which marks the boundary between the basal body and transitional zone. In addition, details of the structures in the transition zone, as described previously by Dute and Kung (1978), are mostly visible: the terminal plate (magenta arrow in Figures 3H and 4H), the intermediate plate (magenta dotted arrow in Figures 3H and 4H) and the axosome (magenta arrow head in Figures 3H and 4G), composed of a central globule (whose size of 68 nm in diameter is consistent with previous measurement) resting on a curved plate, from which the central pair of axonemal microtubules originates (black arrows in Figure 4H). Interestingly, although the present tomograms do not really focus on this zone, it seems that only one of the central microtubules enters the axosomal globule, as stated by Dute and Kung (1978) (black arrow in Figures 3G and 4I). The internal space of basal bodies presents the characteristic organization initially described by Dippell (1968, 1976), with several cartwheels in the proximal end (between 2 and 6; Iftode, 1996) which can be identified by their central hub (red arrowheads in Figures 3G–3I), as well as a fine filamentous system associated with dense granules, which cover the distal two-thirds of the lumen, until the terminal plate (red asterisk in Figures 3D–3J and 4D–3J), and which has been interpreted successively as nucleic acid (Dippell, 1976) or glycogen (Mignot et al., 1993).
Multiple-axis tomography of basal bodies
Research article
Figure 3 Sections of the first multiple-axis P. tetraurelia tomographic reconstruction Panels correspond to coronal sections taken every 5 voxels, starting at plane 40, from a 310 voxels × 310 voxels × 200 voxels multiple-axis reconstructed tomogram. Black arrows, microtubule-related structures; magenta arrows and arrow heads, transition-zone-related structures; red arrow heads and asterisks, internal-space-related features; yellow arrows, position of epiplasm around basal body structure; yellow asterisks, alveoli. Scale bar, 250 nm.
With regards to the immediate environment of the basal bodies, characteristic structures may also be identified in both tomograms. Thus the epiplasmic scales appear as a thick ring, encircling each basal body, aligned with the terminal plate (yellow arrows in Figures 3 and 4). These epiplasmic scales clearly
show a free space between the terminal plate and the epiplasm, as described previously by Iftode et al. (1996) (yellow dotted arrows in Figures 3E–3F and 4G–4I). Above the epiplasm, the clear zones correspond to the subpellicular vacuoles (called alveoli), which lie under the cell membrane surrounding
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Figure 4 Sections of the second multiple-axis P. tetraurelia tomographic reconstruction Panels correspond to coronal sections taken every 5 voxels, starting at plane 45, from a 310 voxels × 310 voxels × 200 voxels multiple-axis reconstructed tomogram. Black arrows, microtubule-related structures; magenta arrows and arrow heads, transition-zone-related structures; red arrow heads and asterisks, internal-space-related features; blue arrows, branching points of the kinetodesmal fibres; yellow arrows, position of epiplasm around basal body structure, yellow asterisks, alveoli. Scale bar, 250 nm.
the cilia (yellow asterisks in Figures 3 and 4). Finally, the blue arrows in Figures 4(D) and 4(F) reveal the three branching points of the kinetodesmal fibres on defined microtubule triplets at the proximal end of the basal bodies.
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Discussion Methods to elucidate 3D structures of subcellular components constitute one of the largest assets of modern biology, because they allow the understanding of the structure–function relationships of
Multiple-axis tomography of basal bodies
cellular processes. Over the last 20 years, following the automation of the image recording process under the microscope, the technical development in electron microscopes and sample preparations, and improvements in storage and computing power of data-processing equipment have resulted in a new method for structural analysis, transmission electron tomography. The first approaches performing electron tomography were carried out on a single axis. The inconvenience of this approach is the missing wedge, resulting in a loss of information. In order to compensate for this information loss, a dual-axis approach was proposed (Mastronarde, 1997). Nevertheless, even if dual-axis results in a clear improvement of the fulfilment of the Fourier space, which changes from a missing wedge to a missing pyramid, it still remains incomplete. This suggested that the use of microscopes equipped with high-tilt angle goniometers would be helpful. However, microscopes with high-resolution polar pieces are not compatible with high-tilt angle goniometers (tilt angle ◦ >+ −60 ) and require the use of costly, specially designed high-tilt holders. To overcome this problem and obtain the best completion of the Fourier space, conical recording geometries (Radermacher, 1988; Lanzavecchia et al., 2005) have been proposed. This approach consists of recording projections of an object at different orientations by rotating the holder on the horizontal plane after tilting. However, conical tomography presents two requirements to produce a 3D reconstruction. First, a rotary holder is needed. Secondly, conical tomography needs to finish the recording procedure. We have tested another possible alternative approach, which we denoted as multiple-axis tomography, to cover the missing wedge without requiring high-tilt angles during image recording. In this approach tilt-series are recorded independently at a different orientation on the plane after rotating the sample on the holder. Multiple-axis tomography does not strictly require the use of rotary holders as the grid can be manually oriented after recording each tilt series. And with regards to sample damage which can be an important issue, the tilted-series already recorded can be combined to obtain a 3D reconstruction. Consequently, we propose to record the maximum possible tilt series in the following order for rotation: 0, 90, 45, 135, 30, 120, 60, 150◦ and other intermediate rotation angles.
Research article We have tested multiple-axis tomography on phantom volumes. The performed tests have demonstrated that, in terms of COD, the obtained volumes are better in multiple-axis approach than with the single- or dual-axis techniques. Consequently, it seems possible to perform correct tomographic recon◦ structions by using a tilt-angle record series of + −45 by rotating the grid in the horizontal plane at six different angles. This criterion allows us to conclude that the best approach is a high-tilt multiple axis, as expected because it corresponds to the best fulfilment of the Fourier space. Interestingly, the medium-tilt multiple-axis method presents the second best COD score. Single- and dual-axis methods show similar COD scores, probably by the use of an identical image number to perform the 3D reconstructions, combined with the effects of the missing wedge and the missing pyramid that are reduced in the hightilt or medium-tilt multiple-axis approaches. This similarity between single- and dual-axis results has been also observed in a recent work that proposes a novel dual-axis iterative algorithm for electron tomography (Tong et al., 2006). Finally, unsurprisingly, the lower COD has been obtained in the case of low-tilt multiple-axis in which the missing cone is the most important. Therefore, our results suggest that medium-tilt multiple-axis can be an alternative to performing electron tomographic reconstructions when using an electron microscope without high◦ tilt devices (tilt angle >+ −60 ). This conclusion is also supported by the visual comparison of equivalent sections in the reconstructed volumes. Thus there exists a clear loss of information in low-tilt multiple-axis when compared with the other approaches (Figure 2). The effect of the missing wedge in high-tilt single-axis is indicated by the elongation of the borders of the reconstructed feature (Figure 2B) and the blurred aspect of the feature limits (Figure 2H). In the dual-axis reconstruction the elongation is reduced, but appears in two perpendicular directions (Figure 2C) and the feature limits remain blurred at the horizontal borders (Figure 2I). In the multiple-axis reconstructed volumes, the elongation effect disappears (Figures 2D–2F) and the blurred aspect of the feature limits depends on the tilt range (Figures 2J–2L). Subsequently, visual comparison of the volumes suggests that medium-tilt multiple axis generates equivalent results to the dual axis, without the requirement to record images at high-tilt angles
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therefore avoiding the use of high-tilt goniometers or holders. Nevertheless, multiple-axis tomography also requires specialized software to combine volumes, which implies the correct 3D alignment of all reconstructions. To this purpose we have tested three algorithms (RA, RFA and PSPC) and validated them by comparing the original phantom and the final merged volumes. Our results show that the three approaches are similar, since, visually, volumes are equivalent and CODs are comparable. However, RA and RFA are faster than PSPC. RFA presents the advantage that no-reference volume is used which makes the result independent of the data set. In addition, RFA approach has been successfully used to combine several volumes coming from different independent objects of the same biological specimen (Ofverstedt et al., 1997). For these reasons, we have selected RFA as the most adaptable algorithm to perform multiple-axis tomographic reconstructions in an experimental data set from Paramecium cells recorded without any high-tilt angle device. The results obtained on this experimental data set show the major characteristic features of Paramecium basal bodies (Dippell, 1968; Dute and Kung, 1978), such as the microtubule sheath, transition zone, internal space and cartwheel components. As expected, highresolution details, such as the microtubules capping at the proximal end (black arrows in Figure 3D,E and 4C,D), as described previously in Chlamydomonas reinhardtii by using high-tilt dual-axis tomographic approaches on a JEOL JEM1000 electron microscope operated at 750 kV (O’Toole et al., 2003), can also be observed using a multiple-axis approach. One of the major limitations of the multiple-axis tomography approach is the number of projections required. The recording of these projections can damage a sample due to the total electron dose received. A possible approach to decrease the total dose can be to reduce the number of projections recorded at low-tilt angles, which does not involve an important loss of information. However, in the case of cryo-tomography on vitrified specimens, the electron dose has to be kept at a subcritical level in order to prevent any alteration of the sample (Grimm et al., 1998). Therefore, multiple-axis tomography can not be adapted for frozen hydrated specimens, which means that its application will be restricted to samples embedded in plastic resins, in which the section thickness remains
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Table 1 Shifts and rotations applied to each phantom Rotation (◦ )
Shift (pixels) Phantom
dx
dy
dz
rx
ry
rz
1
0
0
0
0.0
0.0
0.0
2
2
−1
0
2.3
5.2
−62.1
3
0
−1
0
−5.3
2.7
0.8
4
1
2
−1
1.0
−2.0
25.0
5
−1
0
1
−0.8
−1.2
90.3
6
1
2
−1
0.0
5.0
−150.6
constant after exposure to the electron beam for a time dependent on the type of resin (Luther, 2001; Boudier et al., 2005), or to materials resistant to the electron beam. In conclusion, we propose a new approach, multiple-axis tomography, to compensate for the missing information in other forms of tomography. This approach should contribute to the understanding of biological subcellular structures, making electron tomography accessible to most of the laboratories equipped with standard transmission electron microscopes. The software required for alignment and merging of volumes in multiple-axis approaches presented in this work is freely available from the authors as a plug-in for the Java-based freeware imageanalysis software ImageJ (http://rsb.info.nih.gov/ij/; Abramoff et al., 2004).
Material and methods Phantom data sets
A 128 pixels × 128 pixels × 128 pixels initial phantom volume was built using ImageJ software (Figure 1). From this phantom, two different data sets have been created to test multiple-axis tomography algorithms. First, for evaluation of multipleaxis tomography accuracy (data set 1), the initial phantom volume was rotated along the axis perpendicular to the horizontal plane by 0, 30, 45, 60, 90 and 120◦ to generate six different volume files. For each one of these volume files, projections (128 pixels×128 pixels) were computed by tilting the volumes along the same single-tilt axis placed on the horizontal plane located at the centre of the volume height. Tilt angles varied from −70 to +70◦ with an increment interval of 0.5◦ . To each one of the 1686 calculated projection images a Gaussian noise (average, 1; S.D., 10% of the maximum value) has been added by using ImageJ to represent better electron microscopy data. Second, for 3D-alignment procedure implementation (data set 2), the shifts and rotations shown in Table 1 were applied to the initial phantom to generate six misaligned volumes, representing a practical case for multiple-axis tomography. For each one of the misaligned volumes a projection set was computed as described for data set 1, except that the tilt-angle increment was fixed to 1◦ instead of 0.5◦ . Then 3D reconstructions were
Multiple-axis tomography of basal bodies
computed from each projection set using the weighted-backprojection algorithm with arbitrary geometry (Frank, 1992) to simulate an experimental procedure resulting in missing wedges in six different orientations. Evaluation of multiple-axis tomography accuracy
Data set 1 was used to compare accuracy of single-, dualand multiple-axis tomographic approaches. For single axis, 281 ◦ ◦ ‘noisy’ projections (tilt angle, + −70 ; angle increment, 0.5 ) of the 0◦ -rotated initial phantom were used to compute a volume. ◦ For dual axis, 282 noisy projections (tilt angle, + −70 ; angle increment, 1◦ ) from 141 projections of the 0◦ - and 141 projections of the 90◦ -rotated initial phantom were used to calculate a 3D reconstruction. For multiple axis, three different volumes were ◦ computed. First, 282 noisy projections (tilt angle, + −69◦ ; angle ◦ increment, 3 ) arising from 47 projections of each 0 -, 30◦ -, 45◦ -, 60◦ -, 90◦ - and 120◦ -rotated starting phantom. Second, ◦ 282 noisy projections (tilt angle, + ; angle increment, 2◦ ) −46 ◦ arising from 47 projections of each 0 -, 30◦ -, 45◦ -, 60◦ -, 90◦ and 120◦ -rotated starting phantom. Third, 282 noisy projec◦ ◦ tions (tilt angle, + −23 ; angle increment, 1 ) arising from 47 projections of each 0◦ -, 30◦ -, 45◦ -, 60◦ -, 90◦ - and 120◦ -rotated starting phantom. This approach allows the use a comparable number of projections in the evaluated cases (single, dual and multiple axis). The accuracy of the reconstructions was estimated by calculating the COD (Draper and Smith, 1981) between each one of the five calculated volumes and the initial phantom. The COD has been recently proposed as a measure of how well the reconstruction fits the test data (Tong et al., 2006). 3D-Alignment procedure implementation for multiple-axis tomography
Volume alignment on the space along the Cartesian axes x, y and z has been performed using the phantom volumes described previously to implement three 3D-alignment procedures. Shifts (d x , d y and d z ) and rotations (rx , ry and rz ) between pairs of volumes were calculated using the following procedure: 1. A matrix containing the shifts (d x , d y and d z ) and rotations (rx , ry and rz ) values was initialized to 0. 2. Each volume (reference and volume-to-alignment) of a pair was projected along z-axis. 3. An angular interval (r) and an angular increment (δr) that will be used to rotational alignment were defined by the user. 4. Rotation (r z ) was calculated by cross-correlation of the two projections using r and δr × 10 as the angular interval and angular increment respectively. 5. Computed r z was stored on a geometrical transformation matrix assigned to the volume-to-alignment as rz . 6. New angular intervals were defined as rx = r/10, ry = r /10 and rz = r/10. 7. The corresponding geometrical transformation matrices were applied to the reference and the volume-to-alignment. 8. Rotations r x , r y and r z were computed by cross-correlation in angular intervals rx , ry and rz with angular increments δrx = rx /2; δry = ry /2 and δrz = rz /2 on the biggest ellipsoid containing not null data. 9. New values for r x , r y , r z were defined as rx /2, ry /2, rz /2 respectively if rx , ry and rz were identical with the newly computed r x , r y and r z , or as rx , ry , rz if rx , ry and rz were different to r x , r y and r z .
Research article 10. r x , r y , r z were assigned as rx , ry and rz respectively. 11. The geometrical transformation matrix assigned to the volume-to-alignment was actualized with the computed r x , r y and r z values as rx , ry and rz respectively. 12. If δr δrx and δr δry and δr δrz , then go to step 13 otherwise go to step 6. 13. The corresponding geometrical transformation matrices were applied to the reference and the volume-to-alignment. 14. The shifts d x , d y and d z were computed by crosscorrelation on the biggest centred parallelepiped, having 2n pixel sides (where n is an integer) fitting in the volumes. 15. If d x = d x and d y = d y and d z = d z then go to step 16 otherwise stop. 16. The geometrical transformation matrix assigned to the volume-to-align was actualized with the computed d x , d y , d z values as d x , d y and d z respectively. 17. Repeat from step 2. Multiple volume alignment was performed by using three different procedures. The first procedure, RA, uses a volume as a reference to align all the other volumes. The second procedure, RFA, aligns two randomly chosen volumes to compute an average volume. This volume is used as reference to align another randomly chosen volume. Once this last volume is aligned, a new average volume is computed with all the volumes already treated. This average is a new reference to align the next randomly chosen volume. This procedure is repeated until the end of the whole volume data set. Finally, the third procedure, PSPC, aligns a subpopulation, containing a power-of-two number of randomly selected volumes from the original data set. This alignment is performed using volumes in pairs to compute their averages. The averaged volumes are then aligned in pairs and new averages are then computed from each pair. This procedure is followed until a single average is obtained. This average is then used as a reference to align the whole original data set. RFA and PSPC are adaptations for the 3D space of the two-dimensional RFA (Penczek et al., 1994; Marco et al., 1996) algorithms used in single particle analysis. After computing initial shifts and rotations by RA, RFA or PSPC, shifts and rotations were improved by using the refinement procedure described by Penczek et al. (1994) adapted to a 3D space. Alignment procedures, which do not require cubic arrays, have been implemented in Java as a plug-in for ImageJ that can be also launched in batch mode. Programs have been run on a SUN Sparc III (1.2 GHz, 4 Gbyte RAM) or on a DELL Latitude D610 Centrino (1.8 GHz, 1 Gbyte RAM). In the Centrino processor, alignment of 6 volumes 128 voxels × 128 voxels × 128 voxels, 32 bits, takes 3 h 14 min, 3 h 16 min and 3 h 35 min for RA, RFA and PSPC respectively. Validation of the alignments has been performed by applying the geometric transformations matrix found for the initial phantom after the alignment procedure and calculating the COD existing between them. Biological sample preparation
The wild-type strain used in this study is P. tetraurelia d4-2, derived from stock 51 (Sonneborn, 1974). Cells were grown at 27◦ C in grass infusion (wheat grass powder, Pines International), inoculated with Klebsiella pneumoniae and supplemented with 0.4 µg/ml β-sisterol.
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For electron tomography, cells were permeabilized for 5 min in PHEM buffer (60 mM Pipes, 25 mM Hepes, 10 mM EGTA, 2 mM MgCl2 , pH 6.9) containing 0.5% Triton X-100 and rinsed twice in the same buffer. Then, cell pellets were fixed for 90 min in 2% glutaraldehyde, 3% tannic acid in 0.05 M cacodylate buffer (pH 7.3). After washing in fixing buffer, samples were post-fixed for 60 min at 4◦ C in 1% osmium tetroxide in 0.05 M cacodylate buffer. Fixation was followed by dehydration through a series of ethanol and propylene oxide baths before Epon embedding. Semi-thin sections (250–300 nm) were collected on to copper-coated slot grids. Sections were briefly contrasted with uranyl acetate for 4 min, followed by Reynold’s lead citrate for 3 min, before examination. Multiple-axis tomographic reconstruction of P. tetraurelia basal bodies
Real tomographic tilt series were acquired from P. tetraurelia semi-thin sections in a Philips CM120 electron microscope, at ×8000 nominal magnification, operating at 120 kV. Six tilt series were recorded, after stabilization of the resin, using an automatic acquisition plug-in developed at our laboratory running on Gatan Digital Micrograph (version 3.1) software which controls a ssCCD (slow-scan charge-coupled-device) Gatan cam◦ era (1 k, 24 µm). Each tomographic series (+ −45 with an angle increment of 1◦ ) was acquired by rotating the grid in the horizontal plane at nominal angles of 0, 30, 45, 60, 90 and 120◦ . Images belonging to each tilt series were aligned and then cropped into 512 pixel × 512 pixel subimages. Subimages coming from a tilt series were subsequently aligned before computing six independent 3D reconstructions. The alignment and reconstruction procedures were performed without fiducial markers on a PC Linux (Intel Centrino, 1.3 GHz, 1 Gbyte RAM) by using a custom-built ImageJ interface for IMOD (Kremer et al., 1996).
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Research article
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Received 12 December 2005/9 February 2006; accepted 27 February 2006 Published as Immediate Publication 27 February 2006, doi:10.1042/BC20050097
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