for most macromolecular assemblies. However, the local resolution
varies more substantially, ranging from 3.0 to 5.0 Å (see Fig. 2c).
The enzyme is dynamic and there are conformational changes
apparent in multiple regions, with the unprotected ends of
dsDNA resolved to ~5 Å or worse. There is also compositional
heterogeneity, as the filaments are symmetrized from multiple species containing a distinct number of underlying asymmetric units.
In summary, the global resolution of a 3D volume does not ensure
that all regions can be interpreted equally, and local resolution
analysis is a fundamental measure that informs the experimentalist
about variations in resolution, which helps with structural
interpretations.
3.3.3 Interpreting
the Shape of the 3D FSC
Volume
The 3D FSC can be displayed and visualized as an isosurface at a
fixed threshold (e.g., 0.143 for half-map and 0.5 for map-model).
Another way to represent the information content in 3D FSC
volumes is to display the central slice and color the volume according to the Fourier radius, which is directly related and can be
converted to the spatial frequency and resolution (see Note 17).
These different displays are shown in Fig. 3 for a severely anisotropic reconstruction containing a large missing cone. Within the
3D FSC volumes, the uncorrelated regions showing missing density correspond to the direction of preferred orientation, and thus
the Z-direction relative to the electron beam (see Fig. 4). Rotating
the maps in Chimera will change the color, as well as the out-ofplane Z resolution that is displayed in the second window (see
Notes 15 and 16). Displaying 3D FSC volumes is complementary
to displaying the Euler angle distribution profiles, but provides
additional, quantitative insight pertaining to directional resolution.
The Euler angle profiles giving rise to the AAV2 and HA reconstructions discussed below are shown in Fig. 6 (see Note 18). For a
perfectly isotropic sample, the shape of the 3D FSC volume should
be a sphere. Expectedly, this is the case for the icosahedrally symmetric reconstruction of AAV2 (see Fig. 7a). In contrast, for an
anisotropic sample like HA, the 3D FSCs will deviate from spherical
to varying extents. In the half-map 3D FSCs, both the reconstructions from untilted and tilted images show a volume with some
evidence of the missing cone. (Fig. 7b top untilted and bottom
tilted). The most anisotropic reconstructions will have 3D FSCs
that will have a clear indication of a missing cone (in practice, they
may appear “pancake-shaped”). For the particular case of HA,
there is likely some amount of overfitting evident in the half-map
3D FSCs, especially for the reconstruction from untilted images.
This explains the presence of some correlations within the 3D FSC
in regions that should normally correspond to the missing cone.
For this reason, it is often useful to display the 3D FSC volumes at
different thresholds, as indicated in Fig. 8 (see Note 19). For the
Local and Directional Resolution in Cryo-EM Maps
175
varies more substantially, ranging from 3.0 to 5.0 Å (see Fig. 2c).
The enzyme is dynamic and there are conformational changes
apparent in multiple regions, with the unprotected ends of
dsDNA resolved to ~5 Å or worse. There is also compositional
heterogeneity, as the filaments are symmetrized from multiple species containing a distinct number of underlying asymmetric units.
In summary, the global resolution of a 3D volume does not ensure
that all regions can be interpreted equally, and local resolution
analysis is a fundamental measure that informs the experimentalist
about variations in resolution, which helps with structural
interpretations.
3.3.3 Interpreting
the Shape of the 3D FSC
Volume
The 3D FSC can be displayed and visualized as an isosurface at a
fixed threshold (e.g., 0.143 for half-map and 0.5 for map-model).
Another way to represent the information content in 3D FSC
volumes is to display the central slice and color the volume according to the Fourier radius, which is directly related and can be
converted to the spatial frequency and resolution (see Note 17).
These different displays are shown in Fig. 3 for a severely anisotropic reconstruction containing a large missing cone. Within the
3D FSC volumes, the uncorrelated regions showing missing density correspond to the direction of preferred orientation, and thus
the Z-direction relative to the electron beam (see Fig. 4). Rotating
the maps in Chimera will change the color, as well as the out-ofplane Z resolution that is displayed in the second window (see
Notes 15 and 16). Displaying 3D FSC volumes is complementary
to displaying the Euler angle distribution profiles, but provides
additional, quantitative insight pertaining to directional resolution.
The Euler angle profiles giving rise to the AAV2 and HA reconstructions discussed below are shown in Fig. 6 (see Note 18). For a
perfectly isotropic sample, the shape of the 3D FSC volume should
be a sphere. Expectedly, this is the case for the icosahedrally symmetric reconstruction of AAV2 (see Fig. 7a). In contrast, for an
anisotropic sample like HA, the 3D FSCs will deviate from spherical
to varying extents. In the half-map 3D FSCs, both the reconstructions from untilted and tilted images show a volume with some
evidence of the missing cone. (Fig. 7b top untilted and bottom
tilted). The most anisotropic reconstructions will have 3D FSCs
that will have a clear indication of a missing cone (in practice, they
may appear “pancake-shaped”). For the particular case of HA,
there is likely some amount of overfitting evident in the half-map
3D FSCs, especially for the reconstruction from untilted images.
This explains the presence of some correlations within the 3D FSC
in regions that should normally correspond to the missing cone.
For this reason, it is often useful to display the 3D FSC volumes at
different thresholds, as indicated in Fig. 8 (see Note 19). For the
Local and Directional Resolution in Cryo-EM Maps
175