On-lamella dual-axis cryo-electron tomography and modelling of lamella stability

On-lamella dual-axis cryo-electron tomography and modelling of lamella stability | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article On-lamella dual-axis cryo-electron tomography and modelling of lamella stability Moritz Wachsmuth-Melm, Santiago Gomez Melo, Cornelis Mense, Liv Zimmermann, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6497420/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Cryogenic electron tomography (cryo-ET) of cryogenic focused ion beam (cryo-FIB) milled lamellae enables the study of 3D cellular architecture in near-native conditions at nanometer-scale resolution. Cryo-FIB milling is performed iteratively by reducing the FIB current and the distance between rectangular patterns that define the milled area. The resulting cryo-lamellae must remain connected to the cell body, but can fracture during preparation and transfer to a cryo-transmission electron microscope (cryo-TEM), which reduces the throughput. Successful cryo-ET data collection requires loading the EM grid into the cryo-TEM holder with the tilt axis oriented perpendicular to the milling direction. This orientation enables tilting during data acquisition, as the rectangular milling patterns restrict the tilt range and prevent dual-axis tomography. Here, we developed a cryo-FIB trapezoid milling strategy that enables dual-axis cryo-ET. We demonstrate that dual-axis tomograms contain additional 3D information compared to single-axis tomograms and compared to single-axis tomograms after deep learning missing wedge restoration. Hence, dual-axis tomograms offer improved segmentations and provide a valuable training dataset to improve deep learning restoration algorithms. Furthermore, we used a mechanical analysis with finite elements to calculate the build-up of von Mises stresses, commonly used in materials science, to identify fracture points in the lamella and to identify improved lamella designs. This provides a simulation framework to predict and design milling patterns with increased stability. Cryo-focused ion beam milling cryo-electron tomography denoising missing wedge information von Mises stress linear elasticity and finite elements simulations Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Cryogenic focused ion beam (cryo-FIB) milling is the method of choice for producing electron-transparent lamella of vitrified biological samples, which can be studied by cryogenic electron tomography (cryo-ET) [ 1 – 4 ]. Cryo-ET consists of a tilt series acquisition with a defined increment of angle range, typically performed in a dose-symmetric fashion along one tilt axis. Because the lamella has a slab geometry, tilting is typically limited to ± 60°, which leads to missing wedge information in Fourier space. Due to this limitation, tomograms have an anisotropic resolution, and features along the Z-axis are elongated [ 5 , 6 ]. Several approaches, including deep-learning missing wedge restoration algorithms, have been developed to fill in the missing wedge information in Fourier space [ 7 – 10 ]. However, these methods have not been evaluated using on-lamella dual-axis cryo-ET. In addition, in silico restoration of detailed 3D information can be challenging due to the high density and complexity of biological structures in the cell. Dual-axis ET allows to partially complement the missing wedge information and hence can be useful when interpreting complex membranous structures in 3D and improving the accuracy of segmentations [ 11 ]. Cryo-FIB milling approaches currently use rectangular patterns, which lead to a milled lamella attached to perpendicular walls of non-milled remnants of the cell body. The currently used milling geometry enables single-axis tilt series acquisition when the tilt axis is oriented perpendicular to the milling direction. However, it limits or prevents the use of dual-axis tomography, whose application remains to be explored and could augment 3D data quality of cellular material when subtomogram averaging is not applicable. In addition, lamellae produced using rectangular patterns must be loaded onto the microscope stage with an orientation perpendicular to the tilt axis [ 1 ]. To ensure correct alignment, the AutoGrid rim is marked to indicate the grid orientation during loading into Autoloader systems (Thermo Fisher Scientific), which can be technically challenging. The throughput of cryo-FIB milling is steadily increasing due to the increasing use of automation. Several automated software solutions allow coarse milling and the last milling steps to some extent, yielding a final desirable thickness between 150–200 nm [ 12 , 13 ]. During milling, lamella can undergo undesirable deformation or tilting. This is caused mainly by compression in the supporting film and compression forces released during milling. The supporting film, typically made of thin carbon or silicon dioxide, does not compress as much as gold metal, leading to reduced flatness of the film, so-called crinkling [ 14 ]. Lamella tilting or deformations often limit the final milling step, hence producing thicker lamella or lamella with inhomogeneous thickness. Typically, stress relief cuts (also termed micro-expansion joints) are placed in the cell body to release lateral forces applied perpendicular to the milling direction on the lamella, thereby preventing lamella tilting or deformations [ 15 ]. However, the physics of lamella geometry as well as stress points of lamella remain to be studied to inform on better milling geometries and to design patterns which would increase lamella stability and therefore throughput. Here we show that a trapezoid milling pattern enables the performance of dual-axis cryo-ET on lamellae. Dual-axis tomograms have increased 3D information compared to single-axis tomograms, which facilitates automated segmentation and can serve as improved training data for deep-learning missing wedge restoration approaches. Additionally, this study provides insights into physical forces and stress distribution in lamella and makes suggestions for improvement in milling design. We identify the points of fracture onset with the aid of linear elasticity and finite elements simulations, which we mitigate through refining the geometry of the lamella. We show that the point most at risk of fracture is at the connection joint between the lamella and the cell body, and that rounded edges might reduce this risk. Materials and Methods Plunge freezing of cells VeroE6 cells were seeded onto Quantifoil R1.2/20 200 Au mesh grids in a 35 mm cell culture dish coated with SYLGARD™ 184 silicone elastomer. Both grids and dishes were glow-discharged and disinfected with 70% ethanol prior to cell seeding. One day after seeding, grids were removed from the medium and directly transferred to a Leica GP2 plunge freezer set to 80% chamber humidity and 37°C chamber temperature. A 2 µl drop of medium from the cell culture dish was added on the top side of the grid. Grids were blotted for 3.5 seconds and plunge frozen in liquid ethane at -185°C. Cryo-FIB milling of adherent cells Grids were clipped into ThermoFisher CryoFIB AutoGrids and loaded into an Aquilos 2 cryo-FIBSEM. Target cells were selected in MAPS. After the eucentricity adjustment, lamellae were coated with organometallic platinum and milled manually using trapezoid milling patterns. Cryo-FIB milling currents were determined by beam-limiting customised 15-hole aperture strip provided by Thermo Fischer Scientific with 3 x 10, 2 x 30, 2 x 50, 100, 300, 500, 1000, 3000, 7000, 15000, 65000 pA. FIB aperture alignments were performed every other week. The following currents were used: 0.5-1 nA (step 1), 300 pA (step 2), 100 pA (step 3), 50 pA (step 4), 30 pA (step 5 (polishing)). Dual-axis cryo-electron tomography on-lamella acquisition Cryo-ET was performed using a Titan Krios Transmission Electron Microscope (TEM, ThermoFisher Scientific) operated at 300 keV and equipped with a BioQuantum® LS energy filter with a slit width of 15 eV and K3 direct electron detector (Gatan) using SerialEM [ 16 ]. Montaged maps were acquired at 8700× magnification with pixel size 10.68 Å/pixel and approximate defocus of -80 µm. Dual-axis tomography was performed using a dual-axis stage at the Krios G1 that supports rotation of 90°. A and B single-axis tilt series were acquired at 33,000× magnification with a pixel size of 2.671 Å/pixel at -4 µm defocus, with an electron dose of approximately 1.5 e⁻/Ų per projection. A dose symmetric acquisition scheme was used with an A-axis tilt range of + 68° to -52°, start at 8° and B-axis tilt-range + 60° to -60°, start at 0° in 3° increments [ 17 ]. Tilt series were acquired in parallel with PACE tomo [ 18 ]. Projection images were acquired as movies and motion correction and summing on-fly using was done using the SerialEM SEMCCD plugin. Dual-axis tomogram reconstruction Tilt series were aligned using patch tracking (680, 680; seven patches in x and five patches in y direction) and reconstruction was performed using a weighted back-projection algorithm with SIRT-like filter 5 in IMOD [ 19 ]. Contrast transfer function correction in 2D and dose-weight filtering was performed in IMOD prior to tomogram reconstruction. Two tomograms were combined in IMOD using overlapping patches (400×400×200 pixels). Tomograms were binned 3× for figure production. Finite element simulation The finite element simulations solve the linear elasticity equilibrium equations with the aid of the open software framework Dolfinx. The vitrified cell is modelled as an isotropic elastic material with a Young's modulus of 8 GPa and a Poisson's ratio of 0.15 [ 16 ] [ 17 ]. The cell experiences a thermal hydrostatic strain \(\:{ϵ}_{T}={\alpha\:}_{c}\varDelta\:TI\) with thermal expansion coefficient \(\:{\alpha\:}_{c}=20\times\:{10}^{-6}{K}^{-1}\) and temperature difference \(\:\varDelta\:T=-200K\) , and I is the identity matrix. In addition, the bottom surfaces in contact with the substrate have a prescribed displacement of \(\:\overrightarrow{u}={\alpha\:}_{s}\varDelta\:T\overrightarrow{x}\) , which represents the thermal contraction of the silicon oxide substrate with thermal expansion coefficient \(\:{\alpha\:}_{s}=7.9\times\:{10}^{-6}{K}^{-1}\) and undeformed position \(\:\overrightarrow{x}\) . The equations to solve for a displacement field u are thus $$\:\nabla\:\cdot\:\left(\sigma\:\left(ϵ\left(u\right)\right)-\sigma\:\left({ϵ}_{T}\right)\right)=0$$ , $$\:\sigma\:=\lambda\:Tr\left(ϵ\right)I+2\mu\:ϵ,$$ $$\:ϵ=\frac{1}{2}\left(\nabla\:u+\nabla\:{u}^{T}\right)$$ After solving for the displacement field, the von Mises stress is computed as \(\:{\sigma\:}_{vM}=\sqrt{s}\) , with s being the traceless stress tensor \(\:s=\sigma\:-1/3Tr\left(\sigma\:\right)I\) . Peak stresses, used for joints of increasing curvature radius, were calculated by first isolating elements at the surface of the joint. After which the average of the 98th percentile was calculated, because taking the highest value would have likely been akin to measuring the error of the simulation. Geometry The geometry of the meshes was modelled to closely resemble those of the milled cells, orthogonal and Y junction, using version 4.13.1 of Gmsh. For the orthogonal milling pattern, the two cell bodies were modelled to a convex shape by displacing the outer corners of rectangular prisms. Both bodies were based on a prism with dimensions 9.5×30×12 µm, with the corners furthest from the lamella displaced inwards by (0,10,0) µm for the lower two and (3,8,-4) µm for the upper two. Both bodies were given an expansion joint 0.5 µm from the lamella of dimensions 0.5×30×5 µm, with rounded edges of curvature 0.1 µm. We modelled the lamella itself with a rectangular prism of dimensions 12×30×0.2 µm, attached to the bodies at a height of 6 µm. Whenever rounded joints were used, the surface of the joint was parameterised by a one quarter of a cylinder, with the y axis as its horizontal direction. The radius of the cylinder was varied and the cylinder’s centre was set to (r, 0, r) µm from the corner of the joint, to create a tangent line with both the cell body and lamella. The Y junction milling pattern was imitated by modelling the cell bodies as irregular prisms, with eight corners set at Cartesian coordinates (16.5, ± 1.5, 0), (9.7, ± 1.5, 0), (6, ± 1.5, 4), and (9.7, ± 1.5, 8) µm for the right body and the left body mirrored in the yz plane. The expansion joints were again of dimensions 0.5×30×5 µm, with rounded edges of curvature 0.1 µm, and placed at distances (15.4, 0, 1) µm from the edge of the lamella. We modelled the lamella itself as a rectangular prism, with the same dimensions 12×30×0.2 µm, but attached to the bodies at a height of 4 µm. The meshing was conducted at a base resolution of 0.5 µm for the cell body, with a finer resolution field of 0.066 µm around the lamella. A gradual transition between these fields was applied over a distance of 5 µm in all directions. The total number of meshed elements was in the range of 2 6 elements. Results After plunge-freezing VeroE6 adherent cells, EM grids were clipped into FIB-Autogrids (Thermo Fischer Scientific) and loaded into Aquilos 2 Cryo-FIB-SEM. Mapping and eucentric position of lamella sites were performed in MAPS. We used polygonal milling patterns available in the XTUI software of Aquilos 2 cryo-FIB-SEM to create a trapezoid pattern and micromachine a lamella shape compatible with dual-axis tomography. Two isosceles trapezoid patterns were placed so that their shorter bases were facing each other (Fig. 1 A). We used a trapezoid geometry as the first milling pattern with an angle of 150°, allowing for ± 60° angle tilting in the direction parallel to the FIB milling. Isosceles trapezoids have two parallel bases ( b 1 and b 2 ) separated by a height ( h ) and two legs with supplementary congruent angles (150° and 30°), resulting in 180° at each side. To achieve a 60° tilt, the angle at the shorter base must be 150°, and the length of b 1 and b 2 can be calculated based on equation: $$\:{b}_{2}={b}_{1}+2\:h\:cot\left(30^\circ\:\right).$$ For practical use, b 2 should have double the length of b 1 and h needs to be approximately 4 µm to obtain an angle of 150° at the lower base. We used a trapezoid pattern with b 1 = 14 µm and b 2 approximately 29 µm and h = 4.7 µm. In addition, two rectangular patterns were used for stress-release cuts (micro-expansion joints) [ 10 ]. The second polygonal pattern had six vertices to reduce the milling area (Fig. 1 B). Subsequent lamella thinning including the last polishing step was performed in 3 steps using rectangular patterns (Fig. 1 C). All milling steps were performed at a grazing angle of 8–10° and no over-titling was used. SEM was used to monitor each milling step (Fig. 2 ). FIB-Autogrids were loaded into a cassette such that the cut-off was facing to the right and the loading position was verified using a long-distance stereomicroscope. We used SerialEM to acquire medium magnification maps for each lamella at tilt angles 8°, + 68° and − 52° at stage rotation angle 0° and tilt angles 0°, + 60° and − 60°. The nominal rotation between the tilting axes of the two tomograms was approximately 87°. Our data showed that the cell body does not obscure most of the lamella area at extreme angles of both tilt axes, enabling dual-axis tomography (Fig. 3 ). Tilt series were acquired using SerialEM [ 16 ] and in parallel mode using PACE tomo [ 18 ]. A-axis was acquired using a dose-symmetric schema and a starting angle of 8°. Subsequently, the stage was rotated by 90°, and B-axis tilt series were acquired. Tomogram positions for the B-axis were manually selected in the PACE tomo routine. Tomograms were reconstructed and combined in Etomo (IMOD version 5.1.0) [ 19 ]. Using large patches for combining dual-axis tomograms yielded lower errors, consistent with our previous study [ 20 ]. Data and unsupervised segmentations performed in MemBrain [ 21 ] clearly showed increased information in the z-direction and improved interpretability of the cellular structures (Fig. 4 ). We further aimed to compare the data quality between dual-axis tomography and the deep-learning-based missing wedge correction methods IsoNet [ 7 ] and DeepDeWedge [ 10 ] trained on single-axis data. Our data show that these methods are unable to fully restore features perpendicular to the tilt-axis present in dual-axis data (Fig. 5 ). Coupling dual-axis tomography with missing wedge correction by correcting the single-axis tomograms before combination in Etomo improved the data quality mostly along the Z-axis. Exploring different milling strategies prompted us to evaluate the structural stability of lamella, which was done with the aid of linear elasticity theory and the finite element method (FEM). The vitrified cell was modelled as a linear elastic material with a Young's modulus of 8 GPa and a Poisson's ratio of 0.15 [ 22 , 23 ]. Following standard procedures for material behaviour during temperature changes [ 24 ], the sample was subjected to an active strain due to thermal contraction and an additional contractive displacement at the interface with the graphite support film, which contracts less than copper EM grids at a lower temperature (film crinkling) [ 14 ]. The thermal expansion coefficients for cell material and substrate were taken from the literature as \(\:{\alpha\:}_{c}=20\times\:{10}^{-6}{K}^{-1}\) [ 23 ] and \(\:{\alpha\:}_{s}=7.9\times\:{10}^{-6}{K}^{-1}\) [ 14 ], respectively. Two milling patterns were modelled, one with orthogonal T-junction joints and another with the Y-junction joints. Stress release cuts, which were empirically determined to reduce lamella distortions, were included in both milling patterns. Details of the simulation setup may be found in Materials and Methods. The simulated undeformed geometry of the orthogonally milled cell, along with the displacement field and the resulting deformed geometry, are shown in Fig. 6 A-C. The displacement results corresponding to the Y-type junction are shown in Fig. 7 A-C. Both cases yield similar results; a mostly isotropic contraction across the whole body is observed. The displacement field at the lamella is mostly suppressed, given that its norm is 0.001 µm near the centre of the lamella and up to 0.075 µm in the rest of the body. The largest displacements in the lamella are observed in its outermost surface parallel to the xz plane (Fig. 6 A, 7 A, 6 B and 7 B), where slight buckling is observed in the z direction. The most obvious difference between the junction geometries is the buckling of the joints in the x direction, which is significant in the orthogonal joint (Fig. 6 C), but notably less noticeable in the Y-joint (Fig. 7 C). This is due to the fact that there is a larger distance between the lamella and the joints in the case of the Y junction. We quantify the von Mises stress, related to the Frobenius norm of the traceless part of the stress tensor (see Materials and Methods), to identify weak regions in the vitrified cell prone to fracture. The von Mises stresses for the orthogonal T-joints are shown in Fig. 6 D, 6 E, and 6 F, whereas the analogous results for the Y-joints are depicted in Fig. 7 D and 7 E. In the former geometry, a build-up of stress at the elbow of the joint is observed. Such stress concentration is due to the sharp contact angle, which experiences stresses of up to 30 MPa in comparison to 0.1–15 MPa across most of the remaining body. Similarly, regions above and below the lamella with orthogonal joints show high stress due to the buckling of the joints. In contrast, the Y junction concentrates stress in the lamella itself, ranging between 20 and 37 MPa. Stress in the joints is notably reduced due to the suppression of the buckling. In both geometries high stress is observed at the bottom surfaces, which represent the interface with the substrate. This is a consequence of an idealised geometry with a sharp contact angle; the real contact angle will be rounded, have a larger surface area and thus lower stress. In addition, various stress release cuts were modelled for trapezoid milling patterns. The results indicate that lamella stress is reduced by using Y-shaped stress release cuts instead of vertically placed rectangular ones (Fig. 8 ). Because the elastic equations lead to stress localization at sharp edges, a possible workaround to mitigate the build-up of von Mises stress is to use rounded joints. We explore this alternative by simulating geometries with variable radius of curvature of the joints connecting the lamella to the cell body. Starting with the orthogonal milling pattern, we introduced a curvature ranging up to 1.45 µm and calculated the peak stress. Through the stress distributions in Fig. 9 A, 9 B, and 9 C it is shown that having joints with low radius of curvature drastically lowers stress at the elbow. The calculated stress at the joints has a minimum around a radius of 0.32 µm, as shown in Fig. 8 D, beyond which the increase in material appears to play a larger role. Discussion Cryo-FIB has opened a way to study unperturbed vitrified cellular environments in 3D and molecular resolution. Furthermore, the resolution of protein structure can be improved by subtomogram averaging. Yet, low-abundant proteins, proteins with intrinsically disordered domains, and proteins with small sizes are often difficult to assess by subtomogram averaging. Hence, the interpretation of a cellular crowded environment often relies on direct analysis of the tomograms. Dual-axis cryo-ET contains additional 3D information and provides a tomogram with reduced resolution anisotropy. This facilitates data interpretation, 3D segmentations, and direct visualization of small protein complexes and filamentous structures that can suffer from information loss depending on their orientation to the tilt axis [ 11 ]. Here, we established a cryo-FIB milling a trapezoid pattern to prepare cryo-lamellae compatible with dual-axis cryo-ET (Figs. 1 and 2 ). This approach additionally removes edges of the cell body, thereby enabling dual-axis tomography (Fig. 3 ) and facilitating tilting, even when the Autogrid is not perfectly loaded into the cassette (Thermo Fisher Scientific microscopes). With PACE tomo [ 18 ], the time required for acquiring single- and dual-axis tilt series is no longer a major limiting factor. Our data demonstrate that dividing the electron dose between two orthogonally oriented tilt series enables alignment via patch tracking, followed by reconstruction of two tomograms. These volumes can then be combined into a dual-axis tomogram. We utilized unsupervised 3D segmentations using MemBrain [ 21 ] to demonstrate that dual-axis cryo-ET provides increased information on organelle structure in 3D, outperforming single-axis cryo-ET (Fig. 4 ). Additionally, we compared the 3D information of dual-axis tomograms with those generated using deep-learning algorithms for missing wedge restoration in Fourier space, such as IsoNet [ 7 ] and DeepDeWedge [ 10 ]. Our analysis revealed that deep learning-driven restoration is incomplete and, to some extent, inaccurate (Fig. 5 ). To address this limitation, we propose leveraging dual-axis tomograms as a training dataset to improve the prediction accuracy of deep-learning-based missing wedge restoration methods. The main limitation of dual-axis cryo-ET comes from the accumulated electron dose of the second tilt series. We have previously shown that electron dose can be further decreased when the Volta phase plate is used [ 20 ], and hence, on-lamella dual-axis cryo-ET will in the future benefit from laser phase plate implementation, which shows promising results [ 25 , 26 ]. Despite automation, cryo-FIB lamella preparation remains a major bottleneck of in situ cryo-ET. Due to lateral pressure which is released during milling lamella can bend or crack. To evaluate the stability of lamellae produced by the rectangular and trapezoid milling patterns, we use theoretical modelling to identify stress points on lamella. The FEM simulations confirmed the protective role of the stress-release cuts against thermal wrinkling for the orthogonal geometry; as seen in Fig. 6 A and Fig. 6 C, the contraction causes the joints to buckle inwards, which in turn suppresses the in-plane displacement across the lamella at its centre. As a result, the displacement norm across the lamella is almost two orders of magnitude lower compared to that of the rest of the body (Fig. 6 A). In contrast, the lamella experiences its largest in-plane displacements at the outermost surfaces parallel to the xz plane, where no joints are present, and even buckling in the z direction (Fig. 6 C). Mechanical protection of the lamella against thermal contraction is paramount, given its fragility stemming from its high aspect ratio. Such fragility is confirmed by the von Mises stress distribution (Fig. 6 D, 6 E and 6 F), which exhibits highest values at the elbows of the joints (Fig. 6 D) due to the thinness of the lamella and the sharp contact angle. Similarly, the buckling of the joints generates further weaker regions above and below the lamella. The region below the lamella is particularly stressed, since it is closer to the substrate that contracts with a different thermal coefficient. We thus identify these regions as the weakest regions that are prone to fracture onset. Nonetheless, the joints appear to be less useful in the case of the Y joint (Fig. 7 ), since the lamella of this geometry experiences a higher von Mises stress than the rest of the body (Fig. 7 F). This occurs because the joints are farther away from the lamella. Consequently, their displacement is not affected by the presence of the lamella, as evinced by the lack of buckling (Fig. 7 C), and thus their protective role is reduced compared to the orthogonal case. Hence, the simulation demonstrates that the rectangular hole geometry is not well suited for stress reduction in a Y-type junction However, our data suggests that triangle or Y-shaped stress release cuts are more effective (Fig. 8 ). The mitigation of stress by variation of curvature radius (Fig. 9 ) seems to produce conflicting results: on one hand, Fig. 9 D suggests that round joints reduce stress at the joint and predicts an optimal curvature radius for which the maximum von Mises stress at the joint is minimized. Nevertheless, Fig. 9 A-C show that the rounding of the joints comes at the expense of an increase in the von Mises stress across the lamella itself: for the smallest radius of curvature (Fig. 9 A), the lamella experiences stress of up to 14MPa, whereas the lamella with largest radius (Fig. 9 C) show stress of around 20MPa. We thus reason that no significant protection is offered by rounding the edges. However, the true effect of round edges can only be confirmed experimentally, since the FEM model is highly idealized and does not capture all external factors in the experiment. Conclusions The cryo-FIB milling approach presented here enables the production of cryo-lamellae compatible with dual-axis cryo-ET. Dual-axis tomograms of the cellular environment outperform current missing wedge restoration methods applied to single-axis tomograms. As a result, dual-axis tomograms enhance the interpretability and segmentation accuracy of cryo-preserved cellular structures and can serve as ground truth for deep learning–based missing wedge restoration approaches. In addition, the computational model presented here offers a valuable tool for assessing and optimizing lamella shapes produced by novel milling patterns. Exploring different combinations of junction and stress-release cut geometries represents a promising direction for future research. Abbreviations Cryo ET–cryo–electron tomography Cryo FIB–cryo–focused ion beam FME finite element method Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Funding This work was supported by research grants from the Chica and Heinz Schaller Foundation (Schaller Research Group Leader Programme) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) to P.C. and U.S.S. (project no. SFB1129/3–240245660 –P19 and – SFB-1638/1–511488495 – P03 and Z03). Moreover, this work was also supported by the DFG under Germany’s Excellence Strategy - EXC 2082/1-390761711 (the cluster of excellence 3DMM2O). P.C. acknowledges the DFG Heisenberg programme CH 2158/3 − 1. Author Contribution M.W-M. performed data processing and analysis and prepared figures 4-5.; S.G.M. and C.M. performed modeling of lamellae and prepared figures 6-8. L.Z. prepared the samples; P.C. and U.S.S. conceptualized the study. P.C. prepared Figures 1-3, performed cryo-FIB and cryo-ET. P.C. and U.S.S. wrote the manuscript and obtained funding. All authors reviewed the manuscript. Acknowledgements We thank the Infectious Diseases Imaging Platform (IDIP) at the Center for Integrative Infectious Disease Research Heidelberg and the cryo-EM network at the Heidelberg University (HD-cryoNET) for support and assistance. The authors gratefully acknowledge the data storage service SDS@hd supported by the Ministry of Science, Research, and the Arts Baden-Württemberg (MWK), the German Research Foundation (DFG) through grant INST 35/1314-1 FUGG and INST 35/1503-1 FUGG. Data Availability Tomograms will be deposited in EMDB database upon publication. References Lam V, Villa E: Practical Approaches for Cryo-FIB Milling and Applications for Cellular Cryo-Electron Tomography. Methods Mol Biol 2021, 2215:49–82. Marko M, Hsieh C, Moberlychan W, Mannella CA, Frank J: Focused ion beam milling of vitreous water: prospects for an alternative to cryo-ultramicrotomy of frozen-hydrated biological samples. J Microsc 2006, 222(Pt 1):42–47. Rigort A, Bauerlein FJ, Villa E, Eibauer M, Laugks T, Baumeister W, Plitzko JM: Focused ion beam micromachining of eukaryotic cells for cryoelectron tomography. Proc Natl Acad Sci U S A 2012, 109(12):4449–4454. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6497420","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":457972482,"identity":"1b6e3252-0364-4130-8a98-80a0aa734826","order_by":0,"name":"Moritz Wachsmuth-Melm","email":"","orcid":"","institution":"Heidelberg University","correspondingAuthor":false,"prefix":"","firstName":"Moritz","middleName":"","lastName":"Wachsmuth-Melm","suffix":""},{"id":457972484,"identity":"0e0a3976-712a-4124-9c8a-e83ce7079858","order_by":1,"name":"Santiago Gomez Melo","email":"","orcid":"","institution":"Heidelberg University","correspondingAuthor":false,"prefix":"","firstName":"Santiago","middleName":"Gomez","lastName":"Melo","suffix":""},{"id":457972487,"identity":"c65c5cb8-a6c5-44a6-a41e-a27419719840","order_by":2,"name":"Cornelis Mense","email":"","orcid":"","institution":"Heidelberg University","correspondingAuthor":false,"prefix":"","firstName":"Cornelis","middleName":"","lastName":"Mense","suffix":""},{"id":457972488,"identity":"b9b17547-a840-4448-86c1-954b31e0d9c8","order_by":3,"name":"Liv Zimmermann","email":"","orcid":"","institution":"Heidelberg University","correspondingAuthor":false,"prefix":"","firstName":"Liv","middleName":"","lastName":"Zimmermann","suffix":""},{"id":457972489,"identity":"0bc9669a-a8f7-4caa-a755-e08726bec00d","order_by":4,"name":"Ulrich S. Schwarz","email":"","orcid":"","institution":"Heidelberg University","correspondingAuthor":false,"prefix":"","firstName":"Ulrich","middleName":"S.","lastName":"Schwarz","suffix":""},{"id":457972490,"identity":"88af8af0-c126-47bb-82f1-76e873639778","order_by":5,"name":"Petr Chlanda","email":"data:image/png;base64,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","orcid":"","institution":"Heidelberg University","correspondingAuthor":true,"prefix":"","firstName":"Petr","middleName":"","lastName":"Chlanda","suffix":""}],"badges":[],"createdAt":"2025-04-21 15:38:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6497420/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6497420/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83198516,"identity":"9b09f3f9-cf83-4354-9492-4236165caa20","added_by":"auto","created_at":"2025-05-21 06:03:27","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":301825,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTrapezoid cryo-FIB milling. a-f) \u003c/strong\u003eCryo-FIB images of different milling steps.\u003cstrong\u003e a)\u003c/strong\u003e Two isosceles trapezoids (filled with diagonal yellow stripes and indicated by numbers 3 and 4) are used as a step 1 milling pattern. Isosceles trapezoid bases b1, b2, height h and angles are defined. Patterns 1 and 2 represent stress-release cuts. \u003cstrong\u003eb)\u003c/strong\u003e Polygonal milling patterns 1 and 2 are used as a step 2 milling pattern. \u003cstrong\u003ec-f)\u003c/strong\u003eFIB images after step 1, step 2, before and after the polishing step.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/a219e1c3847bf9c4277088c1.png"},{"id":83200231,"identity":"54b82e68-54e4-46cd-9c74-32b4fe461efc","added_by":"auto","created_at":"2025-05-21 06:11:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":230439,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSEM images of trapezoid cryo-FIB milling. a-e) \u003c/strong\u003eSEM images of different milling steps.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/d3d034970e83489a40dfe69d.png"},{"id":83198517,"identity":"862ecdd0-fdd8-4453-99df-26944709719a","added_by":"auto","created_at":"2025-05-21 06:03:27","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":236159,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCryo-TEM assessment of the dual-axis tilting range with a trapezoid milled cryo-lamella. a-f) \u003c/strong\u003eCryo-TEM maps were acquired at A- and B-axes and at indicated angles. Ice contamination highlighted by coloured circles was used as fiducial markers to assess lamella electron transparency at different angles. Tilt axis is indicated by an orange dashed line. d) The width of the lamella is indicated by a white double arrow and the yellow dashed square indicates an approximate area that is accessible at ±60° during tilting along the B-axis.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/4fe39e0c3c8e57d0a50e1c7f.png"},{"id":83200800,"identity":"168af6ee-e90c-4cdf-9ea8-c4be15d4abda","added_by":"auto","created_at":"2025-05-21 06:19:27","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":2029064,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSingle-axis versus dual-axis on-lamella cryo-ET. a-c) \u003c/strong\u003eOrthogonal slices of tomograms reconstructed from single-axis tomograms A and B, and of a dual-axis tomogram. Each single-axis tomogram was reconstructed from a tilt series acquired with a total dose 65\u003csup\u003e \u003c/sup\u003ee\u003csup\u003e-\u003c/sup\u003e/Å\u003csup\u003e2\u003c/sup\u003e. \u0026nbsp;Dual-axis tomogram was reconstructed from tilt series A and B, where even frames were removed from each projection to have a final dose of 65\u003csup\u003e \u003c/sup\u003ee\u003csup\u003e-\u003c/sup\u003e/Å\u003csup\u003e2\u003c/sup\u003e. Green and pink lines indicate orthogonal xz and yz slices, which are shown below in green and pink frames. \u003cstrong\u003e(d-f) \u003c/strong\u003eMemBrain segmentations are shown below with orange arrows highlighting differences.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/54cecf1ac320dacb01397a87.png"},{"id":83200799,"identity":"3114351e-3449-4798-aa76-46a2462ef8ef","added_by":"auto","created_at":"2025-05-21 06:19:27","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":727917,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of deep learning restoration algorithm and dual-axis tomography. \u003c/strong\u003eSingle-axis \u003cstrong\u003e(a-c)\u003c/strong\u003e and dual-axis \u003cstrong\u003e(d-f)\u003c/strong\u003e tomograms denoised with cryoCARE \u003cstrong\u003e(a,d)\u003c/strong\u003e, denoised with cryoCARE and missing wedge corrected with IsoNet \u003cstrong\u003e(b,e)\u003c/strong\u003e, or denoised and missing wedge corrected with DeepDeWedge \u003cstrong\u003e(c,f)\u003c/strong\u003e. Missing wedge corrected dual-axis tomograms were corrected before combination in Etomo. Orange arrows indicate missing information, which is completed in the dual-axis tomogram.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/7330840ad85bf98d1159db5b.png"},{"id":83198519,"identity":"eb24b4b2-1871-45f5-8125-ec367046f4a3","added_by":"auto","created_at":"2025-05-21 06:03:27","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":127639,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFinite element simulation of the mechanical response of lamella with orthogonal joints to thermal strain. a-b) \u003c/strong\u003eDisplacement field magnitude \u003cstrong\u003e(a) \u003c/strong\u003eand vector field \u003cstrong\u003e(b)\u003c/strong\u003e of a simulated geometry with right angle joints. \u003cstrong\u003ec)\u003c/strong\u003e Deformed configuration of the lamella after straining, augmented by a factor of 15 for clarity. \u003cstrong\u003ed-f) \u003c/strong\u003eVon Mises stress for slices along the center xz plane \u003cstrong\u003e(d)\u003c/strong\u003eand zy plane \u003cstrong\u003e(e)\u003c/strong\u003e, the latter of which is zoomed in to resolve the field at the lamella \u003cstrong\u003e(f)\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/3925a8ef6525354a8e53d86d.png"},{"id":83200233,"identity":"19dd47d4-d91a-400c-b4b3-12f9e210020c","added_by":"auto","created_at":"2025-05-21 06:11:27","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":96783,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFinite element simulation of the mechanical response of lamella with Y junction joints to thermal strain. a-b) \u003c/strong\u003eDisplacement field magnitude \u003cstrong\u003e(a)\u003c/strong\u003e and vector field \u003cstrong\u003e(b)\u003c/strong\u003e of a simulated geometry with Y-joints. \u003cstrong\u003ec)\u003c/strong\u003e Deformed configuration of the lamella after straining, augmented by a factor of 15 for clarity. \u003cstrong\u003ed-e)\u003c/strong\u003e Von Mises stress for slices through the centre of the lamella along the xz plane \u003cstrong\u003e(d)\u003c/strong\u003e and zy plane \u003cstrong\u003e(e)\u003c/strong\u003e. \u003cstrong\u003ef) \u003c/strong\u003eIsotropic view for the von Mises stress results.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/21c83e5fbbf08bd88b918776.png"},{"id":83198523,"identity":"4490c382-d583-4a44-bc96-cfe0bde68ff0","added_by":"auto","created_at":"2025-05-21 06:03:27","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":120507,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCalculated average stress at the lamella body Y-joint for different stress-release cuts or their absence. a-d) \u003c/strong\u003eVon Mises stress distribution in the lamella region of orthogonally milled cells. \u003cstrong\u003e(a)\u003c/strong\u003e no expansion joints \u003cstrong\u003e(b)\u003c/strong\u003estress-release cuts placed vertically to the lamella \u003cstrong\u003e(c)\u003c/strong\u003e triangular stress release cuts \u003cstrong\u003ed)\u003c/strong\u003e Y-shaped stress-release cuts.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/80e902ba67cf3a9a714d6dfd.png"},{"id":83198520,"identity":"87ed78c3-af10-4185-b909-837c90aa0d65","added_by":"auto","created_at":"2025-05-21 06:03:27","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":114546,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCalculated average stress at lamella body joint for different curvature radii. a-c) \u003c/strong\u003eVon Mises stress distribution zoomed in to the lamella region of orthogonally milled cells with joint curvature radius 0 μm \u003cstrong\u003e(a)\u003c/strong\u003e, 0.32 μm \u003cstrong\u003e(b)\u003c/strong\u003e, and 1.45 μm \u003cstrong\u003e(c)\u003c/strong\u003e. \u003cstrong\u003ed)\u003c/strong\u003e Peak von Mises stress set out against the curvature radius.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/6f4700a2607efc2f356182bb.png"},{"id":83201797,"identity":"8b33d924-8f1a-42c5-a78c-1a90af661bcb","added_by":"auto","created_at":"2025-05-21 06:35:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5258508,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6497420/v1/2a22b8d3-a998-4641-a23b-ce6480c4d182.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On-lamella dual-axis cryo-electron tomography and modelling of lamella stability","fulltext":[{"header":"Introduction","content":"\u003cp\u003eCryogenic focused ion beam (cryo-FIB) milling is the method of choice for producing electron-transparent lamella of vitrified biological samples, which can be studied by cryogenic electron tomography (cryo-ET) [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Cryo-ET consists of a tilt series acquisition with a defined increment of angle range, typically performed in a dose-symmetric fashion along one tilt axis. Because the lamella has a slab geometry, tilting is typically limited to \u0026plusmn;\u0026thinsp;60\u0026deg;, which leads to missing wedge information in Fourier space. Due to this limitation, tomograms have an anisotropic resolution, and features along the Z-axis are elongated [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Several approaches, including deep-learning missing wedge restoration algorithms, have been developed to fill in the missing wedge information in Fourier space [\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. However, these methods have not been evaluated using on-lamella dual-axis cryo-ET. In addition, \u003cem\u003ein silico\u003c/em\u003e restoration of detailed 3D information can be challenging due to the high density and complexity of biological structures in the cell. Dual-axis ET allows to partially complement the missing wedge information and hence can be useful when interpreting complex membranous structures in 3D and improving the accuracy of segmentations [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Cryo-FIB milling approaches currently use rectangular patterns, which lead to a milled lamella attached to perpendicular walls of non-milled remnants of the cell body. The currently used milling geometry enables single-axis tilt series acquisition when the tilt axis is oriented perpendicular to the milling direction. However, it limits or prevents the use of dual-axis tomography, whose application remains to be explored and could augment 3D data quality of cellular material when subtomogram averaging is not applicable. In addition, lamellae produced using rectangular patterns must be loaded onto the microscope stage with an orientation perpendicular to the tilt axis [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. To ensure correct alignment, the AutoGrid rim is marked to indicate the grid orientation during loading into Autoloader systems (Thermo Fisher Scientific), which can be technically challenging.\u003c/p\u003e \u003cp\u003eThe throughput of cryo-FIB milling is steadily increasing due to the increasing use of automation. Several automated software solutions allow coarse milling and the last milling steps to some extent, yielding a final desirable thickness between 150\u0026ndash;200 nm [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. During milling, lamella can undergo undesirable deformation or tilting. This is caused mainly by compression in the supporting film and compression forces released during milling. The supporting film, typically made of thin carbon or silicon dioxide, does not compress as much as gold metal, leading to reduced flatness of the film, so-called crinkling [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Lamella tilting or deformations often limit the final milling step, hence producing thicker lamella or lamella with inhomogeneous thickness. Typically, stress relief cuts (also termed micro-expansion joints) are placed in the cell body to release lateral forces applied perpendicular to the milling direction on the lamella, thereby preventing lamella tilting or deformations [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. However, the physics of lamella geometry as well as stress points of lamella remain to be studied to inform on better milling geometries and to design patterns which would increase lamella stability and therefore throughput.\u003c/p\u003e \u003cp\u003eHere we show that a trapezoid milling pattern enables the performance of dual-axis cryo-ET on lamellae. Dual-axis tomograms have increased 3D information compared to single-axis tomograms, which facilitates automated segmentation and can serve as improved training data for deep-learning missing wedge restoration approaches. Additionally, this study provides insights into physical forces and stress distribution in lamella and makes suggestions for improvement in milling design. We identify the points of fracture onset with the aid of linear elasticity and finite elements simulations, which we mitigate through refining the geometry of the lamella. We show that the point most at risk of fracture is at the connection joint between the lamella and the cell body, and that rounded edges might reduce this risk.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003ePlunge freezing of cells\u003c/h2\u003e \u003cp\u003eVeroE6 cells were seeded onto Quantifoil R1.2/20 200 Au mesh grids in a 35 mm cell culture dish coated with SYLGARD\u0026trade; 184 silicone elastomer. Both grids and dishes were glow-discharged and disinfected with 70% ethanol prior to cell seeding. One day after seeding, grids were removed from the medium and directly transferred to a Leica GP2 plunge freezer set to 80% chamber humidity and 37\u0026deg;C chamber temperature. A 2 \u0026micro;l drop of medium from the cell culture dish was added on the top side of the grid. Grids were blotted for 3.5 seconds and plunge frozen in liquid ethane at -185\u0026deg;C.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eCryo-FIB milling of adherent cells\u003c/h3\u003e\n\u003cp\u003eGrids were clipped into ThermoFisher CryoFIB AutoGrids and loaded into an Aquilos 2 cryo-FIBSEM. Target cells were selected in MAPS. After the eucentricity adjustment, lamellae were coated with organometallic platinum and milled manually using trapezoid milling patterns. Cryo-FIB milling currents were determined by beam-limiting customised 15-hole aperture strip provided by Thermo Fischer Scientific with 3 x 10, 2 x 30, 2 x 50, 100, 300, 500, 1000, 3000, 7000, 15000, 65000 pA. FIB aperture alignments were performed every other week. The following currents were used: 0.5-1 nA (step 1), 300 pA (step 2), 100 pA (step 3), 50 pA (step 4), 30 pA (step 5 (polishing)).\u003c/p\u003e\n\u003ch3\u003eDual-axis cryo-electron tomography on-lamella acquisition\u003c/h3\u003e\n\u003cp\u003eCryo-ET was performed using a Titan Krios Transmission Electron Microscope (TEM, ThermoFisher Scientific) operated at 300 keV and equipped with a BioQuantum\u0026reg; LS energy filter with a slit width of 15 eV and K3 direct electron detector (Gatan) using SerialEM [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Montaged maps were acquired at 8700\u0026times; magnification with pixel size 10.68 \u0026Aring;/pixel and approximate defocus of -80 \u0026micro;m. Dual-axis tomography was performed using a dual-axis stage at the Krios G1 that supports rotation of 90\u0026deg;. A and B single-axis tilt series were acquired at 33,000\u0026times; magnification with a pixel size of 2.671 \u0026Aring;/pixel at -4 \u0026micro;m defocus, with an electron dose of approximately 1.5 e⁻/\u0026Aring;\u0026sup2; per projection. A dose symmetric acquisition scheme was used with an A-axis tilt range of +\u0026thinsp;68\u0026deg; to -52\u0026deg;, start at 8\u0026deg; and B-axis tilt-range\u0026thinsp;+\u0026thinsp;60\u0026deg; to -60\u0026deg;, start at 0\u0026deg; in 3\u0026deg; increments [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Tilt series were acquired in parallel with PACE tomo [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Projection images were acquired as movies and motion correction and summing on-fly using was done using the SerialEM SEMCCD plugin.\u003c/p\u003e\n\u003ch3\u003eDual-axis tomogram reconstruction\u003c/h3\u003e\n\u003cp\u003eTilt series were aligned using patch tracking (680, 680; seven patches in x and five patches in y direction) and reconstruction was performed using a weighted back-projection algorithm with SIRT-like filter 5 in IMOD [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Contrast transfer function correction in 2D and dose-weight filtering was performed in IMOD prior to tomogram reconstruction. Two tomograms were combined in IMOD using overlapping patches (400\u0026times;400\u0026times;200 pixels). Tomograms were binned 3\u0026times; for figure production.\u003c/p\u003e\n\u003ch3\u003eFinite element simulation\u003c/h3\u003e\n\u003cp\u003eThe finite element simulations solve the linear elasticity equilibrium equations with the aid of the open software framework Dolfinx. The vitrified cell is modelled as an isotropic elastic material with a Young's modulus of 8 GPa and a Poisson's ratio of 0.15 [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe cell experiences a thermal hydrostatic strain \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ϵ}_{T}={\\alpha\\:}_{c}\\varDelta\\:TI\\)\u003c/span\u003e\u003c/span\u003e with thermal expansion coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{c}=20\\times\\:{10}^{-6}{K}^{-1}\\)\u003c/span\u003e\u003c/span\u003e and temperature difference \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:T=-200K\\)\u003c/span\u003e\u003c/span\u003e, and \u003cem\u003eI\u003c/em\u003e is the identity matrix. In addition, the bottom surfaces in contact with the substrate have a prescribed displacement of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{u}={\\alpha\\:}_{s}\\varDelta\\:T\\overrightarrow{x}\\)\u003c/span\u003e\u003c/span\u003e, which represents the thermal contraction of the silicon oxide substrate with thermal expansion coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{s}=7.9\\times\\:{10}^{-6}{K}^{-1}\\)\u003c/span\u003e\u003c/span\u003e and undeformed position \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{x}\\)\u003c/span\u003e\u003c/span\u003e. The equations to solve for a displacement field u are thus\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\nabla\\:\\cdot\\:\\left(\\sigma\\:\\left(ϵ\\left(u\\right)\\right)-\\sigma\\:\\left({ϵ}_{T}\\right)\\right)=0$$\u003c/div\u003e\u003c/div\u003e,\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\sigma\\:=\\lambda\\:Tr\\left(ϵ\\right)I+2\\mu\\:ϵ,$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:ϵ=\\frac{1}{2}\\left(\\nabla\\:u+\\nabla\\:{u}^{T}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAfter solving for the displacement field, the von Mises stress is computed as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{vM}=\\sqrt{s}\\)\u003c/span\u003e\u003c/span\u003e, with \u003cem\u003es\u003c/em\u003e being the traceless stress tensor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s=\\sigma\\:-1/3Tr\\left(\\sigma\\:\\right)I\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003ePeak stresses, used for joints of increasing curvature radius, were calculated by first isolating elements at the surface of the joint. After which the average of the 98th percentile was calculated, because taking the highest value would have likely been akin to measuring the error of the simulation.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eGeometry\u003c/h2\u003e \u003cp\u003eThe geometry of the meshes was modelled to closely resemble those of the milled cells, orthogonal and Y junction, using version 4.13.1 of Gmsh. For the orthogonal milling pattern, the two cell bodies were modelled to a convex shape by displacing the outer corners of rectangular prisms. Both bodies were based on a prism with dimensions 9.5\u0026times;30\u0026times;12 \u0026micro;m, with the corners furthest from the lamella displaced inwards by (0,10,0) \u0026micro;m for the lower two and (3,8,-4) \u0026micro;m for the upper two. Both bodies were given an expansion joint 0.5 \u0026micro;m from the lamella of dimensions 0.5\u0026times;30\u0026times;5 \u0026micro;m, with rounded edges of curvature 0.1 \u0026micro;m. We modelled the lamella itself with a rectangular prism of dimensions 12\u0026times;30\u0026times;0.2 \u0026micro;m, attached to the bodies at a height of 6 \u0026micro;m. Whenever rounded joints were used, the surface of the joint was parameterised by a one quarter of a cylinder, with the y axis as its horizontal direction. The radius of the cylinder was varied and the cylinder\u0026rsquo;s centre was set to (r, 0, r) \u0026micro;m from the corner of the joint, to create a tangent line with both the cell body and lamella.\u003c/p\u003e \u003cp\u003eThe Y junction milling pattern was imitated by modelling the cell bodies as irregular prisms, with eight corners set at Cartesian coordinates (16.5, \u0026plusmn;\u0026thinsp;1.5, 0), (9.7, \u0026plusmn;\u0026thinsp;1.5, 0), (6, \u0026plusmn;\u0026thinsp;1.5, 4), and (9.7, \u0026plusmn;\u0026thinsp;1.5, 8) \u0026micro;m for the right body and the left body mirrored in the yz plane. The expansion joints were again of dimensions 0.5\u0026times;30\u0026times;5 \u0026micro;m, with rounded edges of curvature 0.1 \u0026micro;m, and placed at distances (15.4, 0, 1) \u0026micro;m from the edge of the lamella. We modelled the lamella itself as a rectangular prism, with the same dimensions 12\u0026times;30\u0026times;0.2 \u0026micro;m, but attached to the bodies at a height of 4 \u0026micro;m.\u003c/p\u003e \u003cp\u003eThe meshing was conducted at a base resolution of 0.5 \u0026micro;m for the cell body, with a finer resolution field of 0.066 \u0026micro;m around the lamella. A gradual transition between these fields was applied over a distance of 5 \u0026micro;m in all directions. The total number of meshed elements was in the range of 2\u003csup\u003e6\u003c/sup\u003e elements.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eAfter plunge-freezing VeroE6 adherent cells, EM grids were clipped into FIB-Autogrids (Thermo Fischer Scientific) and loaded into Aquilos 2 Cryo-FIB-SEM. Mapping and eucentric position of lamella sites were performed in MAPS. We used polygonal milling patterns available in the XTUI software of Aquilos 2 cryo-FIB-SEM to create a trapezoid pattern and micromachine a lamella shape compatible with dual-axis tomography. Two isosceles trapezoid patterns were placed so that their shorter bases were facing each other (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA). We used a trapezoid geometry as the first milling pattern with an angle of 150\u0026deg;, allowing for \u0026plusmn;\u0026thinsp;60\u0026deg; angle tilting in the direction parallel to the FIB milling. Isosceles trapezoids have two parallel bases (\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e) separated by a height (\u003cem\u003eh\u003c/em\u003e) and two legs with supplementary congruent angles (150\u0026deg; and 30\u0026deg;), resulting in 180\u0026deg; at each side. To achieve a 60\u0026deg; tilt, the angle at the shorter base must be 150\u0026deg;, and the length of \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e can be calculated based on equation:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{b}_{2}={b}_{1}+2\\:h\\:cot\\left(30^\\circ\\:\\right).$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor practical use, \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e should have double the length of \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eh\u003c/em\u003e needs to be approximately 4 \u0026micro;m to obtain an angle of 150\u0026deg; at the lower base. We used a trapezoid pattern with \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;14 \u0026micro;m and \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e approximately 29 \u0026micro;m and h\u0026thinsp;=\u0026thinsp;4.7 \u0026micro;m. In addition, two rectangular patterns were used for stress-release cuts (micro-expansion joints) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The second polygonal pattern had six vertices to reduce the milling area (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB). Subsequent lamella thinning including the last polishing step was performed in 3 steps using rectangular patterns (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC). All milling steps were performed at a grazing angle of 8\u0026ndash;10\u0026deg; and no over-titling was used. SEM was used to monitor each milling step (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFIB-Autogrids were loaded into a cassette such that the cut-off was facing to the right and the loading position was verified using a long-distance stereomicroscope. We used SerialEM to acquire medium magnification maps for each lamella at tilt angles 8\u0026deg;, +\u0026thinsp;68\u0026deg; and \u0026minus;\u0026thinsp;52\u0026deg; at stage rotation angle 0\u0026deg; and tilt angles 0\u0026deg;, +\u0026thinsp;60\u0026deg; and \u0026minus;\u0026thinsp;60\u0026deg;. The nominal rotation between the tilting axes of the two tomograms was approximately 87\u0026deg;. Our data showed that the cell body does not obscure most of the lamella area at extreme angles of both tilt axes, enabling dual-axis tomography (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTilt series were acquired using SerialEM [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] and in parallel mode using PACE tomo [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. A-axis was acquired using a dose-symmetric schema and a starting angle of 8\u0026deg;. Subsequently, the stage was rotated by 90\u0026deg;, and B-axis tilt series were acquired. Tomogram positions for the B-axis were manually selected in the PACE tomo routine. Tomograms were reconstructed and combined in Etomo (IMOD version 5.1.0) [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Using large patches for combining dual-axis tomograms yielded lower errors, consistent with our previous study [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Data and unsupervised segmentations performed in MemBrain [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] clearly showed increased information in the z-direction and improved interpretability of the cellular structures (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe further aimed to compare the data quality between dual-axis tomography and the deep-learning-based missing wedge correction methods IsoNet [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] and DeepDeWedge [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] trained on single-axis data. Our data show that these methods are unable to fully restore features perpendicular to the tilt-axis present in dual-axis data (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Coupling dual-axis tomography with missing wedge correction by correcting the single-axis tomograms before combination in Etomo improved the data quality mostly along the Z-axis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eExploring different milling strategies prompted us to evaluate the structural stability of lamella, which was done with the aid of linear elasticity theory and the finite element method (FEM). The vitrified cell was modelled as a linear elastic material with a Young's modulus of 8 GPa and a Poisson's ratio of 0.15 [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Following standard procedures for material behaviour during temperature changes [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], the sample was subjected to an active strain due to thermal contraction and an additional contractive displacement at the interface with the graphite support film, which contracts less than copper EM grids at a lower temperature (film crinkling) [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The thermal expansion coefficients for cell material and substrate were taken from the literature as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{c}=20\\times\\:{10}^{-6}{K}^{-1}\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{s}=7.9\\times\\:{10}^{-6}{K}^{-1}\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], respectively. Two milling patterns were modelled, one with orthogonal T-junction joints and another with the Y-junction joints. Stress release cuts, which were empirically determined to reduce lamella distortions, were included in both milling patterns.\u003c/p\u003e \u003cp\u003eDetails of the simulation setup may be found in Materials and Methods.\u003c/p\u003e \u003cp\u003eThe simulated undeformed geometry of the orthogonally milled cell, along with the displacement field and the resulting deformed geometry, are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA-C. The displacement results corresponding to the Y-type junction are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eA-C. Both cases yield similar results; a mostly isotropic contraction across the whole body is observed. The displacement field at the lamella is mostly suppressed, given that its norm is 0.001 \u0026micro;m near the centre of the lamella and up to 0.075 \u0026micro;m in the rest of the body. The largest displacements in the lamella are observed in its outermost surface parallel to the xz plane (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA, \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eA, \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eB), where slight buckling is observed in the z direction. The most obvious difference between the junction geometries is the buckling of the joints in the x direction, which is significant in the orthogonal joint (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eC), but notably less noticeable in the Y-joint (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eC). This is due to the fact that there is a larger distance between the lamella and the joints in the case of the Y junction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe quantify the von Mises stress, related to the Frobenius norm of the traceless part of the stress tensor (see Materials and Methods), to identify weak regions in the vitrified cell prone to fracture. The von Mises stresses for the orthogonal T-joints are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eD, \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eE, and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eF, whereas the analogous results for the Y-joints are depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eD and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eE. In the former geometry, a build-up of stress at the elbow of the joint is observed. Such stress concentration is due to the sharp contact angle, which experiences stresses of up to 30 MPa in comparison to 0.1\u0026ndash;15 MPa across most of the remaining body. Similarly, regions above and below the lamella with orthogonal joints show high stress due to the buckling of the joints. In contrast, the Y junction concentrates stress in the lamella itself, ranging between 20 and 37 MPa. Stress in the joints is notably reduced due to the suppression of the buckling. In both geometries high stress is observed at the bottom surfaces, which represent the interface with the substrate. This is a consequence of an idealised geometry with a sharp contact angle; the real contact angle will be rounded, have a larger surface area and thus lower stress.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn addition, various stress release cuts were modelled for trapezoid milling patterns. The results indicate that lamella stress is reduced by using Y-shaped stress release cuts instead of vertically placed rectangular ones (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBecause the elastic equations lead to stress localization at sharp edges, a possible workaround to mitigate the build-up of von Mises stress is to use rounded joints. We explore this alternative by simulating geometries with variable radius of curvature of the joints connecting the lamella to the cell body. Starting with the orthogonal milling pattern, we introduced a curvature ranging up to 1.45 \u0026micro;m and calculated the peak stress. Through the stress distributions in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eA, \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eB, and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eC it is shown that having joints with low radius of curvature drastically lowers stress at the elbow. The calculated stress at the joints has a minimum around a radius of 0.32 \u0026micro;m, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eD, beyond which the increase in material appears to play a larger role.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eCryo-FIB has opened a way to study unperturbed vitrified cellular environments in 3D and molecular resolution. Furthermore, the resolution of protein structure can be improved by subtomogram averaging. Yet, low-abundant proteins, proteins with intrinsically disordered domains, and proteins with small sizes are often difficult to assess by subtomogram averaging. Hence, the interpretation of a cellular crowded environment often relies on direct analysis of the tomograms. Dual-axis cryo-ET contains additional 3D information and provides a tomogram with reduced resolution anisotropy. This facilitates data interpretation, 3D segmentations, and direct visualization of small protein complexes and filamentous structures that can suffer from information loss depending on their orientation to the tilt axis [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eHere, we established a cryo-FIB milling a trapezoid pattern to prepare cryo-lamellae compatible with dual-axis cryo-ET (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This approach additionally removes edges of the cell body, thereby enabling dual-axis tomography (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and facilitating tilting, even when the Autogrid is not perfectly loaded into the cassette (Thermo Fisher Scientific microscopes). With PACE tomo [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], the time required for acquiring single- and dual-axis tilt series is no longer a major limiting factor. Our data demonstrate that dividing the electron dose between two orthogonally oriented tilt series enables alignment via patch tracking, followed by reconstruction of two tomograms. These volumes can then be combined into a dual-axis tomogram. We utilized unsupervised 3D segmentations using MemBrain [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] to demonstrate that dual-axis cryo-ET provides increased information on organelle structure in 3D, outperforming single-axis cryo-ET (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Additionally, we compared the 3D information of dual-axis tomograms with those generated using deep-learning algorithms for missing wedge restoration in Fourier space, such as IsoNet [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] and DeepDeWedge [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Our analysis revealed that deep learning-driven restoration is incomplete and, to some extent, inaccurate (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). To address this limitation, we propose leveraging dual-axis tomograms as a training dataset to improve the prediction accuracy of deep-learning-based missing wedge restoration methods. The main limitation of dual-axis cryo-ET comes from the accumulated electron dose of the second tilt series. We have previously shown that electron dose can be further decreased when the Volta phase plate is used [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], and hence, on-lamella dual-axis cryo-ET will in the future benefit from laser phase plate implementation, which shows promising results [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDespite automation, cryo-FIB lamella preparation remains a major bottleneck of \u003cem\u003ein situ\u003c/em\u003e cryo-ET. Due to lateral pressure which is released during milling lamella can bend or crack. To evaluate the stability of lamellae produced by the rectangular and trapezoid milling patterns, we use theoretical modelling to identify stress points on lamella. The FEM simulations confirmed the protective role of the stress-release cuts against thermal wrinkling for the orthogonal geometry; as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eC, the contraction causes the joints to buckle inwards, which in turn suppresses the in-plane displacement across the lamella at its centre. As a result, the displacement norm across the lamella is almost two orders of magnitude lower compared to that of the rest of the body (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA). In contrast, the lamella experiences its largest in-plane displacements at the outermost surfaces parallel to the xz plane, where no joints are present, and even buckling in the z direction (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eC). Mechanical protection of the lamella against thermal contraction is paramount, given its fragility stemming from its high aspect ratio. Such fragility is confirmed by the von Mises stress distribution (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eD, \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eE and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eF), which exhibits highest values at the elbows of the joints (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eD) due to the thinness of the lamella and the sharp contact angle. Similarly, the buckling of the joints generates further weaker regions above and below the lamella. The region below the lamella is particularly stressed, since it is closer to the substrate that contracts with a different thermal coefficient. We thus identify these regions as the weakest regions that are prone to fracture onset.\u003c/p\u003e \u003cp\u003eNonetheless, the joints appear to be less useful in the case of the Y joint (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e), since the lamella of this geometry experiences a higher von Mises stress than the rest of the body (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eF). This occurs because the joints are farther away from the lamella. Consequently, their displacement is not affected by the presence of the lamella, as evinced by the lack of buckling (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eC), and thus their protective role is reduced compared to the orthogonal case. Hence, the simulation demonstrates that the rectangular hole geometry is not well suited for stress reduction in a Y-type junction However, our data suggests that triangle or Y-shaped stress release cuts are more effective (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe mitigation of stress by variation of curvature radius (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) seems to produce conflicting results: on one hand, Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eD suggests that round joints reduce stress at the joint and predicts an optimal curvature radius for which the maximum von Mises stress at the joint is minimized. Nevertheless, Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eA-C show that the rounding of the joints comes at the expense of an increase in the von Mises stress across the lamella itself: for the smallest radius of curvature (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eA), the lamella experiences stress of up to 14MPa, whereas the lamella with largest radius (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eC) show stress of around 20MPa. We thus reason that no significant protection is offered by rounding the edges. However, the true effect of round edges can only be confirmed experimentally, since the FEM model is highly idealized and does not capture all external factors in the experiment.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe cryo-FIB milling approach presented here enables the production of cryo-lamellae compatible with dual-axis cryo-ET. Dual-axis tomograms of the cellular environment outperform current missing wedge restoration methods applied to single-axis tomograms. As a result, dual-axis tomograms enhance the interpretability and segmentation accuracy of cryo-preserved cellular structures and can serve as ground truth for deep learning\u0026ndash;based missing wedge restoration approaches.\u003c/p\u003e \u003cp\u003eIn addition, the computational model presented here offers a valuable tool for assessing and optimizing lamella shapes produced by novel milling patterns. Exploring different combinations of junction and stress-release cut geometries represents a promising direction for future research.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCryo\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eET\u0026ndash;cryo\u0026ndash;electron tomography\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCryo\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eFIB\u0026ndash;cryo\u0026ndash;focused ion beam\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eFME\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003efinite element method\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eEthics approval and consent to participate\u003c/h2\u003e \u003cp\u003eNot applicable\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication\u003c/strong\u003e \u003cp\u003eNot applicable\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported by research grants from the Chica and Heinz Schaller Foundation (Schaller Research Group Leader Programme) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) to P.C. and U.S.S. (project no. SFB1129/3\u0026ndash;240245660 \u0026ndash;P19 and \u0026ndash; SFB-1638/1\u0026ndash;511488495 \u0026ndash; P03 and Z03). Moreover, this work was also supported by the DFG under Germany\u0026rsquo;s Excellence Strategy - EXC 2082/1-390761711 (the cluster of excellence 3DMM2O). P.C. acknowledges the DFG Heisenberg programme CH 2158/3\u0026thinsp;\u0026minus;\u0026thinsp;1.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eM.W-M. performed data processing and analysis and prepared figures 4-5.; S.G.M. and C.M. performed modeling of lamellae and prepared figures 6-8. L.Z. prepared the samples; P.C. and U.S.S. conceptualized the study. P.C. prepared Figures 1-3, performed cryo-FIB and cryo-ET. P.C. and U.S.S. wrote the manuscript and obtained funding. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eWe thank the Infectious Diseases Imaging Platform (IDIP) at the Center for Integrative Infectious Disease Research Heidelberg and the cryo-EM network at the Heidelberg University (HD-cryoNET) for support and assistance. The authors gratefully acknowledge the data storage service SDS@hd supported by the Ministry of Science, Research, and the Arts Baden-W\u0026uuml;rttemberg (MWK), the German Research Foundation (DFG) through grant INST 35/1314-1 FUGG and INST 35/1503-1 FUGG.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eTomograms will be deposited in EMDB database upon publication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLam V, Villa E: Practical Approaches for Cryo-FIB Milling and Applications for Cellular Cryo-Electron Tomography. \u003cem\u003eMethods Mol Biol\u003c/em\u003e 2021, 2215:49\u0026ndash;82.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMarko M, Hsieh C, Moberlychan W, Mannella CA, Frank J: Focused ion beam milling of vitreous water: prospects for an alternative to cryo-ultramicrotomy of frozen-hydrated biological samples. \u003cem\u003eJ Microsc\u003c/em\u003e 2006, 222(Pt 1):42\u0026ndash;47.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRigort A, Bauerlein FJ, Villa E, Eibauer M, Laugks T, Baumeister W, Plitzko JM: Focused ion beam micromachining of eukaryotic cells for cryoelectron tomography. \u003cem\u003eProc Natl Acad Sci U S A\u003c/em\u003e 2012, 109(12):4449\u0026ndash;4454.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSchaffer M, Engel BD, Laugks T, Mahamid J, Plitzko JM, Baumeister W: Cryo-focused Ion Beam Sample Preparation for Imaging Vitreous Cells by Cryo-electron Tomography. \u003cem\u003eBio Protoc\u003c/em\u003e 2015, 5(17).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKudryashev M: Resolution in Electron Tomography. 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Lifshitz EM, Kosevich AM: Theory of Elasticity, 3rd edn; 1986.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDu DX, Fitzpatrick AWP: Design of an ultrafast pulsed ponderomotive phase plate for cryo-electron tomography. \u003cem\u003eCell Rep Methods\u003c/em\u003e 2023, 3(1):100387.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRemis J, Petrov PN, Zhang JT, Axelrod JJ, Cheng H, Sandhaus S, Mueller H, Glaeser RM: Cryo-EM phase-plate images reveal unexpected levels of apparent specimen damage. \u003cem\u003eJ Struct Biol\u003c/em\u003e 2024, 216(4):108150.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Cryo-focused ion beam milling, cryo-electron tomography, denoising, missing wedge information, von Mises stress, linear elasticity and finite elements simulations","lastPublishedDoi":"10.21203/rs.3.rs-6497420/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6497420/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCryogenic electron tomography (cryo-ET) of cryogenic focused ion beam (cryo-FIB) milled lamellae enables the study of 3D cellular architecture in near-native conditions at nanometer-scale resolution. Cryo-FIB milling is performed iteratively by reducing the FIB current and the distance between rectangular patterns that define the milled area. The resulting cryo-lamellae must remain connected to the cell body, but can fracture during preparation and transfer to a cryo-transmission electron microscope (cryo-TEM), which reduces the throughput. Successful cryo-ET data collection requires loading the EM grid into the cryo-TEM holder with the tilt axis oriented perpendicular to the milling direction. This orientation enables tilting during data acquisition, as the rectangular milling patterns restrict the tilt range and prevent dual-axis tomography. Here, we developed a cryo-FIB trapezoid milling strategy that enables dual-axis cryo-ET. We demonstrate that dual-axis tomograms contain additional 3D information compared to single-axis tomograms and compared to single-axis tomograms after deep learning missing wedge restoration. Hence, dual-axis tomograms offer improved segmentations and provide a valuable training dataset to improve deep learning restoration algorithms. Furthermore, we used a mechanical analysis with finite elements to calculate the build-up of von Mises stresses, commonly used in materials science, to identify fracture points in the lamella and to identify improved lamella designs. This provides a simulation framework to predict and design milling patterns with increased stability.\u003c/p\u003e","manuscriptTitle":"On-lamella dual-axis cryo-electron tomography and modelling of lamella stability","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-21 06:03:22","doi":"10.21203/rs.3.rs-6497420/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"107ab88d-97b4-4145-a8ba-56a29b84550c","owner":[],"postedDate":"May 21st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-06T06:24:39+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-21 06:03:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6497420","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6497420","identity":"rs-6497420","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}