have been implemented in the MRC package [20], and subsequently in the 2dx [21] and FOCUS [22] packages, among others
[23]. A technical limitation of 2D electron crystallography is that
samples in the microscope can typically only be tilted up to about
60
for geometric reasons, therefore leaving a cone of missing
information in 3D Fourier space. Because of this, the reconstructed
maps may appear elongated in the z-direction in real space. Furthermore, only if the 2D crystals are perfectly flat and well-ordered,
high-resolution diffraction spots will be observed. Because this is
rarely the case in practice, image processing algorithms were developed to correct for the crystal distortions in silico [24, 25].
One such algorithm, the so-called image unbending [26], has
been particularly successful [3]. This method works by moving
small patches of the 2D crystal image by iteratively comparing
cross-correlation peaks indicating the locations of unit cells in real
space with their predicted positions. However, this approach is
intrinsically limited to distortions in the image plane and cannot
account for azimuth angle variations that are present when 2D
crystals with larger in-plane distortions are imaged at higher tilts.
In order to be able to correct for out-of-plane distortions, such as
“bumps” in the 2D crystal, the patches need to be compared (e.g.,
cross-correlated) against a reference in 3D space, which is essentially what single particle refinement and reconstruction algorithms
do [10]. First attempts in this direction showed promise [27, 28],
but were still limited to low-resolution reconstructions. This was in
part because the datasets analyzed in these works had not yet been
collected on direct electron detectors (DED) [29], and partially
because the algorithms implemented did not account for the very
low signal-to-noise (SNR) ratios of cryo-EM images in a probabilistic manner [30].
We have since then implemented a module in the FOCUS
package that allows the user to export a 2D crystallography project
for processing with standard single particle analysis software. This
not only brings to electron crystallography the maturity that these
packages have achieved in terms of robustness and performance
[31–33], but, more importantly, it opens the possibility of classifying heterogeneous structures [34, 35] coexisting within the 2D
crystals. In the Methods section, we will describe in detail the workflow for processing 2D crystal data within the single particle framework, with an emphasis on practical tips and tricks. The approach
presented here is based on the one we used to process poorly
diffracting 2D crystals of MloK1, a 160 kDa prokaryotic potassium
channel [36, 37]. Using single particle refinements, we were able to
obtain a map of MloK1 at 4 A ˚ resolution and to observe distinct
conformations of its cyclic-nucleotide binding domain (CNBD),
helping to elucidate the mechanism of gating for this channel
[38]. The method is generally applicable to other 2D crystal samples as well.
Single Particle Analysis for High-Resolution 2D Electron Crystallography
269
[23]. A technical limitation of 2D electron crystallography is that
samples in the microscope can typically only be tilted up to about
60
for geometric reasons, therefore leaving a cone of missing
information in 3D Fourier space. Because of this, the reconstructed
maps may appear elongated in the z-direction in real space. Furthermore, only if the 2D crystals are perfectly flat and well-ordered,
high-resolution diffraction spots will be observed. Because this is
rarely the case in practice, image processing algorithms were developed to correct for the crystal distortions in silico [24, 25].
One such algorithm, the so-called image unbending [26], has
been particularly successful [3]. This method works by moving
small patches of the 2D crystal image by iteratively comparing
cross-correlation peaks indicating the locations of unit cells in real
space with their predicted positions. However, this approach is
intrinsically limited to distortions in the image plane and cannot
account for azimuth angle variations that are present when 2D
crystals with larger in-plane distortions are imaged at higher tilts.
In order to be able to correct for out-of-plane distortions, such as
“bumps” in the 2D crystal, the patches need to be compared (e.g.,
cross-correlated) against a reference in 3D space, which is essentially what single particle refinement and reconstruction algorithms
do [10]. First attempts in this direction showed promise [27, 28],
but were still limited to low-resolution reconstructions. This was in
part because the datasets analyzed in these works had not yet been
collected on direct electron detectors (DED) [29], and partially
because the algorithms implemented did not account for the very
low signal-to-noise (SNR) ratios of cryo-EM images in a probabilistic manner [30].
We have since then implemented a module in the FOCUS
package that allows the user to export a 2D crystallography project
for processing with standard single particle analysis software. This
not only brings to electron crystallography the maturity that these
packages have achieved in terms of robustness and performance
[31–33], but, more importantly, it opens the possibility of classifying heterogeneous structures [34, 35] coexisting within the 2D
crystals. In the Methods section, we will describe in detail the workflow for processing 2D crystal data within the single particle framework, with an emphasis on practical tips and tricks. The approach
presented here is based on the one we used to process poorly
diffracting 2D crystals of MloK1, a 160 kDa prokaryotic potassium
channel [36, 37]. Using single particle refinements, we were able to
obtain a map of MloK1 at 4 A ˚ resolution and to observe distinct
conformations of its cyclic-nucleotide binding domain (CNBD),
helping to elucidate the mechanism of gating for this channel
[38]. The method is generally applicable to other 2D crystal samples as well.
Single Particle Analysis for High-Resolution 2D Electron Crystallography
269