but it is regarded as superior with respect to noise and artificial edge enhancements.
Thus, SIRT reconstructions perform well with noisy data typical of cryo-EM and
generally tend to look ‘smoother’ than the corresponding weighted backprojection.
Ultimately, the choice may come down to user preference and perceived aesthetic
qualities of the final result but both represent mathematically correct solutions to the
backprojection problem. More importantly, the choice of reconstruction algorithm
may influence the efficacy of subsequent denoising and segmentation routines.
Electron tomography may yet benefit from alternative reconstruction algorithms that
were abandoned originally due to (then) unrealistic computational requirements.
1.9 Resolution
We have already defined electron tomography as a technique capable of 4 nm
resolution. Resolution is discussed in detail in Chap. 10, and in relation to subtomogram averaging below. Resolution in 3D space is not a trivial concept, and
misleading claims of resolution are sometimes made due to a fundamental
misunderstanding of the Crowther criterion, which relates resolution to sampling
efficiency. Assuming that the object is sampled isotropically, i.e. the angular range
is sampled evenly (which is usual for some forms of tomography but does not
usually apply to electron tomography), the Crowther criterion simply states that the
resolution is a function of the number of unique projections. This seems logical but
it represents a theoretical or ‘best-case’ scenario. For plastic-embedded samples that
seem to tolerate many projections without obvious radiation damage, it is tempting
to record projections with an increment of 1 degree or less, which generates more
than 150 projections. Inserting this number into the formula for the Crowther
criterion produces an impressive number that certainly cannot withstand scrutiny.
The obvious test of this claim is to be able to identify a feature in the tomogram that
demonstrates such resolution. Resolution of better than 0.8 nm should be able to
resolve alpha helices in proteins. The best resolution achieved using cryo- electron
tomography does not exceed 4 nm, nor is it likely to exceed 2 nm in raw data.
Information and resolution are related but information is more important than
unproductive debates [4]. In practice, resolution is degraded by specimen thickness,
interpolation artefacts that occur as a result of the reconstruction algorithm, and in
the case of unstained specimens that require phase contrast via imposed underfocus,
the contrast transfer function (CTF) determined by the chosen defocus value. The
latter is of course addressed by the use of phase plate technology [99]. Perhaps
more obviously, resolution is a function of the magnification, which implies that it
cannot surpass the Nyquist Frequency. For a more thorough treatment of resolution
in electron tomography, the reader is referred to the work of Steven [100] and the
chapter by Penczek [101], as well as Chap. 9. Subtomogram averaging (see below)
is a means of increasing resolution locally where structures are amenable to
averaging.
1 Electron Tomography: A Primer
17
Thus, SIRT reconstructions perform well with noisy data typical of cryo-EM and
generally tend to look ‘smoother’ than the corresponding weighted backprojection.
Ultimately, the choice may come down to user preference and perceived aesthetic
qualities of the final result but both represent mathematically correct solutions to the
backprojection problem. More importantly, the choice of reconstruction algorithm
may influence the efficacy of subsequent denoising and segmentation routines.
Electron tomography may yet benefit from alternative reconstruction algorithms that
were abandoned originally due to (then) unrealistic computational requirements.
1.9 Resolution
We have already defined electron tomography as a technique capable of 4 nm
resolution. Resolution is discussed in detail in Chap. 10, and in relation to subtomogram averaging below. Resolution in 3D space is not a trivial concept, and
misleading claims of resolution are sometimes made due to a fundamental
misunderstanding of the Crowther criterion, which relates resolution to sampling
efficiency. Assuming that the object is sampled isotropically, i.e. the angular range
is sampled evenly (which is usual for some forms of tomography but does not
usually apply to electron tomography), the Crowther criterion simply states that the
resolution is a function of the number of unique projections. This seems logical but
it represents a theoretical or ‘best-case’ scenario. For plastic-embedded samples that
seem to tolerate many projections without obvious radiation damage, it is tempting
to record projections with an increment of 1 degree or less, which generates more
than 150 projections. Inserting this number into the formula for the Crowther
criterion produces an impressive number that certainly cannot withstand scrutiny.
The obvious test of this claim is to be able to identify a feature in the tomogram that
demonstrates such resolution. Resolution of better than 0.8 nm should be able to
resolve alpha helices in proteins. The best resolution achieved using cryo- electron
tomography does not exceed 4 nm, nor is it likely to exceed 2 nm in raw data.
Information and resolution are related but information is more important than
unproductive debates [4]. In practice, resolution is degraded by specimen thickness,
interpolation artefacts that occur as a result of the reconstruction algorithm, and in
the case of unstained specimens that require phase contrast via imposed underfocus,
the contrast transfer function (CTF) determined by the chosen defocus value. The
latter is of course addressed by the use of phase plate technology [99]. Perhaps
more obviously, resolution is a function of the magnification, which implies that it
cannot surpass the Nyquist Frequency. For a more thorough treatment of resolution
in electron tomography, the reader is referred to the work of Steven [100] and the
chapter by Penczek [101], as well as Chap. 9. Subtomogram averaging (see below)
is a means of increasing resolution locally where structures are amenable to
averaging.
1 Electron Tomography: A Primer
17