10.4.1 Alignment of Subtomograms to the Average
Precision of rotational and translational alignment of the particles to the average is a
critical factor particularly for small or membrane associated protein complexes.
Estimation of envelope functions has shown that in order to retain 90% of the signal
at the resolution of 7 Å for a 1-MDa particle the translational error has to be less
than 0.5 Å and the rotational error has to be less than 0.5° for any given particle
[68]. Importantly, for a reliable alignment the signal inside the alignment mask has
to be sufficient to dominate the alignment. Different views of the same particle or
particles recorded at different defocus will have different signal-to-noise ratio; the
mask for particle alignment has to be designed to enable the reliable alignment of
the most particles from the dataset.
Sample movement during image acquisition may be recorded using “movie
mode” recording several consecutive low-dose images with their further aligning
and compensation for drift [25]. Precision of the movie frame alignment affects the
data quality [69], however the current methods of movie alignment seem
sub-optimal for cryo-ET. Fractionating the total dose of 1–3 e
− /Å
2 per projection
can be done only to a few movie frames having close-range correlated noise from
the detector. These neighbouring frames are excluded from alignment for higher
dose single particle acquisition, which is not possible if only few frames are present
[25]. Adjustment of processing methods for sub-frame alignment would further
improve the StA data quality.
Non-perfect alignment of tilt series prior to the generation of tomogram is an
important limiting factor. Simulations with the parameters reasonable for
cryo-conditions and perfectly aligned subtomograms resulted with the resolution of
12 Å [49] with a median angular error in particle alignment of 0.5°. Upon introduction of a misalignment error to the alignment of tilt series with a standard
deviation of 3 Å, the resolution drops to 15 Å; misalignment of 7 Å results in the
resolution drop to 22 Å. One of the consequences of the tilt series misalignment is
reduced to 1-degree precision for the particle alignment to the average. For
pseudo-crystalline arrangements the lack of signal may be compensated by
including more than one copy of the molecule of interest to contribute to the
alignment. Schur and colleagues used 7 copies of the 50 kDa GAG in the final
structure which resulted in atomic resolution [67]. In another study, a *250 kDa
ion channel 5HT-3 in lipid vesicles did not allow precise alignment; therefore four
neighbouring protein copies were used for alignment. However, the mutual
arrangement of the protein copies was not fixed and classification into multiple
classes had to be performed in order to minimize heterogeneity for given classes
[64].
As aligned particles share the information to the reference only to a certain
resolution, the conservative part of this resolution range should be used for alignment. As discussed earlier in the Sect. 10.3.1 the tomograms only contain reliable
resolution up to 3–6 nm. The use of higher frequencies results in a higher alignment
precision, however if there is not enough signal it will lead to overfitting similar to
10 Resolution in Electron Tomography
275
Precision of rotational and translational alignment of the particles to the average is a
critical factor particularly for small or membrane associated protein complexes.
Estimation of envelope functions has shown that in order to retain 90% of the signal
at the resolution of 7 Å for a 1-MDa particle the translational error has to be less
than 0.5 Å and the rotational error has to be less than 0.5° for any given particle
[68]. Importantly, for a reliable alignment the signal inside the alignment mask has
to be sufficient to dominate the alignment. Different views of the same particle or
particles recorded at different defocus will have different signal-to-noise ratio; the
mask for particle alignment has to be designed to enable the reliable alignment of
the most particles from the dataset.
Sample movement during image acquisition may be recorded using “movie
mode” recording several consecutive low-dose images with their further aligning
and compensation for drift [25]. Precision of the movie frame alignment affects the
data quality [69], however the current methods of movie alignment seem
sub-optimal for cryo-ET. Fractionating the total dose of 1–3 e
− /Å
2 per projection
can be done only to a few movie frames having close-range correlated noise from
the detector. These neighbouring frames are excluded from alignment for higher
dose single particle acquisition, which is not possible if only few frames are present
[25]. Adjustment of processing methods for sub-frame alignment would further
improve the StA data quality.
Non-perfect alignment of tilt series prior to the generation of tomogram is an
important limiting factor. Simulations with the parameters reasonable for
cryo-conditions and perfectly aligned subtomograms resulted with the resolution of
12 Å [49] with a median angular error in particle alignment of 0.5°. Upon introduction of a misalignment error to the alignment of tilt series with a standard
deviation of 3 Å, the resolution drops to 15 Å; misalignment of 7 Å results in the
resolution drop to 22 Å. One of the consequences of the tilt series misalignment is
reduced to 1-degree precision for the particle alignment to the average. For
pseudo-crystalline arrangements the lack of signal may be compensated by
including more than one copy of the molecule of interest to contribute to the
alignment. Schur and colleagues used 7 copies of the 50 kDa GAG in the final
structure which resulted in atomic resolution [67]. In another study, a *250 kDa
ion channel 5HT-3 in lipid vesicles did not allow precise alignment; therefore four
neighbouring protein copies were used for alignment. However, the mutual
arrangement of the protein copies was not fixed and classification into multiple
classes had to be performed in order to minimize heterogeneity for given classes
[64].
As aligned particles share the information to the reference only to a certain
resolution, the conservative part of this resolution range should be used for alignment. As discussed earlier in the Sect. 10.3.1 the tomograms only contain reliable
resolution up to 3–6 nm. The use of higher frequencies results in a higher alignment
precision, however if there is not enough signal it will lead to overfitting similar to
10 Resolution in Electron Tomography
275