High-resolution cryo-EM reconstructions in the presence of ... · 42 In a typical cryo-EM SPR...

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High-resolution cryo-EM reconstructions in the presence of 1

substantial aberrations 2

Raquel Bromberga, Yirui Guoa,b, Dominika Boreka,*, Zbyszek Otwinowskia,* 3

a Department of Biophysics, The University of Texas Southwestern Medical Center, Dallas, 4 Texas 75390, USA 5

b Current Address: Ligo Analytics, Dallas, TX 75206, USA 6

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1corresponding authors 9

Dominika Borek 10 Department of Biophysics 11 The University of Texas Southwestern Medical Center 12 Dallas, Texas 75390, USA 13 Phone: (214)645-9577 14 Fax: (214)645-6353 15 Email: [email protected] 16 17 Zbyszek Otwinowski 18 Department of Biophysics 19 The University of Texas Southwestern Medical Center 20 Dallas, Texas 75390, USA 21 Phone: (214)645-6385 22 Fax: (214)645-6353 23 Email: [email protected] 24

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Keywords: cryo-EM, axial aberrations, coma, trefoil, resolution, validation 26 27

.CC-BY-NC 4.0 International licensecertified by peer review) is the author/funder. It is made available under aThe copyright holder for this preprint (which was notthis version posted October 8, 2019. . https://doi.org/10.1101/798280doi: bioRxiv preprint

https://doi.org/10.1101/798280

http://creativecommons.org/licenses/by-nc/4.0/

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The beam-image shift method accelerates data acquisition in cryo-EM single particle 28

reconstruction (cryo-EM SPR) by fast repositioning of the imaging area, but at the cost of more 29

severe and complex optical aberrations. 30

We analyze here how uncorrected anti-symmetric aberrations, such as coma and trefoil, affect 31

cryo-EM SPR results, and then infer an analytical formula quantifying information loss due to their 32

presence that explains why Fourier-shell coefficient (FSC)-based statistics may report 33

significantly overestimated resolution if these aberrations are not fully corrected. We validate our 34

analysis with reference-based aberration refinement for two cryo-EM SPR datasets acquired with 35

a 200 kV microscope in the presence of coma exceeding 40 µm, and obtained 2.3 and 2.7 Å 36

reconstructions for 144 and 173 kDa particles, respectively. 37

Our results provide a description of an efficient approach for assessing information loss in cryo-38

EM SPR data acquired in the presence of higher-order aberrations and address inconsistent 39

guidelines regarding the level of aberrations acceptable in cryo-EM SPR experiments. 40


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Introduction 41

In a typical cryo-EM SPR experiment, some aberrations such as defocus are introduced 42

intentionally while others such as spherical aberration are unavoidable for a given setup (1-3). 43

The significance of the remaining aberrations is evaluated on a case-by-case basis (4, 5). 44

In the analysis of aberrations in cryo-EM SPR, where in one image we record only a small part of 45

the focal plane, we can use an isoplanatic approximation in which aberrations are represented by 46

convolutions, and in Fourier space they depend only on the angle of the scattered electrons. In 47

phase contrast illumination mode, used in cryo-EM SPR, axial aberrations can be divided into two 48

distinct categories depending on the symmetry properties of the image phase shift as a function 49

of a scattering vector. If the phase shift is centrosymmetric, then aberrations will result in 50

modulations of the image power spectrum. If the phase shift is antisymmetric, the power spectrum 51

will not be modulated because aberrations will not affect the amplitude of the image but only its 52

phase. The lowest order of antisymmetric phase shift is a translation, which due to the lack of an 53

absolute coordinate system, can be set to zero. Antisymmetric aberrations of the next, third order 54

are called axial coma and trefoil and these are important for cryo-EM SPR data quality in practice 55

(4-6). Alignment procedures used in cryo-EM SPR minimize coma and trefoil indirectly, for 56

instance by analyzing changes in the image power spectrum due to interactions between beam 57

tilt and spherical aberration (5). The success of this approach and similar ones requires co-58

alignment of the optical axes for multiple lenses, and if the alignment procedures are not properly 59

executed, coma and trefoil may be present and affect the quality of the SPR results, and yet 60

manifest only in specialized analyses (5-8). Furthermore, these and additional, higher-order, 61

antisymmetric aberrations are induced when data are acquired with the beam-image shift method 62

(6-8), in which coordinated electronic shifts of an illuminating beam and an image are used to 63

navigate away from the optical axis. We restrict our discussion here to axial aberrations, but with 64


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the understanding that these aberrations will have different values in different positions of an 65

optical system for data acquired with the beam-image shift method. 66

The acceleration in cryo-EM data acquisition enabled by the beam-image shift method (6-9) has 67

resulted in discussions of the best experimental strategies for data collection, approaches to 68

compensate for or to correct for optical aberrations, and methods to assess modulation and the 69

loss of signal due to the presence of uncorrected optical aberrations (4, 6, 10, 11). Axial coma 70

can be corrected by applying compensating beam tilt during data collection; however, beam tilting 71

does not correct other aberrations (4), and thus the extent to which one can apply beam-image 72

shift without compromising data quality remains open. 73

We found that large values of axial aberrations can be precisely estimated and accurately 74

corrected for, leading to large, case-specific improvements of SPR results. We provide formula 75

for assessing how the levels of uncorrected coma and trefoil affect the resolution of SPR and 76

discuss their impact on the validation statistics. 77

78

Results 79

CTF determination by power spectrum analysis is an inherent part of high-resolution cryo-EM 80

SPR and provides estimates of the magnitude of symmetric aberrations (2). However, phase shift 81

does not modulate the power spectrum, so determination of antisymmetric aberrations has to be 82

performed by other methods (4). 83

In our analysis of antisymmetric aberrations, we utilize an associative property of pure phase shift 84

that also holds when it is combined with image translation (12). Thus, corrections for the presence 85

of antisymmetric aberrations can be split into separate steps and applied in any order, without 86

loss of accuracy in retrieving information. Consequently, for both large and small magnitudes of 87

antisymmetric aberrations, their impact is defined only by the difference between their true and 88


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their assumed or refined values. If their estimates are inaccurate, the difference generates a 89

component of the image phase shift that, after averaging over multiple particles, produces the 90

signal modulation that we analyze here. 91

Antisymmetric aberration is a convolution with signal so in the frequency domain the convolution 92

is represented as the multiplication of a signal and Fourier representation of an aberration. The 93

impact of aberrations on 3D cryo-EM SPR has been theoretically analyzed by considering how 94

images are affected (5, 13). However, cryo-EM SPR relies on averaging multiple particles to 95

increase the SNR. Thus, we investigated how an aberration’s impact will propagate to averaged 96

representations of particles. 97

To this end, we assume a large number of particles which are randomly oriented on a grid with 98

respect to rotation around the beam axis but with potential preferred orientation dependence on 99

the other two Eulerian angles. Averaging all such particles removes the dependence of the 100

average signal on the angle of the aberration in the microscope frame (6). Therefore, the final 101

consequence of an aberration is the resolution-dependent modulation of signal amplitude (6). For 102

each unique projection that is conceptually equivalent to a 2D class average, we can define an 103

angle of particle orientation in the microscope and the difference ∆ between and the 104

characteristic direction of a particular antisymmetric aberration (Fig. S1). Single particles have no 105

force aligning them with this angle, so we can assume that their distribution is uniform with respect 106

to this angle. We then express the maximum phase shift for a particular aberration and 107

resolution, which for coma and trefoil, is: 108

, 2 , (1) 109

where represents resolution and represents electron wavelength. The first index of the 110

aberration coefficients identifies the power dependence on resolution and the other defines 111

angular periodicity in the microscope frame of the phase shift, and so for coma 1 and for 112


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trefoil 3 (14). Coma can also be derived from interactions between beam tilt and spherical 113

aberrations : , 3 so ,3 . This representation may be convenient when one is 114

interested in expressing coma with respect to beam tilt rather than coma values. 115

In weak phase approximation, third order aberrations can be expressed using terms resulting 116

from the Taylor expansion of a wave front: 2 3,1 ∆ 3,1 3,3 3∆ 3,3 . To obtain a modulation 117

term for the signal at a given resolution, we average the wave front over the angular distribution 118

of all possible particles, with the result being the Bessel function of order zero (Fig. 1): 119

, ∆ , ∆ , , (2) 120

To our knowledge, this analytical result has not been noticed before in assessing aberrations 121

despite having highly important consequences for their analysis. As discussed in detail later, the 122

foremost consequence is that the structure factors of the reconstruction may become 123

anticorrelated from the reality in some resolution shells, an effect which can be missed in 124

standard, FSC-based half-maps assessment of resolution (15-17), implying much higher 125

resolution than that achieved. 126

We expect that data acquired with the beam-image shift method will be affected by more than 127

one type of axial aberration. In such a case, aberrations that have the same angular dependence 128

order (second index) but different radial order (first index) will be strongly correlated (5) and these 129

correlations have to be considered when values of aberrations are refined. If in refinement, the 130

data were to have uniform information content across resolutions, the refinement will be 131

orthogonalized by Zernike polynomials with corresponding to the limiting resolution (18). For 132

coma, the corresponding Zernike polynomial is with the first term representing coma and 133

the second representing translation. Consequently, at the resolution limit, two-thirds of the coma-134

produced phase shifts will be compensated for by image translation in refinement. This translation 135

can be executed on the whole image or at the level of particles by shifting their positions in the 136


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image by the same value, with such an effect not being noticeable in a typical refinement. 137

However, the compensation factor is reduced from the value of two-thirds because the signal is 138

much stronger at low resolution than at the resolution limit. We determined for analyzed high-139

resolution cryo-EM SPR datasets (Table 1) that translation produced only about a two-fifths 140

compensating contribution, reducing the maximum value of the coma-induced phase shift by a 141

factor of ~0.6. The compensation due to resolution dependence explains some of the 142

discrepancies in the literature discussing the acceptable limits of coma. For instance, one 143

proposed limit was a phase shift in the direction of coma distortion, and without translational 144

compensation (4, 5). Using our formula (Eq. 2), we found that this will preserve 0.6 ∙ ~0.94 145

of the original signal, a reduction in the SNR that is barely significant, and so the limit is too 146

conservative as it was postulated by Cheng et al. (6). In Cheng et al.’s analysis, the impact of 147

coma was derived from FSC curves calculated from numerical experiments, where a particular 148

value of beam tilt (and corresponding coma) were assumed. FSC-based resolution analysis in 149

the presence of uniform large coma can be misleading because the J0 function oscillates (Fig. 1). 150

When the signal modulation term defined by J0 (Eq. 2) is negative, both halves of the split data 151

are affected, and so the correlation coefficient between halves is positive even if the resulting 152

reconstruction has a negative correlation with the truth. If the coma causes very strong modulation 153

in the FSC (11), then it is easy to recognize the correct resolution limit corresponding to the first 154

zero of the Bessel function J0 (Eq. 1, 2). However, oscillations in the FSC curve may be 155

pronounced or smoothed to different degrees (Fig. 2), even when data sets with very similar 156

values of coma (Table 2) were analyzed. The method that we employed from cisTEM (19) uses 157

only a smooth spherical mask to calculate FSC curves, and so the oscillations could not have 158

come from a molecular mask effect (20). Thus, in the absence of pronounced oscillations, the 159

resolution limit may be significantly overestimated compared to the consideration based on the 160


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first zero of the Bessel function. Consequently, simulation-based procedures relying solely on 161

FSC (6) may grossly underestimate the significance of coma. 162

We tested our approach for two small proteins with particle size 144 kDa and 173 kDa (Fig. 2, 163

Table 1), and we obtained reconstructions of 2.32 Å and 2.70 Å, respectively, in the presence of 164

very high coma, with data acquired with Talos Arctica 200 kV, K2 Gatan camera. An objective 165

aperture, an energy filter, and a phase plate were not used, and numbers of micrographs and 166

particles in data analysis were moderate (Table 1). To our knowledge, these are the highest 167

resolution reconstructions obtained with a 200 kV instrument for particles having molecular mass 168

below 200 kDa and the first high resolution reconstruction for a molecule with mass below 150 169

kDa. We have not found any detrimental effects for correcting coma, even in cases where the 170

generated phase shift is very large, on the order of 10×2(7.2 mrad). We reprocessed data from 171

EMPIAR for 200 kV instruments, applying the same aberration estimation approach to data for 172

the larger molecules of the proteasome (700 kDa, EMPIAR 10185 and 10186) (10) and -173

galactosidase (430 kDa, EMPIAR 10204) (Table 1) (21). We refined coma and trefoil 174

independently on each micrograph. We noticed that coma can fluctuate far above refinement 175

uncertainty and we attribute this observation to differences in the stability of the beam tilt direction 176

between micrographs. In addition, coma refinement has a strong correlation with overall image 177

shift, affecting the accuracy of coma determination. We found that trefoil on the other hand was 178

remarkably stable and has no significant correlation with other parameters of refinement, so 179

variations in its refined value can be used as a good indicator of statistical uncertainty for third 180

order aberrations (Fig. 3). 181

The problem generated by the presence of large coma was analyzed in a recent publication (11) 182

which described the refinement of EMPIAR 10263, dataset III, with coma refinement performed 183

by Relion 3.0 (13) and JSPR (11, 22), with results presented in Fig. 6B in (11). We reprocessed 184

this dataset and obtained a much tighter clustering of coma values, similar to the clustering 185


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observed for our datasets. Relion 3.0 (13) seriously underestimated coma by a factor of ~4 186

compared to our estimate and the average of the JSPR individual refinements per micrograph 187

had a value that was underestimated by twenty-five percent compared to our values. However, 188

we used a similar target function in our refinement procedure to JSPR (11, 22) and Relion 3.0 189

(13), and so the different outcomes are most probably due to differing refinement schemes (11). 190

The results presented in Fig. 6B from reference (11) are consistent with the behavior of our 191

procedure when compared to the results from our first cycle. 192

We observed that only the presence of a large fraction of incorrect particles or particles with 193

grossly incorrect orientation in a micrograph would bias the coma refinement toward the starting 194

point. When starting with coma refined by the previous cycle, re-refining the particle orientation 195

attenuated the bias in the next cycle, so even the presence of a moderate number of bad particles 196

did not affect the convergence of the procedure. We achieved additional improvement, in terms 197

of resolution and spread of coma values, when we changed the null hypothesis regarding coma 198

from a value of zero to the average of the refined coma values. This more appropriate null 199

hypothesis was applied by taking advantage of the associative properties of coma, which allowed 200

us to apply coma phase shift correction to the images; therefore, all the steps in the final round of 201

the data analysis, starting from particle picking, were performed on images corrected by the 202

average value of coma. Subsequent coma refinement, representing a difference from the previous 203

average used in image correction, was still performed independently for all micrographs, but the 204

residual bias resulting from the initial coma value being zero was eradicated. Coma or beam tilt 205

refinement has to use the same type of reference-based target function irrespective of 206

implementation. We would expect that small corrections would be equally well-characterized by 207

all programs. However, local refinements and restraints may have different convergence ranges 208

depending on the implementation, and this is mostly likely the explanation for the differences in 209

results between programs. 210


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Uncorrected aberrations create systematic patterns of phase shift and if such aberration error is 211

constant across a dataset, then the reconstruction will also be altered in a systematic way, not 212

only by losing amplitude but also by flipping its sign at some resolutions. In this case, the FSC 213

curve may undergo oscillations, with the first minimum being the effective resolution limit of the 214

result. Oscillations in the FSC curve are recognized as a qualitative sign of problems with the 215

quality of cryo-EM SPR results (20). We provide here (Eq. 2) an explanation for another possible 216

source of these oscillations. In our glucose isomerase (GI) data acquired with 58 m coma, 217

corresponding to 7.2 mrad beam tilt, before correcting coma we observed four oscillations in the 218

FSC curve resulting from phase shift (Fig. 2) with the map interpretability being inconsistent with 219

the FSC-based resolution indicator. Therefore, if FSC oscillations are encountered, refining coma 220

is highly recommended to diagnose the problem, with the potential outcome being substantial 221

reconstruction improvement by correcting the aberration. 222

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Discussion 224

Although instruments may be aligned quite accurately before data collection, our analyses and 225

those of others (4, 6, 10, 11) indicate that coma can vary significantly between images and the 226

extent of the variation is dataset dependent. For this reason, we recommend refinement of not 227

only overall coma but also coma for individual images. Trefoil typically is not important, but for 228

one pair of EMPIAR datasets (EMPIAR 10185 and EMPIAR 10186) and also our datasets (not 229

shown), it was highly significant. However, even in these cases, only the overall value of trefoil 230

for the dataset was important, with an insignificant level of variations between individual images. 231

Correction for antisymmetric aberrations can be performed during reconstruction (11, 13), but the 232

consequence of the associative property is that it can just as well be performed at the whole 233

micrograph level before reconstruction commences. In the presence of large coma, correcting 234

coma at the image level reduces the point spread function of the imaging system so it may 235


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improve particle masking operations. If the value of these aberrations is known from external 236

calibration, then the image-based correction may simplify applying these corrections to the data 237

without modifying downstream analysis programs. 238

What affects cryo-EM SPRs is the error in the aberration model used and not the magnitude of 239

the aberrations themselves, at least up to the theoretical limit where the image of a point source 240

(e.g. coma) extends outside of the detector. Therefore, it is important to calibrate all aberrations 241

and not only the ones that affect the power spectrum. This can be accomplished prior to data 242

collection or a posteriori by reference-based refinement using the structure being solved. Once 243

appropriate coma calibrations and corrections are used, this means that the procedures where 244

the beam is intentionally tilted can be used on a larger scale. This can provide limited but 245

additional three-dimensional particle information on top of the projection image without any time 246

and precision penalties associated with mechanical rotations. 247

248

Materials and methods 249

Protein expression, purification, and grid preparation: Glucose isomerase (GI), also called 250

xylose isomerase, from Streptomyces rubiginosus was purchased from Hampton Research (23). 251

Protein slurry was dialyzed three times against excess of dH2O and concentrated to ~40 mg/ml 252

with Amicon filter. 253

HemQ protein was one of the structural genomics targets (MCSG APC35880). We have solved 254

its X-ray crystallographic structure (PDB code: 1T0T.pdb) and recently others determined its 255

function (24). Expression and purification of GYMC52_3505 plasmid encoding HemQ in pMCSG7 256

vector with Tobacco Etch Virus (TEV) cleavable N-terminal His6-tag (25) followed previously 257

established protocol (26). After purification and tag cleaving, the protein was extensively dialyzed 258

against 20 mM HEPES pH 7.5 and used at ~28 mg/ml concentration for grid preparation. The 259

plasmid GYMC52-3505 is available from the DNAS Plasmid Repository (https://dnasu.org). 260


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Cryo-EM grids for both proteins were prepared with FEI Vitrobot Mark IV. In each case, 3 µl of 261

protein solution were applied to the grid at 4 °C, 100% humidity followed by 6 s blotting with blot 262

force 20 before grids were plunged into liquid ethane cooled with liquid nitrogen (Fig S2). 263

264

Data acquisition and analysis: The cryo-EM dataset for GI was collected with a 200 kV Talos 265

Arctica microscope equipped with a K2 Gatan camera, with a physical pixel size of 0.91 Å. The 266

phase plate was not used and the objective aperture was not inserted. A total of 202 movies with 267

an exposure time of 100 s/movie were collected. Each movie contains 200 frames with an 268

exposure time of 0.5 s/frame and an electron dose of 140 e/Å2 per movie (Table 1). 269

Both HemQ-57K and HemQ-45K were also collected in the same alignment conditions on a 200 270

kV Talos Arctica microscope with a K2 Gatan camera run in super-resolution mode, with a 271

physical pixel of 0.72 Å for HemQ-57K and 0.91 Å for HemQ-45K. For HemQ-57K, 268 movies 272

were collected with an exposure time of 40 s/movie. Each movie contains 100 frames with an 273

exposure time of 0.4 s/frame and an electron dose of 90 e/Å2 per movie. For HemQ-45K, 257 274

movies were collected with an exposure time of 40 s/movie. Each movie contains 100 frames with 275

an exposure time of 0.4 s/frame and an electron dose of 90 e/Å2 per movie. 276

Complete datasets for EMPIAR deposits 10204, 10185 and 10186 were processed as examples 277

of datasets collected at 200 kV. EMPIAR 10185 and EMPIAR 10186 were collected consecutively 278

on the same instrument with EMPIAR 10185 collected with a traditional setup by moving only the 279

stage, and EMPIAR 10186 collected with the beam-image shift method. We performed image-280

specific correction for coma in both datasets, producing a material improvement in resolution 281

(Table 2). EMPIAR 10263, dataset III, served as an example of a dataset collected at 300 kV with 282

a large coma value that was partially corrected by alternative methods. 283

We processed all datasets with cisTEM (19). We modified the cisTEM pipeline by adding 284

reference-based refinement of aberrations, including coma and trefoil, following the same design 285


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as implemented in Relion 3.0 (11, 13). As discussed in the Results and Discussion sections, 286

multiple cycles that included aberration refinement, orientation refinement, and creation of a new 287

reference (19). In these cycles, the resolution limit of data used for the orientation refinement was 288

selected based on manual assessment of cisTEM’s SNR estimate exceeding a threshold value, 289

typically around ~4. The data collection and analysis statistics are summarized in Table 1. The 290

cryo-EM movies and maps used in data analysis of GI and HemQ proteins are deposited in 291

EMPIAR under [code 1] and [code 2] codes. For figure preparation, we placed models generated 292

by crystallography (5VR0.pdb for GI and 1T0T.pdb for HemQ) into cryo-EM maps, using the rigid 293

body refinement option available in Coot (27, 28). 294

295

Acknowledgements: We thank Tabitha Emde for protein purification and grid preparation for the 296

HemQ protein. We thank the Cryo-Electron Microscopy Facility at UT Southwestern Medical 297

Center which is supported by grant RP170644 from the Cancer Prevention & Research Institute 298

of Texas (CPRIT) for maintaining Talos Arctica microscope. This project has been funded in part 299

with federal funds from the National Institute of Allergy and Infectious Diseases, National Institutes 300

of Health, Department of Health and Human Services, under Contract No. 301

HHSN272201700060C. This project was also supported by the National Institutes of Health 302

(R21GM126406 to DB, and R01GM117080 and R01GM118619 to ZO) and the Department of 303

Energy (DE-SC0019600 to YG). 304

305

Author Contributions: RB, DB, and ZO developed an approach to aberration analysis; RB and 306

ZO implemented the approach; DB acquired data; RB, YG and ZO analyzed data; RB, YG, DB 307

and ZO wrote manuscript. 308

309


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Conflict of interest statement: RB, YG, DB, and ZO are co-founders of Ligo Analytics. YG 310

serves as the CEO of Ligo Analytics. ZO is a co-founder of HKL Research. RB, ZO, and DB are 311

co-inventors listed on a provisional patent application that has been filed on this work. 312


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Figure legends 373

Figure 1. Resolution dependence of third order aberrations on single particle reconstruction. X-374

axis represents reciprocal space resolution, scaled to a = 1 for x = 1 (Eq. 1). Y-axis represents 375

reciprocal space signal modulation of the reconstruction resulting from averaging the aberration. 376

377

Figure 2. FSC plots before (black) and after (red) coma correction and the corresponding final 378

map fragment for three experiments with high beam tilt (coma) values. The statistics from each 379

experiment are presented in Table 1. The vertical dotted grey line represents the first zero of the 380

modulation function (Eq. 1) and the solid line represents the first zero of the modulation function 381

with the assumption that 40% of the coma impact was compensated by image translation. The 382

resolutions corresponding to the first zero values are listed in Table 2. 383

384

Figure 3. Heat maps for coma and trefoil values refined separately per image from the HemQ-385

57K dataset. The leftmost panel shows tight clustering of the coma values, with the center panel 386

magnifying the region of clustering. The right panel shows the values of trefoil, which for this 387

dataset were insignificant. 388

389

Supplemental Figure S1. Definition of the orientation angle for particles coming from the same 390

projection. This angle is not affected by forces generating preferred orientation in the typical setup 391

of the sample grid being perpendicular to the beam. 392

393


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Figure 1 394 395

396


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Figure 2. 397

398


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Figure 3. 399 400

401


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Figure S1. 402 403

404


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Table 1. Data collection and processing

GI HemQ-57K HemQ-45K EMPIAR 10185 EMPIAR 10186 EMPIAR10204

Instrument Talos Arctica 200 kV Cryo-Arm 200

kV Phase plate No No No No No No

Energy filter No No No No No No

Objective aperture No No No Yes Yes Not known

Frames per movie 200 100 100 68 68 49

Electron dose (e/A2/frame) 0.7 0.9 0.9 0.99a 1.0a 1.38

Exposure time (second/frame) 0.5 0.4 0.4 0.25 0.25 Not known

K2 super-resolution mode No Yes Yes Yes Yes No

Detector pixel size (Å) 0.91 0.72 0.91 0.91 0.91 0.885

Data pixel size (Å) N/A 0.36 0.455 0.455 0.455 N/A

Movies collected/deposited 202 268 257 315 260 2161

Movies used for processing 149 258 173 315 260 415

Molecular weight (kDa) 173 144 144 659 659 465

Particle symmetry D2 C5 C5 D7 D7 D2

Total picked particles 114522 156210 236091 109695 91186 157513

Particles after 2D averaging 85527 145966 174776 No 2D classification 82721

Particles used in refinement 61909 81302 129446 85847 78689 52340 a count-based estimation

.C

C-B

Y-N

C 4.0 International license

certified by peer review) is the author/funder. It is m

ade available under aT

he copyright holder for this preprint (which w

as notthis version posted O

ctober 8, 2019. .

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bioRxiv preprint

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24

Table 2. The resolution without and with correction for coma for analyzed datasets.

GI HemQ-45 HemQ-57 EMPIAR 10204

EMPIAR 10185

EMPIAR 10186

Reported resolution [Å] NA NA NA NA 3.1 3.3

FSC0.143 based resolution before correction [Å]

4.1 3.8 4.3 2.5 3.1 3.2

FSC0.143 based resolution after correction [Å]

2.7 2.6 2.3 2.5 2.5 2.4

Coma [µm]/Beam tilt [mrad] 42.7/5.3 56.9/7.0 56.2/6.9 Varieda

Substantial Trefoil and Variable comab

Substantial Trefoil and Variable comab

Trefoil [µm] 0.62 0.79 0.49 0.09 2.74 3.06

Resolution at the first oscillation of with 40% compensation

5.2 5.7 5.7 ND ND ND

aComa varied between movies by more than 10 µm indicating ~1.2 mrad beam tilt variation bEMPIAR 10185 and 10186 were collected consecutively and share the same stable value of trefoil. EMPIAR 10185 was collected with stage shift and has similar coma variation as EMPIAR 10204. EMPIAR 10186 was collected with beam-image shift that induced additional coma variation.


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