Abstract
Actin filaments are polar structures that exhibit a fast growing plus end and a slow growing minus end. According to their organization in cells, in parallel or antiparallel arrays, they can serve, respectively, in protrusions or in contractions. The determination of actin filament polarity in subcellular compartments is therefore required to establish their local function. Myosin binding has previously been the sole method of polarity determination. Here, we report the first direct determination of actin filament polarity in the cell without myosin binding. Negatively stained cytoskeletons of lamellipodia were analyzed by adapting electron tomography and a single particle analysis for filamentous complexes. The results of the stained cytoskeletons confirmed that all actin filament ends facing the cell membrane were the barbed ends. In general, this approach should be applicable to the analysis of actin polarity in tomograms of the actin cytoskeleton.
Keywords: actin filament, electron tomography, polarity of the actin filament, image analysis, cytoskeleton
Graphical Abstract

Highlights
► Actin polarity in the cell was directly determined without myosin decoration. ► Electron tomograms of negatively stained lamellipodia. ► A single particle analysis for filamentous complexes was employed.
Introduction
When myosin heads bind to actin filaments in the absence of ATP, they adopt a tilted arrowhead-like configuration that reflects the inherent polarity of actin monomers in the filament.1,2 Thus, full decoration of actin by myosin has been exploited as a marker for actin filaments and as an indicator of actin polarity in muscle and non-muscle cells.3–5 According to the myosin decoration pattern, actin filaments have been attributed with “barbed” and “pointed” ends, and in vitro studies have demonstrated different polymerization and depolymerization rates at the two ends,6,7 such that, under steady-state conditions, there is a treadmilling of actin monomers through the filament from the barbed end to the pointed end.8–10 In migrating cells, actin serves roles in contraction and in protrusion, whereby the polarity of the actin filaments is the determining factor, antiparallel arrays being required for contraction and parallel arrays for protrusion and unidirectional transport by myosin. These arrays are in continuous flux because the actin cytoskeleton must be continually remodeled, thereby requiring the continuous polymerization and depolymerization of the actin filaments11–13 and actin recycling from protrusive to contractile assemblies.14 Information about their spatial organization and polarity is essential to understand the mechanisms involved in actin filament assemblies. However, the conventional method involves full decoration of actin in cells by myosin and requires that the cells are both permeable and unfixed. In addition, soaking and binding of highly concentrated myosin can lead to modifications in the structure and composition of actin assemblies because the fully decorated actin filament by myosin is more than 3-fold thicker than a bare actin filament. Consequently, the possible misinterpretation of data due to these artifacts can occur, and such processes interfere with data analysis. A less invasive means of determining the polarity of actin filaments in cells in situ would be preferable. Recently, direct observation of the three-dimensional actin filament network at the cell periphery using cryo-electron tomography has been performed.15,16 However, the contrast was poor owing to low-dose imaging requirements and because the density of the cytoplasm is similar to the density of the actin filaments.
More recently, we showed that the actin filament ultrastructure is well resolved in electron tomograms of cytoskeletons embedded in negative stain.17 The high contrast in these preparations allowed the use of a smaller defocus, resulting in a resolution sufficient for direct analysis of the actin polarity by image processing based on single particle analysis.18 We describe here the first analysis of this kind on lamellipodia of negatively stained cytoskeletons.
Analysis Procedures
Overview of the analysis procedures
Electron tomograms of negatively stained cells were acquired as described in Materials and Methods. The electron tomograms containing actin filament networks were analyzed as follows: (1) The actin filaments in the tomogram were traced by hand and extracted. (2) The extracted three-dimensional sub-tomograms of the actin filaments were straightened by correlation with cylinders. (3) A two-dimensional projection was calculated from the straightened filament. (4) The projections were analyzed by the single particle analysis for filamentous complexes,18,19 and the polarity was determined. The image analysis was performed with IMOD20,21 and Eos22 software packages.
Extraction of the actin filaments in the tomograms
Initially, the actin filaments in the tomograms were traced by hand (Fig. 1a) in 3dmod, within the IMOD software package,20,21 to compensate for the intrinsic curvature of the filaments in the cell. The trace was interpolated by a three-dimensional spline curve, and a sub-tomogram was extracted along the spline curve (Fig. 1b).
Fig. 1.
Tracing and straightening the actin filament. (a) An example of traces of the actin filaments in an electron tomogram of a lamellipodium of a Swiss 3T3 cell (Fig. 4) is presented by the red tube. The actin filaments were traced by hand using the IMOD software package.20 (b) The extracted filament according to a rough trace by hand. (c) The averaged two-dimensional projection of the extracted filament sub-tomograms along the filament axis. The vertical axis of the image corresponds to the z-axis defined in Fig. 2c. The density was elongated along the vertical axis because of the missing pyramid problem (Fig. 2). (d) A three-dimensional cylinder for tracing the filament accurately in the extracted sub-tomogram (b). The averaged two-dimensional projection (c) was remapped to each z-plane in the three-dimensional map. (e) A refined trace is presented as a red transparent tube on the subvolume shown in (b). This trace was calculated by a correlation between the sub-tomogram (b) and the three-dimensional cylinder (d). (f) The straightened actin filament according to the refined trace shown in (e).
The extracted sub-tomograms of the actin filaments still showed slight curvature because of the inaccuracy of the traces by hand; however, the extraction along the spline curve compensated for the intrinsic curvature to some extent. To compensate for the remaining curvature, we calculated an averaged two-dimensional projection of the sub-tomograms along the filament axis (Fig. 1c), and we remapped the projection in each z-plane of a three-dimensional map to form a cylinder-like shape (Fig. 1d). An accurate filament trace (Fig. 1e) was determined by correlation between the extracted filament and the cylinder map considering the three-dimensional rotation of the cylinder. Finally, a straightened filament, according to the accurate trace, was calculated (Fig. 1f). The averaged two-dimensional projection to derive the cylinder map was recalculated from the straightened filaments, and the whole procedure was iterated two times.
Two-dimensional projections
The structural data of the filament sub-tomograms have a large anisotropy (Figs. 1c and 2a and b) even when dual-axis tomography was used. This large anisotropy is due to the missing pyramid problem (Fig. 2c).23 Because of this problem, the two-dimensional projected image of the filament varied according to the direction of the projection (Fig. 2a and b). The direction of the electron beam relative to the untilted specimen was defined as the z-axis (Fig. 2c). When the direction of the filament axis was out of the missing pyramid (Fig. 2c), the projection onto the plane, including the filament axis and with the smallest tilt angle against the X–Y plane, was not affected by the missing pyramid (Fig. 2d and e). In contrast, it was difficult to recognize filaments in the projection onto the plane perpendicular to the X–Y plane (Fig. 2f and g) because the equator of the filament was in the pyramid and disappeared. We decided to use the projection onto the plane, which includes the filament axis and the nearest to the X–Y plane (Fig. 2a), to avoid the effects of deformation by the missing pyramid of most filaments (see the legend of Fig. 2 for a detailed description). However, deformation of a small number of filaments that were near parallel with the z-axis was inevitable (Fig. 2h–j).
Fig. 2.
Two-dimensional projections and the missing pyramid. (a) The two-dimensional projection of the actin filament (Fig. 1f) onto the plane, including the filament axis and with the smallest tilt angle against the X–Y plane (d). The filament structure was clearly observed without deformation. (b) The two-dimensional projection of the same filament onto the plane perpendicular to the X–Y plane (f). It was difficult to recognize the location of the filament. (c) A schematic illustration of the missing pyramid with a filament axis in reciprocal space. The z-axis was defined as the electron beam direction relative to the untilted specimen. The zero point in reciprocal space was the center of the white cube. When dual-axis tomography was adopted, there were no data inside the pyramid because of the limited tilt angles for both tilt axes.23 The missing pyramid is presented in red. The yellow line represents one example of the direction of the filament axis of an actin filament in the tomogram. (d) The plane including the filament axis and with the smallest tilt angle against the X–Y plane was superposed on (c). When the filament axis is out of the pyramid, the missing area is not included on the plane, and there is no deformation owing to the missing pyramid. The inversed Fourier transform of this plane is identical with the projection of the filament onto this plane in real space (a and e) by the central slice theorem. The four major layer lines and the equator of the actin filament (Fig. 5) are presented by cyan lines in the plane. The missing pyramid does not have to be considered when we use this projection for further analysis. (e) A simulated projection of a three-dimensional actin filament map onto the plane indicated in (d). The actin filament map determined in the polarity determination procedure is presented. The projection was not deformed by the missing pyramid. (f) The plane perpendicular to the grid plane was superposed on (c) in the same manner as in (d). A large area of the plane in the pyramid has no data, including the equator and the 37-nm layer line. (g) A simulated projection of the three-dimensional actin filament map, which is the same as in (e), onto the plain indicated in (f). Owing to the absence of the equator, the signal of the filament was significantly reduced and deformed. (h) The missing pyramid and the filament with the axis inside the pyramid are presented in the same manner as in (c). (i) The plane including the filament axis and with the smallest angle against the X–Y plane was superposed on (h), in the same manner as in (d). Most of the 5. 1-nm layer line and a part of the 5. 9-nm layer line (Fig. 5) were covered by the pyramid. (j) A simulated projection of the three-dimensional actin filament map, which is the same as in (e), onto the plain indicated in (i). Owing to the absence of the 5.1- and 5. 9-nm layer lines, the signal of each actin subunit was largely weakened, which most likely affects the polarity determination.
Image analysis to determine the polarity of the actin filaments
Since the calculated projections were two-dimensional images, a single particle procedure for filamentous complexes18,19 could be used without any required modifications. The details have been described in a previous paper.18 Briefly, polarity and orientation of each filament was determined by correlating with a reference model. A three-dimensional map was reconstructed according to the determined parameters, and the calculated map was used as the reference model for the next iteration. The procedures were iterated until the polarity had converged. The initial reference model was a three-dimensional map of the actin filament determined from negatively stained specimens of purified and polymerized actin.19 There were many crossings on one filament because of the high density of the filaments in lamellipodia (Fig. 1), and this acted as noise in the polarity determination. A statistical approach was used to avoid misinterpretation. We considered that the polarity was determined when more than two-thirds of the peaks in the correlation graph (Fig. 3d) of one polarity extended above those of the other polarity. We decided to analyze filaments including more than 80 actin subunits (about 220 nm in length). Assuming that the polarity of each peak was randomly determined, we estimated the probability of satisfying the threshold of polarity to be less than 0.75% with a 220-nm filament image, which was considered sufficiently precise. Examples of the results of the polarity determination are presented in Fig. 3. The polarity of 80–90% of the analyzed filaments could be determined in each tomogram.
Fig. 3.
Examples of the determination of the polarity of the actin filament in a lamellipodium of a Swiss 3T3 cell (Fig. 4). (a) Examples of the projection images of the actin filaments. (b) One of the projections of the reference model with the barbed end positioned to the left. (c) One of the projections of the reference model with the barbed end positioned to the right. (d) Examples of the correlation curves to determine the polarity. The horizontal axis represents the position in the filament (yi) with the right side near the membrane. The vertical axis represents the correlation value between the filament image and the reference model. The red thin lines were obtained from the correlation between the filament image and the reference model with the barbed end positioned to the left (b), and the magenta thick lines connect each peak on the thin red line; whereas the green thin lines arise from the correlation with the reference model with the barbed end positioned to the right (c), the cyan thick lines connect each peak on the thin green line. The correlation values in the final iteration are presented. The figures at the bottom right corner of each graph correspond to those in (a). The cyan lines extend above the magenta lines, indicating that the original images represent the barbed end positioned to the right. The details of the analysis are described in Ref. 18.
Results
Polarity of the actin filaments in a lamellipodium of a Swiss 3T3 cell
An actin filament network in a lamellipodium of a Swiss 3T3 cell was analyzed. The polarities of 57 out of 65 analyzed filaments were determined, and filaments with determined polarity are presented in Fig. 4 with the positions of the barbed ends marked. Image analysis showed that all ends facing the lamellipodium tip were the barbed ends, therefore confirming a previous study.24
Fig. 4.
(a) A tomogram of a lamellipodium of a Swiss 3T3 cell. The rough position of the cell membrane is illustrated as a blue curve. The red and yellow rectangles indicate the region presented in (b) and (c) and in (d) and (e), respectively. (b) An example of z-slices of the tomogram (a) is presented to show the quality of the tomogram. Five sequential slices were averaged. The helical arrangement of the actin subunits in each filament is clearly observed. The yellow arrowheads indicate the position of the branches that were most likely induced by the Arp2/3 complexes (Fig. 6). (c) The traces of the actin filaments and the barbed end positions in the tomogram (a) are presented as red tubes and red spheres, respectively, and are superposed on (a). (d) An enlarged view of (a). (e) An enlarged view of (c).
Averaged diffraction pattern of the analyzed filaments
To assess the quality of the filament image, we averaged the diffraction patterns of the 57 filaments with determined polarity in the lamellipodium (Fig. 4). The layer lines were clearly observed up to 5.1 nm (Fig. 5), indicating the high quality of the filament images. The helical parameters were identical with that of the purified actin filament.25
Fig. 5.
Averaged diffraction pattern of the actin filament in the lamellipodium (Fig. 4). The layer lines corresponding to the actin filament structure are clearly observed up to 5 nm.
Relationship of the branch orientation induced by Arp2/3 complexes and the polarity of the actin filaments
In a parallel study,26 we have identified branch junctions in the actin network of lamellipodia and showed that the structure of the branch compares very closely to the in vitro actin–Arp2/3 complex (Figs. 4b and 6a).27,28 In the present study, we analyzed the polarity of actin filaments at branch junctions. The traces and the barbed ends of the filaments that attached to the branches are presented in Fig. 6c and d. The polarities of 37 filaments that attached to the branches were determined, and 36 of these filaments had consistent polarities with the known polarity of the branch induced by the Arp2/3 complex (Fig. 6b). An additional two examples of lamellipodia have also been analyzed: (i) a lamellipodium in a different Swiss 3T3 cell and (ii) a lamellipodium in a fish keratocyte cell. The polarities of 59 filaments in total were determined, and all polarities were consistent with the plus ends of the filaments defined by the orientation of the Arp2/3 complex in an acute angle of the branch (Figs. 7 and 8). These results confirmed the high reproducibility of the polarity determination.
Fig. 6.
Branches of the actin filaments that are most likely induced by the Arp2/3 complexes in the lamellipodium of the Swiss 3T3 cell (Fig. 4). (a) A gallery of the two-dimensional projections of the branches. The branching angles were ∼ 70°, which is consistent with previous knowledge of the branches by Arp2/3 complexes. (b) A schematic illustration of the branch induced by the Arp2/3 complex. The barbed end and the pointed end of the mother filament are indicated by the blue “P” and “B”, respectively. The barbed end and the pointed end of the daughter filament are indicated by the red “P” and “B”, respectively. The green trapezoid represents the Arp2/3 complex. (c) The distribution and the orientation of the branches (in yellow) and the position of the barbed ends (red spheres) of the filament traces (red tubes) that were connected to the branches. The branches corresponding to those indicated by yellow arrowheads in Fig. 4b are indicated by the cyan arrows. Most of the barbed end positions were consistent with the orientation of the branches (b). (c) and (d) were superposed on Fig. 4a.
Fig. 7.
Branches and polarities of the actin filament in a lamellipodium of an NIH 3T3 cell injected with L61Rac. (a) The electron tomogram of a lamellipodium. The red and yellow rectangles indicate the region presented in (b) and (e and f), respectively. (c) and (d) present the same region as (a). (b) An example of z-slices of the tomogram (a). Five sequential slices were averaged. The yellow arrowheads indicate examples of the branch junctions, most likely induced by the Arp2/3 complexes. (c) The orientation and position of the Arp2/3 complex with the polarity of the actin filaments attached to the branches are presented in the same manner as in Fig. 6c. The branches corresponding to those indicated by yellow arrowheads in (b) are indicated by the cyan arrows. (c) and (d) were superposed on (a). (e) An enlarged view of (a). (f) An enlarged view of (d).
Fig. 8.
Branches and polarities of the actin filament in a lamellipodium of a fish keratocyte. (a) An electron tomogram of a fish keratocyte lamellipodium. The red and yellow rectangles indicate the region presented in (b) to (d) and (e) and (f), respectively. (b) An example of z-slices of the tomogram (a). Five sequential slices were averaged. The yellow arrowheads indicate the position of the branches, most likely induced by the Arp2/3 complexes. (c) The orientation and position of the Arp2/3 complex with the polarity of the actin filaments attached to the branches are presented in the same manner as in Fig. 6c. The branches corresponding to those indicated in (b) are indicated by the cyan arrows. (c) and (d) were superposed on (a). (e) An enlarged view of (a). (f) An enlarged view of (d).
Discussion
In the present study, the first determination of the actin filament polarity in a cell without myosin decoration using electron tomography of negatively stained specimens was presented, and the results confirmed that all filament ends facing the cell membrane were the barbed ends in lamellipodia. However, there are still some limitations:
-
(1)
Our current method could be best applied to filaments with the direction out of the missing pyramid (Fig. 2), without a large tilt angle with respect to the X–Y plane. When dual-axis tomography was applied and the ranges of the tilt angles were ± 60° for both axes, the amount of area in the solid angle of the missing pyramid was 2π/3, which is 16.7% of the whole solid angle (4π). This value is small but not negligible when the filaments of interest are near perpendicular to the grid plane. To treat filaments with the direction in the missing pyramid, our current method should be developed to consider deformation of the filament image (Fig. 2h–j) owing to masking of the 5.1- and 5. 9-nm layer lines (Fig. 5) by the missing pyramid.
-
(2)
The thickness of the specimen is limited because of the limited penetration power of the electron beam. High-voltage electron microscopy or STEM tomography techniques29 should be helpful in increasing the sample thickness that can be studied.
-
(3)
The treatment of the cell may change the structure of the actin filament network although a structural change was not detected, except for the observation of the whole thickness shrinkage.17 It is very difficult to achieve sufficient signal to determine the polarity of the filaments by cryo-electron tomography of the whole cell because the cytoplasm has a similar density to the filaments and because of the large thickness of the cell. CEMOVIS30 with very thin slices (∼ 60 nm) may reduce the noise and enable us to analyze the polarity of the filament with more intact conditions than the current method.
Although there are limitations, as described above, our current method was effective in determining the polarity of the filaments with high accuracy. It does not require myosin decorations, which enabled us to analyze the intact actin network without disturbance by myosin. Since determination of the polarities of actin filaments relative to each other, to membranes and to other components in the cell provides important clues about local function, the present approach should find wider applications in future structural studies by electron tomography of actin filament arrays in subcellular compartments.
Materials and Methods
Cells and fixation
Fish keratocytes were prepared from scales of freshly killed brook trout and plated onto Formvar-coated grids as described in Urban et al.17 The cells were simultaneously fixed and extracted for 1 min in a mixture of 0.75% Triton X-100 (Fluka) and 0.25% GA (glutaraldehyde; Agar Scientific) in CB [“cytoskeleton buffer”; 10 mM 4-morpholineethanesulfonic acid, 150 mM NaCl, 5 mM ethylene glycol bis(β-aminoethyl ether) N,N′-tetraacetic acid, 5 mM glucose and 5 mM MgCl2 (pH 6.1)], post-fixed for 15 min in 2% GA in CB containing 1 μg/ml phalloidin and incubated overnight in 2% GA in CB containing 10 μg/ml phalloidin. The grids were negatively stained in an aqueous, neutral solution with (pH 7) 4% sodium silicotungstate (Agar Scientific), containing bovine serum albumin saturated colloidal gold. Swiss 3T3 cells were maintained as described in Urban et al.,17 cultured to confluence overnight and split the next day onto grids pre-coated with poly-l-lysine (0.01%; Sigma) in serum-free medium for 1 h at 37 °C. The cells were simultaneously extracted and fixed with 0.5% Triton X-100 and 0.25% GA in CB and further processed for negative stain electron tomography, as described for the fish keratocytes. NIH 3T3 cells were transfected with L61Rac and with EGFP-Lifeact and plated onto Formvar-coated coverslips to monitor lamellipodia dynamics by fluorescence microscopy. Prior to fixation, selected cells were microinjected with L61Rac to consolidate lamellipodia induction, fixed on the light microscope and processed for negative staining and electron tomography as described by Vinzenz et al.26
Electron tomography
Tilt series of negatively stained cytoskeletons on Formvar-coated NHF-A finder grids (Maxtaform) were acquired around two orthogonal axes on an FEI Tecnai F30 Helium (“Polara”) operating at 300 kV and cooled to approximately 80 K, as described in Urban et al.17 Typically, the tilt range was − 60° to + 60° using the Saxton tilt scheme based on 1° increments from a zero degree tilt at defocus values of − 5 and − 3 μm, and images were recorded on a Gatan UltraScan 4000 CCD camera. The primary on-screen magnification used for image acquisition was 27,500 ×. Reconstructions of tomograms from the tilt series were generated using the IMOD software from the Boulder Laboratory for 3D Electron Microscopy of Cells,20 using gold particles as fiducials for alignment.
The calculated tomograms were visualized by the Chimera31 software.
Acknowledgements
This research was supported by a Grant-in-Aid for Scientific Research (S) (to Y.M.) and a Grant-in-Aid for Young Scientists (B) (to A.N.) from the Ministry of Education, Culture, Sports, Science and Technology of the Japanese Government. This research was also supported by Daiko Research Foundation (to A.N.) and by Austrian Science Fund: projects FWF 1516-B09 and FWF P21292-B09 (to J.V.S.).
Edited by R. Craig
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