A Bayesian approach to single-particle electron cryo-tomography in RELION-4.0

1In recent years, electron cryo-microscopy (cryo-EM) has allowed the 3D imaging of an increasing number of biological macromolecules at resolutions sufficient for de novo atomic modelling. This development, originally driven by advances in detector technology, was further facilitated by novel, robust image processing algorithms. In single-particle analysis, images of multiple copies of isolated macromolecular complexes, or particles, that are suspended in random orientations in a thin layer of vitreous water are combined in a 3D reconstruction. Nowadays, many aspects of single-particle analysis workflows can be performed with only minimal human supervision, for example, the detection, extraction, and initial classification of particles in the images, 3D reconstruction, as well as refinement of the optical parameters and per-particle tracking of electron beam-induced motion. Many of the algorithms that underlie these modern methods are built on solid statistical foundations that require few tunable parameters. This decreases the need for operator expertise and provides objectivity, as well as robustness, in obtaining optimal structures.

2The single-particle approach is, however, limited to investigating isolated protein complexes that are purified to relative homogeneity. To examine these complexes in their crowded physiological environment, electron cryo-tomography (cryo-ET) may be used instead. In the tomographic approach, the sample is tilted multiple times during image acquisition, yielding a so-called tilt series of images from which a 3D tomogram can be computed. In the same manner as single-particle analysis, repeated occurrences of particles in those tomograms can then be aligned and averaged to obtain higher-resolution reconstructions. This process is referred to as subtomogram averaging. Unlike the field of single-particle analysis, labs use many different tools for subtomogram averaging (e.g.;;;;;;;;; ) and many of the tools used require considerable levels of expertise from the operator, often in order to tune parameters that arise from heuristics in the underlying algorithms. This not only provides a barrier for new scientists entering the field, but can also lead to the calculation of suboptimal structures.

3Compared to single-particle analysis, subtomogram averaging faces several unique challenges. In addition to estimating the position and orientation of each particle, the algorithm also has to consider the geometry of the tilt series. Typically, this is solved through a set of preprocessing steps that include estimation of contrast transfer function (CTF) parameters and alignment of the tilt series, followed by the reconstruction of, often inconveniently large, tomograms for the entire field of view. Smaller subtomograms, centred around selected particles, are then extracted from the tomograms and used in a separate process of subtomogram alignment and averaging. The separation between tomogram reconstruction and subtomogram averaging can lead to an accumulation of errors, because errors in the CTF estimation or tilt-series alignments are hard to correct. In addition, because the sample cannot be rotated 180° within the microscope, the subtomograms contain empty regions in Fourier space, the so-called missing wedge, which are difficult to deal with in subtomogram averaging (e.g. see;;; ).

4A fundamental problem with subtomogram averaging as described above is that it transforms the original 2D image data into 3D subtomograms, which are then used as a substitute for experimental data in the alignment algorithm. RELION-2 introduced the concept of a 3D CTF to describe the transfer of information from the 2D images to the subtomograms, which dealt to some extent with the missing wedge and the loss of information through interpolations in the reconstruction algorithm. A drawback of the 3D CTF approach is that it does not deal correctly with the lower resolution regions of Fourier space, where information from different tilt images overlaps. A statistically more attractive approach would be to formulate the optimisation target function directly as a function of the actual 2D images that are measured in the microscope. This has been proposed in an approach called constrained single-particle cryo-ET, where individually boxed particles from the tilt-series images are processed as in single-particle analysis, but their relative orientations are kept fixed. A similar approach was also implemented in the program emClarity. To deal with unknowns in the relative orientations of the particles from the tilt-series images, as well as their CTFs, the program M recently introduced new optimisation approaches that compare reference projections against the 2D particle images. M relies on RELION for alignment and classification of 3D subtomograms that are recalculated from the optimised parameters in M. Nevertheless, this iterative approach allows subtomogram averaging to resolutions that approach those observed for single-particle analysis, even for particles in complex cellular environments.

5Here, we describe a new approach to subtomogram averaging in RELION-4.0 that optimises a regularised likelihood function that approximates the direct use of the 2D images of the tilt series. In order to do so at acceptable computational and implementation costs, we have altered the main refinement program in RELION-4.0 to work with so-called pseudo-subtomograms: explicitly constructed sets of 3D data arrays that contain sums of CTF pre-multiplied 2D tilt-series images, together with auxiliary arrays that contain the corresponding sum of squared CTFs and how often each 3D voxel has been observed. Pseudo-subtomograms no longer aim to represent the actual scattering potential of the underlying particles, in the way that conventional subtomograms would. Instead, they represent a convenient way to implement an approximation to the 2D approach within the existing RELION code. Evaluation of the pseudo-subtomograms by RELION-4.0 approximates the likelihood of observing a hypothetical particle in the images of the entire tilt series, given the current model. Using that likelihood as a metric, operations equivalent to those in single-particle analysis can now be performed on tomographic data, for example, 3D initial model generation, 3D classification, or high-resolution refinement. In addition, we describe new methods for optimising parameters of the tilt series that exploit the increased signal-to-noise ratio in the average structure. Besides optimisation of the tilt-series alignment itself, we also describe methods analogous to CTF refinement for refining descriptors of the optical properties (defocus, astigmatism, and higher-order aberrations) and a method akin to Bayesian polishing to model beam-induced particle motion throughout the tilt series. Once all these parameters have been optimised, new pseudo-subtomograms can be constructed and the alignment can be repeated. The resulting iterative image processing workflow is similar to existing approaches for single-particle analysis in RELION.

6RELION performs maximum a posteriori estimation to find the set of model parameters that maximise the probability of observing the experimental images. Using Bayes’ theorem, we define a regularised likelihood optimisation target function as

7where expresses prior information about the model, that is, that the reconstructed map has limited power in Fourier space, and is the likelihood of observing the data given the model. A marginalised likelihood function is used, where one integrates over the unknown alignments of each individual particle. For simplicity, these integrals are omitted from the notations used in this article.

8The data model assumes independent Gaussian noise on the Fourier components of the cryo-EM images of individual particles. We therefore write the negative log-likelihood of observing a particle in a hypothetical alignment as a sum over a grid of 2D Fourier pixels:

9where is the Fourier transform of the experimental particle image, its contrast-transfer function, denotes the 2D slice out of the 3D Fourier transform of the known map into the view of the particle, and is the noise variance of the frequency band of given by

10for a 2D vector and a matrix that respectively encapsulate the particle’s position and orientation, and the evaluation of is achieved through linear interpolation.

11In tomography, our aim is to approximate that same likelihood on tilt-series data. The equivalent is a sum over the pixels of the relevant regions of all images from the tilt series:

12We model the shifts and rotations as compositions of per-particle and per-image components:

13where we keep the per-particle rotation component,, identical for all images in the tilt series, and only vary, the rotational alignment of the tilt-series images. In turn, the tilt-series alignment is shared among all particles in a given tilt image. The per-particle part of the translation is modelled as a 3D vector,, that can vary over different tilt images. This contrasts with single-particle analysis, where beam-induced motion of the particle can be corrected for as a preprocessing step, so that each particle is associated with a single 2D translation in a motion-corrected image.

14For our pseudo-subtomogram approach, we now approximate the sum over 2D pixels and tilt images in Equation 4 by a sum over 3D voxels in the pseudo-subtomogram:

15Here, the data term, the weight term, and the multiplicity term are 3D arrays in the Fourier domain. Together, they constitute a pseudo-subtomogram. They are constructed as follows:

16where represents linear interpolation with forward mapping, that is, each 2D Fourier pixel is projected into 3D Fourier space, updating the eight closest voxels.

17Ignoring the difference of pre-multiplying the images with their CTFs, Equation 7 aims to be equivalent of Equation 4. The variance is equivalent to, the power of the noise in the individual Fourier components in the 2D images.

18We then optimise Equation 1 by expectation-maximisation, using Equation 7 to construct the likelihood function and using a prior, based on the expected frequency-dependent power of the signal. This leads to the following iterative algorithm:

19where (n) denotes the iteration; the divisions by and in Equation 11 are evaluated element-wise; and and are calculated by averaging over and, respectively, in hollow spheres of radius and thickness 1, described by. The ratio of the terms containing and in Equation 13 corrects the estimate for the power of the signal from the CTF-corrected map by the average CTF2 to account for the fact that the likelihood in Equation 7 was calculated for CTF pre-multiplied images.

20Many proteins are organised in imperfect 2D arrays inside the tomograms, for example, inside membranes or as part of capsid-like structures. Often, the individual protein molecules inside these arrays exhibit limited rotational freedom with respect to the surface normal of the array, although they may be able to rotate freely around that normal. This knowledge is often exploited in subtomogram averaging approaches through local orientational searches, for example, see. This not only accelerates the refinement, as fewer orientations need to be evaluated, it also makes it possible to solve more challenging structures because fewer solutions are allowed. In RELION, local orientational searches are implemented as Gaussian priors on the Cartesian translations and on the three Euler angles that describe rotations. One advantage of using pseudo-subtomogram alignment is that the coordinate system of the pseudo-subtomograms themselves can be chosen arbitrarily. By default, pseudo-subtomograms are created in the same orientation as the tomogram, but the user can choose to orient them in a more meaningful way. For example, by constructing the pseudo-subtomograms with their -axis parallel to the 2D array, using a rotational prior of approximately 90° on the tilt angle will limit the amount of rocking of the particles inside the array, while avoiding singularities in the definition of the Euler angles that occur when the tilt angle is close to 0°.

21Averaging over multiple particles leads to an increased signal-to-noise ratio in the estimated density map. We also implemented procedures that exploit for subsequent re-estimation of parameters that describe the tilt series. These procedures do not require pseudo-subtomograms, but are performed by comparing projections of the density maps directly with the (Fourier) pixels of 2D boxes that are extracted from the tilt-series images, with a sufficient size to hold the CTF-delocalised signal. The various tilt-series parameters are then estimated by minimising the negative log-likelihood as defined in Equation 4, that is, the sum over noise-weighted square differences between the prediction and the observation.

22The tilt-series properties that can be refined fall into two broad categories: optical and geometrical. The optical refinement concerns the different parameters of the CTF, while the geometrical refinement aims to optimise the alignment of the tilt series, as well as the beam-induced motion of the individual particles. Both sets of algorithms are closely related to the corresponding single-particle algorithms in RELION: optical-aberration refinement and Bayesian polishing, respectively. In spite of the similarity between the algorithms, the models that are optimised differ significantly from single-particle analysis. Details of the implementation of the optical and geometrical refinement algorithms are given in Appendix 1. We also note that Bayesian polishing in SPA describes particle motions between individual movie frames. Although our approach for tomography can also consider movie frames, the current implementation uses the same regularisation of particle motions between movie frames within each tilt image as between the movie frames from other tilt images. Because preliminary tests showed limited benefits in considering the movie frames in this manner, only the functionality to model particle motions between the tilt-series images was exposed on the GUI.

23CTF refinement for tomographic data in RELION-4.0 includes optimisation of scale factors that model frequency-dependent radiation damage, defocus, astigmatism, and higher-order symmetrical and antisymmetrical aberrations. Although individual particles within a field of view are at distinct defoci in the tilt-series images, their relative defoci are known from the geometry of the tilt series and the known 3D positions of the particles in the tomogram. Therefore, one can efficiently perform defocus estimation in a single pass, considering all particles in a tilt-series image simultaneously. In order to do so, we modified procedures that were developed for higher-order aberration estimation in single-particle analysis, where the information from all particles in each tilt-series image is condensed into two images that are used to estimate a common phase shift (see Appendix).

24Similar procedures can also be used to model higher-order symmetrical and antisymmetrical aberrations in the tomographic data. Analogously to our single-particle approach, they are modelled using Zernike polynomials and estimated in the same way. Because the higher-order aberrations are often only a limiting factor at relatively high spatial frequencies, a large number of particles are needed to estimate them reliably. Optimally, higher-order aberrations would thus be estimated globally, over the entire data set, and only for cases that yield high-resolution averages. If aberrations change during data collection, data sets may be split into optics groups, for which aberrations are estimated separately. Typically, the third-order antisymmetrical aberrations are the most important ones, that is, trefoil and axial coma, which can both be caused by a tilted beam. The resolution gains that these optimisations will yield depend on the microscope (mis)alignment. Provided alignment has been performed reasonably well, higher-order aberration correction will probably be most useful for reconstructions that extend beyond 3 Å resolution.

25The geometric alignment includes both (rigid) rotational and translational re-alignment of the tilt-series images, as well as the modelling of beam-induced motion of individual particles throughout the tilt series. For the latter, we neglect rotations of the particles, and only model beam-induced translations. By doing so, we can precompute the likelihood of each particle being in each position around its original one, and then look for an alignment that simultaneously maximises the sum of those likelihoods over all tilt-series images and all particles, as well as a prior that ensures spatially coherent motion. This allows us to evaluate the likelihood of a hypothetical particle position by looking up a single interpolated value in an image. In this formulation, the problem becomes equivalent to the Bayesian polishing approach that we originally developed for single-particle analysis, except for the inclusion of a third spatial dimension for the motion.

26We tested our approach on three test cases. Appendix 2—table 1 provides experimental details for each of the data sets; Appendix 2—table 2 provides details on the image processing.

27We tested the workflow above on the cryo-ET data set that was used to determine the structure of the immature capsid lattice and spacer peptide 1 (CA-SP1) regions of the Gag polyprotein from human immunodeficiency virus 1 (HIV-1) (EMPIAR-10164). We used the same subset of five tomograms that were also used to assess the NovaCTF, emClarity, and Warp programs. Introducing 3D CTF correction, and using the alignment parameters from the original analysis by Schur et al., NovaCTF reported a resolution of 3.9 Å. The Warp program introduced local and global motion correction in the tilt-series images, as well as optimisation of CTF parameters. The combination of Warp and subtomogram alignment and averaging in RELION-3 led to a resolution of 3.8 Å. A recent application of emClarity led to a reconstruction to 3.3 Å resolution.

28We used tilt-series projections after movie frame alignment from the original analysis, without any other preprocessing step, along with the tilt-series alignment data, performed with IMOD package, and CTF parameters estimation using CTFFIND4. We used 12,910 particles from the five tomograms subset, reconstructed an initial reference map using the original published particle alignment, and filtered it to 5 Å. A first alignment in 3D auto-refine, followed by averaging of the initial pseudo-subtomograms, led to a resolution of 3.6 Å. This average was then used for a full cycle of pseudo-subtomogram improvement and realignment. We first applied CTF refinement to optimise the defoci of all particles. This improved the resolution only marginally. Subsequent optimisation of the tilt-series geometry, including modelling local particle motion, improved the resolution to 3.5 Å. Finally, realignment of newly generated pseudo-subtomograms led to a resolution of 3.4 Å. A second cycle of these three steps provided 3.3 Å, while a third cycle converged to 3.2 Å (Figure 1a). Geometrical refinement was performed estimating local particle motion. The consideration of deformations did not show additional improvement. In the first cycle, where improvements in both CTFs and geometry are most obvious, the order of applying those optimisations did not alter the final result for this data set. These data and results are also distributed as part of the subtomogram tutorial in RELION-4.0, as described on https://relion.readthedocs.io/en/release-4.0/. Figure 1—figure supplement 1 shows the improvement in map quality during the iterative refinement process; Figure 1—figure supplement 2 shows a comparison with the 3.3 Å map from emClarity.

29Analysis of the complete data set generated a structure at 3.0 Å resolution (Figure 1—figure supplement 1), which is the same resolution obtained using the M and RELION-3 workflow (; Figure 1—figure supplement 3), and is likely limited by flexibility and asymmetry in the CA hexamer.

30We also applied our approach to thin cellular appendages of C. crescentus bacteria known as stalks, which have previously been imaged using cryo-ET. The cell body and cell stalks of C. crescentus cells are covered by a nearly hexagonal, paracrystalline array known as the surface layer (S-layer). The structure of the S-layer was solved using a combination of X-ray crystallography, cryo-EM single-particle analysis, and subtomogram averaging, revealing how the S-layer is attached to bacterial cells by an abundant glycolipid called lipopolysaccharide (LPS). Previously, cryo-ET of the S-layer, using 110 tilt series collected with a dose-symmetric scheme, yielded 51,866 hexamers of the S-layer. This study used a subtomogram averaging approach that is based on a constrained cross-correlation approach implemented in the AV3 MATLAB suite, and which was specifically optimised for the analysis of macromolecules arranged in a lattice. A 7.4 Å reconstruction of the S-layer was obtained, in which alpha-helices were resolved. This reconstruction was improved by application of NovaCTF, leading to a 4.8 Å reconstruction, in which large amino acid residue side chains were resolved. Moreover, density for an LPS molecule was observed near the putative LPS-binding residues of the S-layer, in agreement with a cryo-EM single-particle structure of an in vitro reconstituted coplex. We used the tilt series after movie frame alignment from the initial analysis, along with the tilt-series alignments performed within IMOD, CTF parameters from CTFFIND4, and the Euler angle assignments and subtomogram coordinates from the original analysis. These parameters were imported into RELION-4.0, followed by multiple cycles of pseudo-subtomogram generation and refinement, analogous to the immature HIV-1 data set described above, leading to a 5.6 Å reconstruction of the S-layer hexamer (Figure 2a). Next, we defined a mask around the central pore of the S-layer, corresponding to the inner domain bound to LPS, to perform focused refinements. Another cycle of pseudo-subtomogram reconstruction, CTF refinement, and refinement within the new mask improved the resolution to 4.4 Å. Accounting for per-particle motions with additional cycles of pseudo-subtomogram improvements and refinements increased the resolution of the central pore to 4.0 Å, and the inner domain of the S-layer to 3.7 Å. Further 3D classification without alignments identified a subset of 42,990 subtomograms that gave a 3.5 Å resolution reconstruction of the inner S-layer.

31The 3.5 Å map is in excellent agreement with the single-particle structure of the in vitro reconstituted complex, including the LPS binding site (; see Figure 2—figure supplement 1). Furthermore, divalent metal ions, known to be tightly bound to the inner S-layer, are resolved (Figure 2b). Surprisingly, at lower isosurface contour levels, we also observed a second LPS binding site (Figure 2c and d). The size and shape of this density agree with the structure of the LPS O-antigen, illustrating how improved subtomogram averaging in RELION-4.0 can help uncover new biology.

32Finally, we applied our approach to the Saccharomyces cerevisiae coat protein complex II (COPII), which mediates the transport of newly synthesised proteins from the endoplasmic reticulum (ER) to the Golgi apparatus as part of the secretory pathway. COPII is formed by five proteins that assemble sequentially on the ER membrane to induce remodelling of the bilayer into coated carriers in a process known as COPII budding, while simultaneously selectively recruiting cargo into these budding membrane carriers. COPII budding can be reconstituted in vitro from purified proteins and artificial membranes, to form small, spherical vesicles, or long, straight tubes. Cryo-ET has previously been used to visualise the architecture of COPII on reconstituted tubules. The coat assembles into two concentric layers; the inner layer forms a pseudo helical lattice, which has previously been solved to 4.6 Å resolution using Dynamo-based subtomogram averaging protocols.

33We used the tilt series after movie alignment from the initial analysis, along with the tilt-series alignments performed in Dyname and CTF parameters from CTFFIND4. COPII-coated tubes were manually traced in the resulting tomograms, and particles were extracted by randomly oversampling their surface, with approximate initial orientations assigned based on the cylindrical geometry. Dynamo was used for initial alignment of 8× binned subtomograms to define the centre of the particles and the directionality of individual tubes. We then imported the particle coordinates for processing in RELION-4.0 using 3D refinement at 4× and 2× binning. Since we expect inner coat subunits to arrange in a lattice, we cleaned the data set by excluding any subtomograms that did not conform to the expected geometrical relationship with their neighbouring particles. A first 3D refinement of the unbinned data set gave a map at 4.4 Å resolution, which was further improved to 4.2 Å and 4.0 Å by tilt-series frame alignment and CTF refinement, respectively. Two further rounds of 3D refinement, followed by tilt-series frame alignment and CTF refinement, yielded a final map with a resolution of 3.8 Å (Figure 3).

34At this resolution, most side chains are visible in the map, enabling us to build and refine an atomic model. The improved model will allow the design of point mutants to precisely disrupt interfaces between coat subunits and test their effects in COPII budding.

35We formulate the problem of averaging over multiple identical particles in tomographic tilt series in an empirical Bayesian framework that is based on a statistical model that approximates one for two-dimensional experimental data. The Bayesian framework has proven effective in reducing the number of tunable parameters and in obtaining high-quality reconstructions from single-particle data. The two-dimensional data model describes the experimental images better than alternative approaches that use 3D reconstructed subtomograms as an intermediate. One example of a problem with the intermediate 3D data model is the need for missing wedge correction, which arises from the observation that the experimental images were acquired, incompletely, in three dimensions. Artefacts related to suboptimal missing wedge correction may affect both alignment and classification of particles. By using an approximation to the 2D data model, missing wedge correction is no longer required. Instead, the problem approaches that of single-particle analysis, where projections from different orientations and of different structural states are sorted out simultaneously. Provided the 3D Fourier transform of the distinct classes is fully sampled through the orientation distribution of the raw particles, likelihood optimisation techniques have been highly successful in tackling this problem in single-particle analysis.

36In practice, the implementation in RELION-4.0 does not use stacks of 2D projection images as input for the refinement program that performs alignment and classification. Instead, the concept of 3D pseudo-subtomograms is introduced, where the tilt-series images are Fourier transformed, pre-multiplied with their CTF, and inserted as a slice into a 3D Fourier volume according to the best current estimates for the tilt-series geometry. The use of 3D pseudo-subtomograms allowed reusing existing code for subtomogram averaging in RELION, while input stacks of 2D images would have required significant software development efforts. Nevertheless, in the future we might still choose to implement a true 2D version of the code, which would be more efficient, both in terms of processing time and disk storage requirements. In cases where the number of tilt images is small in comparison to the box size, fewer Fourier pixels need to be examined in a stack of 2D images than in a pseudo-subtomogram, with a corresponding decrease in processing time. Moreover, the likelihood calculation from the 3D pseudo-subtomogram approach requires separate storage of the accumulated squares of the CTFs, and the corresponding multiplicity terms. In contrast, in the 2D approach, only the 2D images need to be stored, as CTF parameters can be calculated on-the-fly and there is no need for a multiplicity term, giving a corresponding decrease in storage requirements. However, if one were to collect tilt series with very fine angular increments or in a continuous manner, then the current implementation may still be preferable.

37Besides the alignment and classification of individual particles, the methods described here also deal with re-estimation of parameters that describe the optical and geometrical features of the tilt series. As soon as an initial average structure has been obtained, its increased signal-to-noise ratio can be exploited to determine these parameters more accurately than what is possible from the raw tilt-series images alone. The implementations in RELION-4.0 again follow those previously implemented for single-particle analysis, where CTF refinement is used for re-estimation of the tilt-series images CTFs, and algorithms akin to Bayesian polishing are used to re-estimate the tilt-series alignment, as well as the movement of individual particles throughout the tilt-series acquisition process. As better tilt-series parameters will allow better pseudo-subtomograms, particle alignment and classification are iterated with the optimisation of the tilt-series parameters.

38Similar tilt-series and CTF optimisation approaches have been implemented in the program M. Compared to M, RELION-4.0 uses computationally more efficient algorithms; M uses GPUs to accelerate the calculations. In both tomography and SPA, RELION-4.0 only models beam-induced translations of the particles, whereas M also models beam-induced rotations. Since SPA routinely reaches 2 Å resolutions without modelling beam-induced rotations, we assumed that the effect of rotations of individual particles throughout the tilt series is not large enough to warrant their correction at typical tomography resolutions. In cases where the data do allow for better than 2 Å resolutions, M could still be used to correct for beam-induced rotations in a postprocessing step, following alignment and classification of the individual particles in RELION. It is likely that adaptation of M, in order to function with the pseudo-subtomograms proposed here, would lead to increased synergy between the two programs. In the meantime, external tools to convert from M parameters to RELION-4.0 are already available (https://github.com/joton/reliontomotools; copy archived at swh:1:rev:bfa43828876ceb77bed0c7eb72f794c79c9de5e6).

39Besides the reduction in tunable parameters that is characteristic of the Bayesian approach, its uptake by researchers that are new to the field is further facilitated through the implementation of a graphical user interface. This interface is already widely used for single-particle analysis and has been extended for the processing of tomographic data in RELION-4.0. Apart from the calculations that will be familiar to users of single-particle analysis, for example, 3D classification, 3D initial model generation, and 3D auto-refinement, the new interface also provides convenient access to the tomography-specific versions for CTF refinement and Bayesian polishing, as well as preprocessing operations to calculate the pseudo-subtomograms. However, tilt-series alignment, tomogram reconstruction, and particle picking are not yet part of the RELION workflow. Efforts to also implement solutions for those steps in a single tomography processing pipeline are ongoing and will be part of future RELION releases. Meanwhile, current import procedures rely on specific preprocessing operations in IMOD, and particle coordinate conversion tools to use in RELION-4.0 are available for a range of third-party software packages. To further facilitate the uptake of this new software by the community, we have provided an online tutorial that uses the publicly available HIV-1 immature capsid data set to describe and illustrate all steps necessary to obtain the results described in Figure 1.

40In summary, we introduce new methods for subtomogram averaging to resolutions that are sufficient for de novo atomic modelling and increase the accessibility of this emerging technique. We envision that our methods will allow more researchers to calculate better structures from tomographic data, which will aid the next revolution in structural biology, where macromolecular complexes are imaged, not in isolation, but in their biologically relevant environment.