Introduction

Cryo-transmission electron microscopy (cryo-EM) has revolutionized life sciences and pharmaceutical research in academia and industry.

Cryo-EM has been shown to only require a few hours to determine the near-atomic resolution structure of proteins that have been frozen as single particles in a thin aqueous layer. The method generally requires that the proteins are available in sufficient concentration as homogeneous populations, adopt sufficiently stable conformations, and are embedded in random orientations in a thin ice layer without excessive adsorption to the air-water interface.

Cryo-EM analysis of proteins suffers from the low signal-to-noise ratio (SNR) in the images, so that only larger protein particles typically bigger than 50 kDa, or larger details in cryo-electron tomography reconstructions of tissue slices can be analyzed at high resolution. The low SNR stems from the fact that for an electron beam, proteins are weak-phase objects and are highly fragile under the beam. Typically, the electron fluence must be limited to below 20 e–/Å2, if a protein is to be imaged at high resolution. Data can be recorded with slightly higher doses if fractionation of the electron dose is used, and recorded frames are resolution-weighted with dose-dependent frequency filters before averaging, to obtain images with higher differential contrast, i.e., signal-to-noise ratio (SNR)1. Cryo-EM furthermore suffers from particle movements under the electron beam, which can be corrected partly during image processing through motion correction in dose-fractionated “movies“2,3,4. Finally, conventional cryo-EM suffers from the oscillating contrast transfer function (CTF), which is dampened towards higher resolution from the limited spatial and temporal coherence of the beam, the detector modulation transfer function (MTF), and non-corrected specimen movements, among others. Phase plates, such as Volta or laser phase plates5,6 partly improve the CTF for low-resolution components, but so far have not yet shown improvements in final resolution.

An alternative data acquisition scheme is scanning transmission electron microscopy (STEM), which uses a focused electron probe that is scanned across the sample, while electron detectors record the number of electrons scattered to a certain angle covered by the detector pixel(s) as a function of the probe position7. Bright-field (BF) STEM images provide only weak phase contrast8, and dark-field (DF) STEM yields high mass-thickness contrast, yet at low dose efficiency, so that STEM was until recently of limited use in the life sciences. STEM Z-contrast imaging, employing annular detectors covering high scattering angles, is based on Rutherford scattering, where the detector signal is approximately proportional to the square of the atomic number and linear to the number of atoms within the interaction volume. This linearity of the high-angle annular DF (HAADF) STEM signal has been exploited for detecting heavier atoms in proteins by cryo-STEM with an ADF signal9. It has also been exploited for mass measurements of protein particles that had been freeze-dried on ultra-thin carbon film supports10,11. Early attempts of high-resolution low-dose aberration-corrected HAADF STEM imaging showed only amplitude contrast and was found unsuitable for life sciences imaging12. However, cryo-STEM tomography, combining BF and DF STEM with sample tilt series to compute a 3D reconstruction of the vitrified specimen13, has shown promising results for thicker biological specimens up to 1 µm diameter. More recently, integrated differential phase contrast (iDPC) STEM was applied to cryo-EM specimens, reaching 3.5 Å resolution for protein 3D reconstructions from data recorded with a quadrant-detector7,14.

Beyond monolithic or segmented detectors, the use of pixelated detectors in STEM allows recording a 2D image of the diffracted probe for each 2D probe position, enabling advanced analysis in this so-called 4D-STEM method15. For example, electron dose-efficient recovery of the specimen’s scattering phase can be achieved by ptychographic processing of the recorded diffraction patterns16. For materials sciences specimens, this method has recently established resolution records in the picometer range17,18. Besides the inverse multi-slice schemes used in that work, which consider multiple scattering events during reconstruction but require comparably high electron doses, several other algorithms exist that employ the single-scattering projection assumption. The latter include direct methods, such as single-sideband ptychography19,20 or Wigner distribution deconvolution21,22 for 4D-STEM datasets recorded with a focused probe, or parallax reconstructions from tilt-corrected BF STEM data23,24,25,26 recorded with a defocused probe, to provide phase information with real-time capabilities. Alternatively, iterative methods, such as the computationally more demanding proximal gradient algorithms such as difference map calculations27, ePIE28, or ptychography reconstructions29,30 can be applied.

4D-STEM with an aberration-free electron beam that is focused onto the specimen typically scans the sample with a narrow Airy disk profile, limited to only a short vertical extension, depending on the convergence semi-angle (CSA) used to form the probe7. 4D-STEM can also be performed with a strongly defocused electron probe (Fig. 1), so that the convergent electron beam illuminates the specimen with a disk large enough to expose an entire typical single-particle protein in the vitrified cryo-EM specimen as one single scattering experiment. This probe can then be scanned across the specimen surface at a step size in the nm range, so that diffraction patterns are recorded from probe positions that share significant overlap in the (x,y) sample plane. This overlap enables phasing of the recorded data for structure reconstruction, and it eliminates the twin-image problem or mirrored reconstructions.

Fig. 1: Experimental setup of 4D-STEM.
figure 1

a A vitrified life sciences sample is illuminated with a convergent electron beam. Electrons are recorded using a pixelated detector. The convergence semi angle (CSA) is in the range of a few mrad. The beam is focused to a plane above or below sample with a defocus in the micrometer range. Figure created in Blender52, using PDB 8J5A as apoferritin model. b An example ptychographic reconstruction of apoferritin. Scale bar: 50 nm. c The sum of three 4D-STEM diffraction patterns. A typical diffraction pattern shows most of the electrons in the bright field (BF) disk of the radius corresponding to the CSA of 6.1 mrad, and some electrons are scattered to higher angles to the dark field (DF) region.

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4D-STEM has recently gained significant momentum from the availability of ultrafast pixelated electron detectors. Extending 4D-STEM to study beam-sensitive biological cryo-EM specimens, however, faces several experimental and computational hurdles. For low-dose experiments, scan strategies must be optimized for most efficient handling of specimen motion and specimen charging. Data processing workflows have to be established that can deal with the very low signal-to-noise ratio in the low-dose datasets and with the enormous quantity of recorded data, reaching terabytes in size for one sample. Nevertheless, significant progress in life sciences 4D-STEM has recently been demonstrated by the application of 4D-STEM ptychography to frozen-hydrated viruses16,31 and virus-like particles32.

Here, we perform low-dose 4D-STEM studies with a defocused beam and ptychographic data processing of frozen-hydrated single particle protein samples (Fig. 1) and show that structures of proteins at sub-nm resolution can be achieved. We implement cryo-electron ptychography with an aberration corrected cryo-EM instrument and fast hybrid pixel detector, and we discuss the current state of automated data collection and data processing.

Results

Ptychography of cryo-EM samples

Ptychographic data were recorded with an aberration-corrected, convergent electron beam as “probe” that was focused below the sample.

However, ptychography reconstructs both the complex-valued sample exit wave and the complex-valued electron probe function including its aberrations. As such, aberration correction is not strictly a requirement for the work presented here since CSAs of only 4–6 mrad and larger defocus values around 2 μm were used.

For the 4 mrad CSA and 2 µm defocus, the probe corresponded to a beam diameter on the sample of ~16 nm. A beam dwell time of 250 µs and a STEM step size of 2 nm, corresponding to 84% beam overlap for two adjacent circular probes, were used. Using a fluence of ~0.5 e−/Å2 per probe position, an average total electron fluence of ~35 e−/Å2 was applied to the sample during one scan of 128 × 128 positions. The low electron dose and parameters used in our experiments meant that on average less than 20% of the detector pixels received an electron for one probe position, making the recorded diffraction patterns very noisy.

A dataset of gold nanoparticles on a carbon film was collected before beginning experiments to calibrate rotation angles and CSA, and a diffraction pattern with the specimen removed from the beam path was recorded to serve as estimation for the probe-forming aperture in the iterative reconstruction algorithm. Data collection was then performed with a setup as shown in Fig. 2. The software SerialEM33 was used to control the Titan Krios instrument, take real-space TEM images of the grid, and compile a table of X,Y coordinates, indicating the specimen locations that have ice holes with suitable ice thickness and a high particle density. After this, the instrument was switched to STEM mode with a convergent beam, and a custom Python script was used for automated 4D-STEM data collection. Data collection was performed at approximately 144 specimen locations per hour, each comprising a 128 × 128 position 4D-STEM scan, and resulted in approximately 310 GB of raw data per hour before compression.

Fig. 2: The ptychography data collection workflow.
figure 2

A python client running on the SerialEM Server controls the electron microscope via the SerialEM software, and coordinates the TVIPS USG scan generator, the Dectris ELA camera recording, and the multi-GPU processing of recorded diffraction patterns. Computers: gray. Software: white. Microscope: dark gray. Reconstructed images: white. Dotted line: The parallax reconstruction is used to provide on-the-fly feedback about the data collection and serve as aberration estimate.

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Data collection was monitored in real-time by computing a parallax (or tilt-corrected BF-STEM) reconstruction with the py4DSTEM software34. This enabled fast, yet reliable, phase reconstructions to guide acquisition, and provided the probe estimate necessary for the more computationally-intensive ptychographic reconstructions. Higher-resolution ptychography reconstructions of the scattering potentials were calculated offline with py4DSTEM on a 4-GPU computer, obtaining up to 70 ptychographic reconstructions per hour.

Structural analysis of proteins

The cryo-electron ptychography pipeline was applied to apoferritin (ApoF) protein, the phi92 bacteriophage, the tobacco mosaic virus (TMV), and 2D crystals of bacteriorhodopsin (BR). To document the outstanding quality of the ApoF protein and its suitability for high-resolution data collection, apoferritin was also imaged by conventional TEM (CTEM), before being studied using the 4D-STEM pipeline.

Conventional Cryo-EM imaging of Apoferritin

This spherical apoferritin particle is a protein complex of approximately 12 nm diameter with a particle weight of 485 kDa. Its octahedral 24-fold symmetry and unusually robust structural integrity make it the ideal test specimen for high-resolution assays35,36. Conventional TEM (CTEM), using dose-fractionated cryo-EM on a Titan Krios G4 equipped with a 300 kV cold-FEG electron source and a Falcon4i direct electron detector was used to record 9846 dose-fractionated real-space images, from which 1'899'133 ApoF particles were automatically selected and analyzed with the software cryoSPARC37, resulting in a 3D map from 411'705 particles at a resolution of 1.09 Å (Supplementary Figs. 2 and 3). Data showed a ResLog B-factor of 24.5 Å2, indicating that the ApoF sample and the obtained cryo-EM grid preparations were of outstanding quality and not limiting resolution for a structural analysis (Supplementary Table 1).

The same protein sample was also used for dose-fractionated real-space cryo-EM imaging on a different Titan Krios G4, which also was equipped with a 300 kV cold-FEG and a Falcon4i detector, but in addition was equipped with a Cs probe corrector above the sample. From 450 dose-fractionated real-space images, 37,592 particles were automatically selected and analyzed with cryoSPARC, resulting in a 3D map from 22,504 particles at a resolution of 1.49 Å (Supplementary Figs. 4). Data showed a Guinier plot B-factor of 24.1 Å2 (Supplementary Table 1).

Cryo-electron ptychography of Apoferritin, Phi92 bacteriophage, and TMV

4D-STEM was then used on the same ApoF grid as before with the Cs probe corrected Titan Krios, recording data with a CSA of 4 mrad. Online parallax reconstructions computed during data collection provided instant feedback on the quality of the data collection. Offline computed higher-resolution reconstructions were done by ptychography computation of the sample scattering potentials, which are obtained when assuming an amplitude function of unity and computing the resulting image only based on the reconstructed phase information24. Obtained 2D potential images were subjected to automated particle picking, resulting in 13’655 particles. Particle classification, alignment and 3D reconstruction using cryoSPARC37 resulted in a 3D map of the protein from 11’552 particles at a resolution of 5.8 Å (Fig. 3a, Supplementary Figs. 5 and 8, and Supplementary Table 1).

Fig. 3: Cryo-electron ptychography reconstructions of proteins.
figure 3

a Apoferritin. b Bacteriophage Phi92 tail protein. c Tobacco mosaic virus (TMV). From left to right: Ptychographic image reconstruction (Scale bars are 30 nm); The same image Fourier transformed, showing circular amplitude oscillations (Scale bars are 0.5 nm−1); The 3D reconstruction of the protein; A cross-section of the 3D reconstruction for a and a bottom view of the 3D reconstructions for b and c.

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4D-STEM was also used to study the Phi92 bacteriophage, using a CSA of 5.1 mrad. Data processing, using helical reconstruction for the bacteriophage’s sheath was conducted using cryoSPARC, while the capsid reconstruction was performed using RELION38,39, resulting in a reconstruction of the Phi92 sheath from 1600 particles at 8.4 Å resolution, and of the Phi92 capsid from 182 particles at 12.1 Å resolution (Fig. 3b, Supplementary Figs. 6 and 8, and Supplementary Table 1).

4D STEM was also applied to study the tobacco mosaic virus (TMV), using a CSA of 6.1 mrad. Processing of the ptychography potential maps with RELION resulted in a reconstruction from 2120 particles at 6.4 Å resolution (Fig. 3c, Supplementary Figs. 7 and 8, and Supplementary Table 1).

Cryo-electron ptychography of bacteriorhodopsin 2D crystals

4D-STEM was also applied to study the projection map of glucose-embedded bacteriorhodopsin (BR) 2D crystals. These single-layer phospholipid membrane protein 2D crystals have a lateral size of roughly 500 nm and a thickness of roughly 6 nm40. The crystals contain BR trimers that are embedded in the membrane in a P3-symmetric hexagonal lattice of 6.3 nm lattice spacing (120° included angle). A 4D-STEM dataset was recorded from 256 × 256 positions at 4 mrad CSA with a total dose of 19 e−/Å2. Parallax and a ptychography reconstructions were computed from this one dataset, which both showed crystal diffraction spots in their Fourier transforms (Supplementary Fig. 9).

Crystallographic processing with the FOCUS software41 allowed the reconstruction of the projection maps at around 6 Å resolution from the parallax and the ptychography reconstructions. The parallax map required a correction of the oscillating CTF by Wiener filtration, while the ptychography map allowed reconstruction of the correct projection map without any CTF correction.

The intensity of the diffraction spots above background, and the intensity of the background intensity in the vicinity of the diffraction spots was evaluated in FOCUS, showing a faster decay (i.e., stronger negative B factor) of intensities for the parallax reconstruction than for the ptychography reconstruction (Supplementary Fig. 9, and Supplementary Table 1).

Discussion

Semi-automated 4D-STEM was implemented as a cryo-electron ptychography pipeline and applied to several biological test specimens. For reconstructing micrographs from recorded datasets, the single-slice ptychography reconstruction implemented in the py4DSTEM software was used. This algorithm refines the estimate for the Probe and the Object from the measured intensities in the recorded diffraction patterns as amplitude constraints in Fourier space, and by exploiting the knowledge about the position overlap in real space. The Probe and Object are iteratively refined, using a stochastic gradient descent algorithm. In the initiation of the projection algorithm, an empirically determined hyper-parameter tuning is also integrated, which improves convergence24.

For CTEM imaging, the contrast transfer function (CTF) of the instrument is well characterized and its correction provides access to the highest resolution, including correction of higher-order aberrations39. Leidl et al. (2023) recently demonstrated that for thicker biological specimens, multiple electron scattering needs to be taken into account if structural data significantly beyond 1.2 Å resolution were to be recovered42.

For 4D-STEM, the CTF of the method is dependent on the reconstruction algorithm as well as acquisition parameters used.

For ptychography reconstructions, we reconstructed 2D potential maps for the sample. This was done with the iterative ptychography algorithm implemented in py4DSTEM by setting the amplitudes in each iteration to “1”, so that all specimen signal was directed towards the phase map. The computed Fourier transformations of such “potential maps” show for 4D-STEM datasets recorded with a defocus of 2 µm the presence of ring like amplitude oscillations (Fig. 3). The width of the rings is wider (with more narrow dark gaps) when data closer to focus are recorded (Supplementary Fig. 9). From these ptychography potential maps, a correctly phased reconstruction can be obtained without CTF correction16,30,43.

In contrast, for parallax reconstructions, Thon-ring amplitude oscillations are present (Supplementary Fig. 9), which require CTF correction including phase flipping to give access to correct structural data (Supplementary Fig. 10).

Electron ptychography has established resolution records for materials sciences specimens, while the algorithms for signal reconstruction and our understanding of the mechanism of contrast formation are still under active development. For life sciences samples, cryo-electron ptychography promises to also give access to the highest resolution and contrast. The absence of an oscillating or zero-crossing CTF in ptychography is highly attractive for tomography data collection, where the reconstruction of unique features from single datasets is of interest. Significant technical challenges remain that should be addressed to further improve the resolution of the method. These include the implementation of dose fractionation during data collection, which further reduces the signal-to-noise ratio of the collected diffraction pattern; reconstructed sub-frames should then be resolution-weighted and averaged, as commonly done in real-space cryo-EM1,2. Further required optimizations concern the level of scan precision (noise in the scan coordinates), data collection speed (camera speed and data transfer speed), post-processing algorithms under the very low dose constraints for life sciences specimens, and the extension to tomographic 3D reconstructions in combination with multi-slice algorithms24,44.

The frozen hydrated preparations of the proteins apoferritin, phi92 phage, and TMV studied here by 4D-STEM and ptychography resulted in 3D reconstructions at sub-nm resolutions from small datasets. Nevertheless, this resolution is still worse than what is achievable by conventional cryo-EM from similarly sized datasets (Supplementary Fig. 4). Resolution improvements in life sciences 4D-STEM are expected from collecting data with a larger CSA. This, however, causes a lower tolerance for sample height variations when collecting large datasets, making data collection and data processing more challenging. The CSA of 4–6 mrad was chosen here as a compromise. We also applied 4D-STEM without correcting for the resolution-limiting effects of specimen beam damage or beam-induced particle motion, and we did not correct for the CTF of the ptychography method. Even if the ptychography CTF does not show contrast reversals, correction of its varying amplitude would still be required to fulfill the assumptions of equal noise contributions across all resolution ranges for the maximum likelihood processing underlying the cryoSPARC and RELION software packages. Dose fractionation and dose-dependent frequency weighting, combined with correction for particle movement, and a CTF correction that normalizes the noise profile, would all increase the resolution performance of the 4D-STEM ptychography method.

The strong SNR of cryo-electron ptychography evident in the reconstructed images, the trustworthiness of the projections obtained from the purely positive CTF, and the potential of multislice reconstructions to produce a volumetric reconstruction with modest depth resolution, suggests that 4D-STEM combined with cryo-electron ptychography tomography bears great potential for 3D reconstructions of biological tissue samples. Combined with tilting, the out-of-plane information in multi-slice ptychography results in an improved Crowther Criterion measure, scaling with the number of “super-slices” used45. For cellular samples, where the uniqueness of the sample does not allow the averaging of signal from multiple particles, and where thicker slices of the sample are often of interest, the high SNR of cryo-electron ptychography is especially promising to gain insight into the structural arrangement of smaller structures in cells and tissue.

Methods

Protein expression and purification

For apoferritin, the plasmid encoding the mouse heavy chain apoferritin was graciously donated by Masahide Kikkawa46. The plasmid was transformed into E. coli BL21 (DE3) cells. A saturated overnight culture was inoculated into 500 mL LB media containing Kanamycin, and grown at 37 °C and induced with 1 mM IPTG for 3 hours after reaching an OD600 of 0.6. The pellet was harvested at 5000 × g and resuspended in 20 mL Buffer A (300 mM NaCl, 20 mM HEPES 7.5, 10 mM EDTA), lysed by sonication and then centrifuged for 30 minutes at 20,000 × g at 4 °C. The supernatant was collected and heated at 70 °C for 10 min in a 50 mL tube on a heatblock until milky. The supernatant was mixed by inversion and heated for 5 more minutes. The mixture was centrifuged for 30 min at 20,000 × g at 4 °C. The supernatant (~20 mL) was precipitated with 6.65 g of ammonium sulfate, stirring at 4 °C for 10 min. This corresponds to ~50–55% ammonium sulfate saturation at 20 °C. The mixture was centrifuged for 30 minutes at 20,000 × g at 4 °C. The pellet was then resuspended in 2 mL of Buffer A and dialyzed with a 12–14 kDa membrane in 2 L of Buffer A but containing only 2 mM EDTA. The sample was further purified by size exclusion chromatography and loaded directly onto a Superose 6 10/300 GL column with a mobile phase of 150 mM NaCl, 10 mM HEPES 7.5. Peak fractions that corresponded to 24-mer-sized apoferritin were pooled and reinjected for a second round of size exclusion chromatography. Peak fractions were concentrated to 8 mg/mL, using a 100 kDa concentrator and frozen at −80 °C.

The bacteriophage Phi92 sample, initially obtained by Petr Leiman (Texas University Medical Branch, TX, USA), was a kind gift from Davide Demurtas (EPFL, Lausanne, Switzerland).

The tobacco mosaic virus (TMV) sample, initially obtained by Ruben Diaz-Avalos (La Jolla Institute for Immunology, CA, USA), was a kind gift from Philippe Ringler (University of Basel, Switzerland).

The bacteriorhodopsin (BR) 2D crystal sample was a kind gift from Richard Henderson (MRC, Cambridge, UK).

Real-space cryo-EM data collection and processing of a large ApoF dataset

3 µL aliquots of the apoferritin at 8 mg/ml were applied onto Ultrafoil gold 1.2/1.3 grids, and plunge frozen in liquid ethane with a Leica EM GP2 plunger (4 °C, 100% rel. humidity, 30 s waiting time, 3 s blotting time).

For conventional (real-space) cryo-EM, data were collected in automated manner using EPU v.3.0 on a cold-FEG fringe-free Thermo Fisher Scientific (TFS) Titan Krios G4 TEM, operating at 300 kV with aberration-free image shift (AFIS), and recording data with a Falcon 4i (TFS) electron counting direct detection camera in electron counting mode. The data were collected at a nominal magnification of 250 kx (pixel size is 0.3 Å at the specimen level) and a total dose of 40 (e−/Å2) for each exposure. The data from the 1.5 s exposures were stored as electron event recording (EER) files. The data from 3 × 3 neighboring ice holes in the carbon films were collected using beam and/or image shifting, while compensating for the additional coma aberration (AFIS). The data were collected with the nominal defocus range of −0.3 to −0.9 µm. With an average throughput of 922 images per hour, a total number of 9846 movies were collected within one 12-h session.

In total, 9846 movies were imported into cryoSPARC v4.4.1 (eer_upsamp_factor=2, eer_num_fractions=80). Upsampled EER movies were drift-corrected and dose-weighted with Patch Motion Correction (res_max_align=4, output_fcrop_factor=1/2), and the contrast transfer function (CTF) was estimated with Patch CTF Estimation (amp_contrast=0.07, res_max_align=3, df_search_min=1000, df_search_max=20000).

After rejection of bad images based on CTF Fit resolution (2–5 Å) and Relative Ice Thickness (1–1.2) parameters, 8609 images were used for further processing. Initial particle picking was performed on a subset of 50 images with Blob Picker, using ring blobs of 110–120 Å diameters, NCC score of 0.3, Power Score of 261–712, and a minimum relative separation distance (diameter) of 0.5. Picked particles were extracted with a box size of 720 pixels, Fourier cropped to 120 pixels (binning 6 × 6 times) and subjected to the streaming reference-free 2D classification.

Two best 2D class averages were selected as templates for the Template Picker, using a particle diameter of 126 Å and an angular sampling of 10 degrees. In total, 1,899,133 particles were picked. Picked particles were inspected with Inspect Particle Picks, and the best 1,104,665 particles were extracted with a box size of 720 pixels, Fourier cropped to 120 pixels, and subjected to the 3 rounds of reference-free 2D classification and Heterogeneous Refinement. A small subset of the 5005 particles was used for the ab-initio structure building with 3 classes.

The best 544,845 particles were re-extracted with a box size of 800 pixels and further refined with Homogeneous Refinement to the resolution of 1.21 Å (B-factor = 23 Å2). Custom parameters of Homogeneous Refinement included the application of octahedral (O) symmetry, per-particle defocus optimization using a Defocus Search Range of 4000 Å, per-group CTF parameter optimization with fitting the beam tilt, beam trefoil, spherical aberration, anisotropic magnification, and correction for the curvature of the Ewald sphere.

Refined particles were split into 9 optical groups with Exposure Group Utilities using Action “split”. Grouped particles were further refined with Homogeneous Refinement to the resolution of 1.15 Å (B-factor = 19 Å2). Custom parameters of Homogeneous Refinement include application of octahedral (O) symmetry, an initial low-pass filter of 15 Å, a dynamic mask threshold of 0.3, a dynamic mask near value of 4 and far value of 8, defocus refinement, global CTF refinement, and correction for the curvature of the Ewald sphere.

Refined particles were used as an input to Local Motion correction using a maximum alignment resolution of 2 Å and a B-factor of 20 Å2 during alignment. Overlapping particles were removed with a minimum separation distance of 120 Å. The remaining 411,705 particles were subjected to Reference Based Motion Correction with default settings and further refined with Homogeneous Refinement (defocus refinement, global CTF refinement, and correction for the curvature of the Ewald sphere) to the resolution of 1.09 Å (B-factor = 18 Å2). A ResLog B-factor analysis was performed in CryoSPARC, which reported a ResLog B-factor of 24.3 Å2 (Supplementary Table 1).

An atomic model for apoferritin was re-built manually from the previously deposited model (PDB ID 8J5A) with COOT v0.9.647, and iterated with rounds of refinement with Servalcat48 and Molprobity v4.5.249. After each round of refinement, side-chains were manually inspected and adjusted in COOT with Molprobity.

Real-space cryo-EM data collection and processing on a probe corrected instrument

To compare with the 4D-STEM Data, ApoF were collected with the same instrument as used for 4D-STEM work. This is a Thermo-Fisher Scientific (TFS) Titan Krios G4, operated at 300 kV, and equipped with a Cs probe corrector (Probe Cs = 0 mm). Real-space TEM images were recorded with a Falcon 4i (TFS) direct detection camera in electron counting mode at a nominal magnification of 250 kx (pixel size is 0.3153 Å at the specimen level) with a defocus range of −0.3 to −0.8 µm. Each exposure had a total dose of 28 (e−/Å2) and was stored as an electron event representation (EER) file.

A total of 1319 EER files were acquired and imported into cryoSPARC v4.4.1 for processing. Without any up-sampling, raw EER recordings were dose-fractionated into 32 frames (with 0.875 e−/Å2 per frame) and drift-corrected. After preprocessing and contrast transfer function (CTF) estimation, a total of 913 micrographs were selected based on CTF-cutoff value 3.4 Å and ice filtering. A further subset of 450 micrographs were randomly selected to pick roughly 37,592 particles that are comparable to the low-dose ptycho-dataset of ApoF (38,425 particles). After initial 2D classification, 40% of the particles were excluded and the remaining 22,504 particles were re-extracted and re-centered to undergo ab-initio and homogeneous refinement in cryoSPARC. Further correction of defocus, global CTF refinement and Ewald sphere curvature correction yielded a map with the FSC 0.143 at 1.70 Å. To increase the quality and resolution of the reconstruction, per-particle local drift correction was performed based on the reference map. Homogeneous refinement of these reference-based motion corrected particles improved the resolution of ApoF to 1.49 Å (B-factor = 24.1 Å2).

4D-STEM data collection

Ptychographic data were recorded with the same probe-corrected TFS Titan Krios G4 as above, equipped with a cold FEG electron source operated at 300 kV, TVIPS Universal Scan Generator (USG), Falcon 4i camera (TFS), and a Dectris ELA hybrid pixel detector. The microscope was operated in STEM mode with a CSA of 4–6 mrad and a defocus of ~2 µm, resulting for the 4 mrad CSA in a beam diameter on the sample of ~16 nm. Data were collected with a beam dwell time of 250 µs, and a STEM step size of 2 nm, corresponding to 84% beam overlap for two adjacent circular probes. Using a fluence of ~0.5 e−/Å2 per probe position, an average total electron fluence of ~35 e−/Å2 was applied to the sample during one scan. To avoid the physical gaps between the segments of the ELA detector, data were recorded on only one of the detector segments of 256 × 256 pixels. The STEM camera length was set so that the edge of that 256 × 256 px square was at 6.58 mrad. The low dose regime and parameters used in our experiments resulted in less than 20% of the detector pixels, on average, recording an electron at all. Dose fractionation, not employed here, could have been implemented by repeatedly scanning the same specimen location several times with an even lower dose, which would have further reduced the dose per pattern.

To improve convergence of the ptychographic reconstruction, especially under low-dose conditions, we optimized the alignment of the STEM probe before data acquisition, using the Probe Corrector S-CORR software by TFS on a standard gold cross-grating sample. Optimization of the aberrations up to twice the CSA that was later used for data collection, here to a semi-angle of 8 mrad, took approximately 10 min. We then collected a calibration dataset before beginning experiments to aid the optimization in the py4DSTEM software. Finally, a vacuum image of the probe was recorded in diffraction space to serve as an estimate for the probe-forming aperture in the iterative reconstruction algorithm.

For data collection, the software SerialEM33 was used to control the Titan Krios instrument and record a grid atlas at low magnification in image mode. Suitable grid squares on that atlas were manually selected, and for each of these, SerialEM was used still in conventional TEM mode with parallel illumination, to record grid square maps. These maps were then used to semi-automatically compile a table of X,Y coordinates, indicating the specimen locations where ice holes had suitable ice thickness and a high particle density. After this, the instrument was switched to STEM mode with a convergent beam, and a home-built Python script was used for automated 4D-STEM data collection, performing the following steps:

  1. 1.

    Controlling the microscope via SerialEM commands to position the instrument specimen stage.

  2. 2.

    Preparing the ELA detector for capturing frames.

  3. 3.

    Activating the TVIPS scan generator for acquisition.

  4. 4.

    Compressing and saving the recorded diffraction patterns for further analysis.

Data collection was performed at approx. 144 specimen locations per hour and resulted in approx. 310 GB of raw data per hour before compression. Data collection could be further accelerated by recording larger ptychography scans at each stage position, and by further accelerating the camera recording and data storage speeds, which all would have increased the amount of data recorded.

Data analysis: parallax and ptychographic reconstructions

Each of the acquired 4D-STEM datasets were analyzed using the py4DSTEM software34 using the following steps:

Preprocessing

  • Data loading and flat-field correction: Electron diffraction patterns from one scan in h5 format were loaded, flat-field normalized, and hot/dead pixel corrected by replacing values of identified non-functional pixels with median values computed from their neighbors. Scan metadata such as scan step size were stored separately.

  • Extraction of key parameters: Following normalization, the mean diffraction pattern was computed to identify the pixels inside the brightfield disk. The diameter of this disk was subsequently used for reciprocal space pixel size calibration and in the parallax reconstruction algorithm.

Parallax reconstruction

  • Cross-correlation of virtual brightfield images: Each pixel inside the brightfield disk was used to form a virtual brightfield (VBF) image corresponding to a tilted planewave illumination. The VBF images were iteratively aligned (starting with a large bin value to boost signal) using cross-correlation to obtain a vector field.

  • Aberration-fitting using aligned vector field: The obtained cross-correlation vector field – which is proportional to the gradient of the aberration surface – was used to fit low-order aberrations across the field of view, notably defocus and the relative rotation between real and reciprocal-space coordinate systems.

  • Phase-flipping CTF correction: The estimated low-order aberrations were then used to correct the aligned brightfield image by phase-flipping negative portions of the CTF. Note that the steps listed up to here for a parallax reconstruction24 are computationally inexpensive. The CTF-corrected aligned brightfield image was used to monitor the acquisition in “real-time”.

Ptychographic reconstruction

  • Object and probe preprocessing: The scattering potential was initially assumed to be empty, and the probe was initialized using an aperture obtained by the mean of a 4D-STEM measurement over vacuum and the estimated aberration surface from the parallax reconstruction.

  • Single-slice reconstruction: The object and probe were jointly reconstructed using a batched stochastic gradient descent algorithm. The error was monitored using the L2 norm of the difference between the measured diffraction intensities and those modeled using the “single-slice approximation” model. Convergence was typically achieved within 30 iterations, i.e., 30 passes through the batched diffraction patterns, the order of which was randomized between passes to accelerate convergence.

  • Object and probe constraints: The scattering potential was assumed to be a pure-phase object, i.e., its amplitude was fixed to unity during the iteration. The probe aperture (i.e., its Fourier amplitude) was replaced by the vacuum measurement mean at each iteration, while the aberration surface was fitted to a low-order Zernike-like expansion up to radial and angular order 3, to ensure smoothness and remove residuals24.

  • Potential map postprocessing: The reconstructed micrograph was cropped if necessary and saved for subsequent analysis. See Supplementary Fig. 10 to compare different ptychography data models.

The workload was distributed across four GPUs, each processing a single dataset. This parallel approach allowed the processing of 70 datasets per hour with a 4-GPU computer.

4D-STEM ptychography structure determination of proteins

For apoferritin, ninety cryo-electron ptychography datasets (i.e., 4D-STEM scans) were acquired using SerialEM. A grid atlas was initially acquired using the Falcon4i camera, from which suitable grid squares were manually identified to compile grid square maps and identify suitable acquisition locations. The ice thickness at these locations was estimated to be thin, as they only showed single layers of clearly contrasted ApoF particles. At these locations, automated ptychography scans with a CSA of 4 mrad were started, using an average total electron fluence of ~35 e−/Å2 per scan.

Ptychography reconstructions of the sample potential maps, which are obtained when assuming an amplitude function of unity and computing the resulting image only based on the reconstructed phase information, were obtained at a pixel size of 1.5 Å/px. These potential maps were imported as MRC image files into cryoSPARC37. Micrographs were subjected to automated particle picking, resulting in 38,425 particles (Supplementary Fig. 4). 2D classification identified 10 classes. The class averages were used as templates to refine the automated particle picking, resulting in 13,665 particles. After another 2D classification and selection of the best classes, a total of 11,552 particles were used for ab-initio 3D structure determination. No further correction for any remaining contrast transfer function was applied.

The resulting 3D map was analyzed by gsFSC with the 0.143 cutoff criterion, showing a final resolution of 5.8 Å of the map (Fig. 3a, and Supplementary Figs. 5 and 8, and Supplementary Table 1).

For the Phi92 bacteriophage, eighty-three 4D-STEM datasets were acquired using the same methodology as before, but at a CSA of 5.1 mrad. The micrographs were recorded at a total electron dose of approximately 49 e-/Ų. The pixel size of the final micrographs was 1.44 Å/px.

The 2D ptychographic micrographs obtained were imported as MRC image files into both cryoSPARC37 and RELION38,39 for subsequent analysis. The helical reconstruction process of the bacteriophage’s sheath was conducted using cryoSPARC, while the capsid reconstruction was performed using RELION.

Initial manual particle picking of the bacteriophage sheath in cryoSPARC yielded 2420 particles. Following 2D classification and selection of the best classes, 1600 particles were utilized for ab-initio 3D reconstruction. The helical parameters employed in this process included a helical rise of 35.30 Å and a twist of 26.3 degrees. The final processing stage involved non-uniform refinement (NU-Refine) with a Z fraction set at 50%, resulting in an 8.4 Å resolution map of the Phi92 sheath.

Concurrently, manual particle picking of the capsid in RELION resulted in the identification of 356 particles. After a similar 2D classification process, 182 particles were selected for the final 3D reconstruction. This approach yielded a 12.1 Å resolution map of the Phi92 capsid (Fig. 3b, Supplementary Figs. 6 and 8, and Supplementary Table 1).

For the tobacco mosaic virus (TMV), forty-three 4D-STEM datasets were acquired, following the same protocol as before, but with a CSA of 6.1 mrad. The datasets were acquired at a total dose of approximately 32 e−/Ų per micrograph, and with a pixel size of 1.15 Å/px.

These 2D ptychographic micrographs were imported as MRC image files into the RELION software. The initial phase of manual particle picking of TMV in RELION resulted in 3400 particles. Subsequent 2D classification and the selective process for the best classes reduced the number to 2120 particles, which were then used for the ab-initio 3D reconstruction. Using helical parameters for the processing of a helical rise of 1.38 Å and a twist of 22.036 degrees resulted in a 6.4 Å resolution map of the TMV (Fig. 3c, Supplementary Figs. 7 and 8, and Supplementary Table 1).

For the bacteriorhodopsin (BR) 2D crystals, one single 4D-STEM dataset was acquired, following the same protocol as before, but with a CSA of 4.0 mrad. The dataset was acquired at a total dose of approximately 19 e-/Ų per micrograph, and with a pixel size of 0.98 Å/px.

The 2D parallax reconstruction (without prior CTF correction) and the 2D ptychographic reconstruction were imported as MRC image files into the FOCUS software41. The entire processing and evaluation was performed automatically in FOCUS. For the parallax reconstruction, the programs gCTF or CTFFIND3 were used to determine the defocus of 1.098 µm. For the ptychography reconstruction, no CTF was determined. The crystal lattice and crystal spots were automatically detected. The crystal lattice was computationally straightened by warping (unbending) the real-space image to yield sharper diffraction spots. Amplitudes above background, as well as phases for each spot, and the background amplitudes around each spot were measured. These were used for generation of a projection map. The amplitudes and background values were plotted against the resolution of the spots in Excel (Supplementary Fig. 9, and Supplementary Table 1).

ResLog B-factor estimation

The information content of the recorded data from conventional TEM and 4D-STEM ptychography imaging was evaluated by calculation of the FSC0.143 and the Guinier-plot amplitude falloff B-factor. In addition, the Reconstruction “ResLog” B-factor35,50 was calculated for the real-space datasets. With the latter, the number “#” of particles required to reach a resolution of “d” Angstrom, can be calculated as:

$${{\rm{\#}}}=\bigg(\frac{1}{{N}_{{asym}}}\bigg)\cdot \bigg[{\bigg(\frac{\langle{s}\rangle}{\langle{n}\rangle}\bigg)}^{2}\cdot \, \frac{{30}{\pi }}{{N}_{e}\cdot {\sigma }_{e}\cdot d}\bigg] \cdot {e}^{\frac{B}{{2}\cdot {d}^{2}}}$$
(1)

with \({N}_{{asym}}\) being the number of asymmetric units in the particles, \(\frac{\langle S\rangle }{\langle N\rangle }\) being the signal-to-noise ratio of the electrons in the recorded data, \({\sigma }_{e}=0.004 \, {{\text{\AA}}}^{2}\) being the elastic cross-section of carbon, \({N}_{e}\) being the used electron dose, \(d\) being the real-space resolution in Å, and \(B\) being the ResLog B-factor in \({{\text{\AA }}}^{2}\).

This can be simplified to:

$${{\rm{\#}}}={const}\cdot {e}^{\frac{B}{2\cdot {d}^{2}}}$$
(2)

The ResLog B-factor in Å2 can be calculated, based on the relation:

$${ln}({{\#}})=B\cdot \frac{1}{2\cdot {d}^{2}}+{offset},\, {{\rm{with}}}\, {{offset}}={ln}({const}).$$
(3)

When computing the resolution \(d\) of a reconstruction with smaller subsets of \(\#\) number of particles and plotting \({\mathrm{ln}}(\#)\) as a function of \(\frac{1}{2\cdot {d}^{2}}\), the ResLog B-factor becomes apparent as the slope of a line fitted through the experimental data points (Supplementary Fig. 8).

The computed FSC0.143, Guinier-plot B-factors, and ResLog B-factor are given in Supplementary Table 1.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.