Breakthroughs in single-particle cryo-electron microscopy (cryo-EM) technology have
made near-atomic resolution structure determination possible. Cryo-EM has resolved
over four thousand structures at near-atomic resolutions (2–4 Å).
It is rapidly becoming the method of choice for structure determination of membrane
proteins, large assemblies, and multi-protein complexes partly because it does not
require a crystal and partly because it can accommodate specimens with heterogeneous
composition and/or conformation.
This powerful technique is now capable of resolving protein complexes to better than
2 Å resolution
and has been used to solve 3.7 Å resolution structure of RNA as small as ~40 kilodaltons.
Two years ago, we obtained a 1.75 Å resolution apoferritin structure
using ~70,000 particle images through 10 h of data collection using a Gatan K2 detector
in a Titan Krios G3i electron microscope. Recently the K3 and Falcon 4 detectors were
installed on two of our Titan Krios G3i electron microscopes at the Stanford-SLAC
Cryo-EM Center, providing us with three times the data collection rate. In this study,
using the same apoferritin, we first collected a new dataset using the K3 detector
to find out what is the highest resolution structure achievable. The dataset was collected
in the electron counting mode using “Faster Acquisition” in EPU, with a throughput
of ~520 movie stacks per hour and a data acquisition result of 8000 movie stacks per
16 h (Supplementary information, Table S1). Using a standard image processing pipeline (Supplementary
information, Fig. S1a),
a density map of apoferritin with a resolution of 1.34 Å was obtained from ~900,000
particles (Fig. 1a–d). In addition, we also collected a second dataset using a Falcon
4 detector in the electron counting mode (MRC format, not EER format) with a throughput
of ~500 movie stacks per hour, resulting in ~7700 movie stacks from a 15 h data collection.
A 1.36 Å resolution map of apoferritin was obtained from ~500,000 particles (Supplementary
information, Fig. S1b–e and Table S1). Both maps have comparable resolution based
on the Fourier Shell correlation of 0.143 threshold
and similar Gaussian “B-factor”, relating the falloff in resolution of the reconstructions
to the numbers of particles
(Supplementary information, Fig. S1f, g). This “B-factor” indicates the quality of
the map, which is caused by a combination of the experimental limitations of the specimen
and the instrument, and the errors inherent in the computational image processing
pipeline. In comparing the atom positions between the two independently optimized
models from these maps, they were found to have a root mean square deviation (RMSD)
of 0.27 Å for all atoms, 0.07 Å for backbone atoms, and 0.41 Å for side chain atoms.
These results validate the reproducibility and precision of the maps obtained from
two independent data sets and instruments.
Atomic resolution structure of apoferritin determined from a 300 kV Titan Krios G3i
electron microscope with K3 detector.
a Representative motion-corrected cryo-EM micrographs. The scale bar represents 200 Å.
b Reference-free 2D class averages of computationally extracted particles. c Resolution
variation maps for the final 3D reconstruction. d Cryo-EM density map of an extracted
single subunit. e Twenty representative amino acids extracted from the 1.34 Å resolution
map. The amino acids were selected based on the type of side chain (polar, charged,
and hydrophobic). Each residue is shown on a higher density display level (0.045 in
Chimera, left) or lower density display level (0.008 in Chimera, right), showing separable/resolved
atoms or shapes of atoms including hydrogen atoms, respectively. f Representative
residues with alternate conformations of side chains. A/B/C represents different side-chain
conformations. The residues in e and f are shown by elements (grey, carbon; red, oxygen;
blue, nitrogen; yellow, sulfur; white, hydrogen). g, h A representative helix was
extracted from the cryo-EM density map (g) and the model-generated map using B’ factors
(h). i Water molecules are shown around a small portion of the helix. j A radial distance
plot between water and O atoms in the protein shows a sharp peak at 2.8 Å resolution.
k A histogram of Q-scores for placed waters shows that most are placed in well-resolved
peaks with Q-scores of 0.8 and higher.
Our maps show separable atom densities at a properly chosen contour level, well-resolved
side-chain atom densities, and even some indications of hydrogen densities as exemplified
from the 1.34 Å resolution map (Fig. 1e). The presence and direction of the density
for hydrogen, even though they are not distinctly resolved, are visually compelling.
Furthermore, the difference between the oxygen (O) and the nitrogen (N) atoms in Asparagine
(Asn) and Glutamine (Gln) residue side chains, where the N has extended density for
its hydrogen (H) atoms, whereas the O appears circular in an end-on view, allows one
to distinguish these two atoms, which informs whether the atom is a hydrogen bond
donor or acceptor. The same is the case for the O vs. C atoms in Threonine (Thr),
wherein the terminal methyl group is roughly triangular in shape, and the O again
appears circular in an end-on view, and allows one to unambiguously differentiate
Thr from Valine (Val). However, the side chains of ~12 residues cannot be clearly
identified in either map due to multiple rotameric conformations (a few examples shown
in Fig. 1f), which may be caused by their inherent or electron radiation-induced dynamic
The Molprobity and PDB reports of our two models rank very highly in all the assessment
scores on the adherence of models to the chemical properties of proteins (Supplementary
information, Fig. S2). Generally speaking, it is difficult to assess the fit of a
model to a density map by visual display, partly because of the choice of contour
display and partly because of the variation of resolvability throughout the map (Fig. 1c,
d; Supplementary information, Fig. S1e). Though the overall resolutions of maps are
reported based on the Fourier shell correlation (Supplementary information, Fig. S1f),
some side chains and residues are less resolved. We used Q-scores, a recently proposed
cryo-EM structure validation method, to measure the resolvability of individual atoms.
Q-scores were shown to correlate strongly to the resolution of the map, with the best
score normalized to 1.0. Supplementary information, Fig. S3a shows the per-residue
Q-score plot for our two maps range between 0.85 and 0.88; most residues have average
Q-scores at or above the expected level for this resolution.
However, a few dips in the plot can be seen, indicating lower average Q-scores at
turns or loops between helices. Visual inspection of the residues with lower Q-scores
confirms that the side chains are less resolved for these residues. Such residues
tend to have alternate conformers (Fig. 1f) and be on the exterior surface of the
Traditionally, individual B-factor of atoms used in X-ray crystallography is used
to assess the atom position uncertainty in crystallography and is a weighting factor
to allow computing model-based structural factors identical to the observed structural
factors. Note that the crystallographic B-factors are not the same as the “B-factor”
as described above although both have the same mathematical representation of a Gaussian
function for describing the speed of the falloff in Fourier space. The crystallographic
B-factors are estimated by iterative and simultaneous refinements of agreement in
Fourier amplitudes between observed and computed values, and Fourier phase estimation.
In cryo-EM, the modeling software yields crystallographic equivalent B-factors also
known as atomic displacement parameters. However, these parameters generally are not
optimized to match a model-based map with the experimental map.
We thus introduce B’ factors derived from per-atom Q-scores; the calculation involves
a simple scale factor determined empirically by testing which value makes the resulting
model-derived map match the cryo-EM map better by Fourier Shell Correlation (Supplementary
information, Fig. S3b–e). The B’ factors for each atom, which will be deposited to
the PDB along with their coordinates, serve the same purpose as the crystallographic
B-factors in such a way that we can compute a model-based map, which can match optimally
with the experimental cryo-EM density map (Fig. 1g, h; Supplementary information,
Fig. S3 and Data S1).
Resolving water molecules is an important metric for assessing the quality of a true
atomic resolution map. We assigned water molecules in our maps using a procedure based
on three criteria (Supplementary information, Data S1): a signal to noise threshold
to ignore background noise (2-sigma/RMSD above average), the distance between putative
water and the closest protein atoms, and the criteria that distinguish water from
ions as outlined in reference (Fig. 1i–k).
The distributions show that the procedure places water on well-resolved peaks with
Q-scores of 0.5 and higher, even though Q-scores were not used in the selection procedure
itself. The radial-distance plot shown in Fig. 1j shows a peak at 2.8 Å between water
atoms and nearby O atoms in the protein, as expected.
Recently, two non-peer-reviewed preprints report 1.22 Å and 1.25 Å resolution apoferritin
using new electron optics (i.e., cold field emission gun, second-generation spherical
aberration lens corrector/monochromator), which are aimed to optimize the high-resolution
by minimizing the deleterious effects of electron energy spread or lens aberration.
In our study, we show two ~1.35 Å resolution structures of the apoferritin without
these hardware upgrades. We here selected four representative residue types for a
detailed comparison at the individual atom level among these 4 cryo-EM maps, in addition
to a 1.01 Å resolution crystal structure,
and a 1.75 Å resolution cryo-EM map (Supplementary information, Fig. S4).
As expected, the two 1.22 Å and 1.25 Å resolution cryo-EM maps have slightly higher
Q-scores based on numerical ranking as well as slightly better atomic separations
based on visual inspection than our 1.34 Å and 1.36 Å resolution maps.
Another assessment of these cryo-EM structures was to compare the number of water
molecules placed in different cryo-EM maps with the criteria described above (Supplementary
information, Fig. S5). As expected, more water molecules were found in higher-resolution
maps: 216, 217, 170, 165, and 126 waters per protomer in the 1.22 Å, 1.25 Å, 1.34 Å,
1.36 Å, and 1.75 Å resolution maps, respectively (Supplementary information, Fig. S5).
Sharper peaks were observed in the distances between the water molecules and the adjacent
protein atoms at higher resolution, meaning that higher resolution maps localize water
molecules more accurately (Supplementary information, Fig. S5a–e). Molprobity results
showed only a few of the water molecules placed with our procedure were found to clash
(3 in the 1.34 Å resolution map and 8 in the 1.36 Å resolution map) (Supplementary
information, Fig. S2).
When comparing different cryo-EM maps, many water molecules found in one map were
also found within 1.0 Å in the other maps (Supplementary information, Fig. S5f). Between
our two 1.34 Å and 1.36 Å resolution maps, 72% of the water atoms were within 1.0 Å
of each other. We also found that our water placement matches 10% better with the
1.25 Å resolution map (human apoferritin, same as ours) than with the 1.22 Å resolution
map (mouse apoferritin), probably due to the difference in species. This is supported
by the observation of a bigger difference in the water placement between the 1.22 Å
and 1.25 Å resolution maps. Based on these comparisons, it is encouraging to note
that a high percentage of water molecules placed in cryo-EM maps from the same species
agree, suggesting good reproducibility of water positions across data sets recorded
in different electron microscopes with different sample preparations. When comparing
our cryo-EM maps to the X-ray structure, a lower percentage (~42%) of water molecules
were within the same 1.0 Å distance (Supplementary information, Fig. S5f, g). Given
the differences in composition and concentration of the solvent and the chemical environment
(protein packing in X-ray crystal vs vitrified single particles in cryo-EM), it is
not surprising that there are differences in water positions. Such discrepancy also
applies to ion placements (Supplementary information, Data S1). In placed ions, positions
compared amongst cryo-EM maps showed lower similarity (~34%) due to different solvent
and chemical environments. In comparing our two cryo-EM maps, 11 ions including 7
divalent and 4 monovalent ions were found in equivalent positions within 1.0 Å to
each other. However, water and ion identification is still under active research even
in atomic resolution X-ray structures,
and it is an emerging and potentially important area in cryo-EM map analysis.
From the overall and detailed evaluation, our 1.34 and 1.36 Å resolution cryo-EM maps
show similar characteristic atomic features as the 1.22 Å and 1.25 Å resolution cryo-EM
maps and the 1.01 Å resolution crystal structure, and all are certainly better than
the 1.75 Å resolution map (Supplementary information, Figs. S4, S5). Such similarity
is borne out by the RMSD of all atoms to be around 0.2 Å between ~1.2 Å and ~1.3 Å
resolution maps. Nevertheless, the quantitative assessment of the atom resolvability
shows a slight improvement of 1.22–1.25 Å over 1.34–1.36 Å resolution cryo-EM maps
(Supplementary information, Figs. S4, S5). Our results demonstrate that an atomic
resolution structure can be obtained on a 300 kV Titan Krios G3i microscope using
the K3 or Falcon 4 detectors with or without an energy filter (Supplementary information,
Table S1), which thus gives users having this kind of instrumentation the possibility
of performing single-particle cryo-EM analysis at the atomic resolution level. Practically
speaking, structures should be sufficient to describe the atom locations in a macromolecular
complex equally well in this range of resolution between 1.2–1.3 Å. However, there
could still be great interest in the chemical and pharmacological chemistry community
to seek more detailed information better than 1.0 Å resolution for understanding basic
chemistry and drug design.
Finally, we would like to remind that apoferritin, with its high stability, rigidity,
and symmetry, can easily be resolved at atomic resolution by either cryo-EM or X-ray
crystallography. However, many biological samples are compositionally or conformationally
heterogeneous, as well as often difficult to prepare with the current cryo-freeze
These technical hurdles can hinder solving their structures at atomic resolution.
Achieving atomic resolution structures is not yet a routine task, but with the further
development of cryo-specimen preparation, hardware, and software, it should be possible
to apply this approach to an even broader spectrum of macromolecules in the context
of chemistry to understand the mechanism and/or to apply it in the drug design pipeline.