particles. Particles are superimposed, classified, and averaged, reinforcing signal,
averaging-out noise, and—provided the specimen is present in a diversity of orientations—producing a complete dataset without a missing wedge of data in
Fourier space, as described fully in Chap. 9. Alignment of subtomograms is the
crucial first step in subtomogram averaging, typically using a global or restrained
six-dimensional rotational and translational search. Optimal alignments are typically deterministic [87, 88], although a maximum likelihood approach has also now
been implemented [51]. Alignment algorithms must take into account the missing
data from the tomogram for optimal alignment, usually achieved by downweighting missing Fourier components. Intimately interdependent with alignment is
classification of heterogeneity, and typically these two processes are performed
simultaneously. Because the alignment step is the critical step to determine the
highest possible quality subtomogram average, DDD cameras offer considerable
advantage by enabling better alignment (in addition to the better data for averaging). Determining the resolution of a subtomogram average is achieved using the
‘Gold standard’ approach to calculate the FSC as used in single particle analysis
[89], fully described in Chap. 10.
3.5.4 Visualization and Interpretation of Denoised
Tomograms
Subsequent to denoising via filtering or averaging, the tomographic volume is now
ready for visualization and interpretation. Visualization may simply involve analysis of slices of the tomogram, or volumetric representation in which the tomogram
is viewed as a 3-D box, with density represented by opacity of voxels (3-D pixels).
Another common approach is segmentation, described in Chap. 12, in which
boundaries of structures are represented as 3-D surfaces. Although many automatic
and semi-automatic segmentation algorithms have been described [81], due to the
low signal-to-noise ratio, segmentation is usually a manual task despite being
inherently slow and subjective. In contrast, the signal-to-noise ratio of subtomogram averages is generally high enough to render boundaries of structures automatically using a density threshold to generate an isosurface.
How can the user identify structures in a tomogram? A number of approaches
can be used. “Visual proteomics” is an approach to determining the composition of
the cytoplasm using tomography. The dense, heterogenous mixture of hundreds of
types of macromolecular complexes in the cytoplasm is intractable to visualize and
assign manually, necessitating automated assignment approaches. Template
matching uses a template macromolecular complex (such as a ribosome or chaperone) to search a tomographic volume for significant matches. Template matching
performs well for large structures above approximately one megadalton [90]. Where
the identity of structure is unclear, imaging mutants with removed or enriched
components provides evidence on the identity of a structure [91]. Although a
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J. L. Ferreira et al.
averaging-out noise, and—provided the specimen is present in a diversity of orientations—producing a complete dataset without a missing wedge of data in
Fourier space, as described fully in Chap. 9. Alignment of subtomograms is the
crucial first step in subtomogram averaging, typically using a global or restrained
six-dimensional rotational and translational search. Optimal alignments are typically deterministic [87, 88], although a maximum likelihood approach has also now
been implemented [51]. Alignment algorithms must take into account the missing
data from the tomogram for optimal alignment, usually achieved by downweighting missing Fourier components. Intimately interdependent with alignment is
classification of heterogeneity, and typically these two processes are performed
simultaneously. Because the alignment step is the critical step to determine the
highest possible quality subtomogram average, DDD cameras offer considerable
advantage by enabling better alignment (in addition to the better data for averaging). Determining the resolution of a subtomogram average is achieved using the
‘Gold standard’ approach to calculate the FSC as used in single particle analysis
[89], fully described in Chap. 10.
3.5.4 Visualization and Interpretation of Denoised
Tomograms
Subsequent to denoising via filtering or averaging, the tomographic volume is now
ready for visualization and interpretation. Visualization may simply involve analysis of slices of the tomogram, or volumetric representation in which the tomogram
is viewed as a 3-D box, with density represented by opacity of voxels (3-D pixels).
Another common approach is segmentation, described in Chap. 12, in which
boundaries of structures are represented as 3-D surfaces. Although many automatic
and semi-automatic segmentation algorithms have been described [81], due to the
low signal-to-noise ratio, segmentation is usually a manual task despite being
inherently slow and subjective. In contrast, the signal-to-noise ratio of subtomogram averages is generally high enough to render boundaries of structures automatically using a density threshold to generate an isosurface.
How can the user identify structures in a tomogram? A number of approaches
can be used. “Visual proteomics” is an approach to determining the composition of
the cytoplasm using tomography. The dense, heterogenous mixture of hundreds of
types of macromolecular complexes in the cytoplasm is intractable to visualize and
assign manually, necessitating automated assignment approaches. Template
matching uses a template macromolecular complex (such as a ribosome or chaperone) to search a tomographic volume for significant matches. Template matching
performs well for large structures above approximately one megadalton [90]. Where
the identity of structure is unclear, imaging mutants with removed or enriched
components provides evidence on the identity of a structure [91]. Although a
80
J. L. Ferreira et al.