curves is therefore computed over distinct angular directions, and
these individual 1D curves are compiled into a 3D array that we
term the 3D FSC. This 3D FSC can be visualized as an isosurface
density just like any other map within a visualization software (e.g.,
in Chimera) and at some threshold value. When projections are
evenly distributed within the Fourier transform and individual
lattice points are approximately equally sampled across any individual shell, the directional resolution should not vary with different
viewing angles. In such a scenario, the directional resolution is
isotropic. However, when projections are not evenly distributed,
there could be large variations in apparent structural features
depending on the viewing angle, and the directional resolution is
anisotropic. As a result, structural features might be elongated in
one direction, which could lead to misinterpretations of the density
and problems during derivation or refinement of the atomic model.
As we showed recently, this will also affect the global resolution
[18]. Careful examination of the 3D FSC, especially under conditions when anisotropy can be significant, can lead to a better
understanding of how experimental data is affected.
Due to the geometry of the imaging experiment, the direction
that is parallel to the electron beam shows the poorest resolution
for preferentially oriented samples. If the electron beam is assumed
to be along the Z direction, then the X/Y plane of Fourier space
should be best resolved, whereas resolution curves along Z (e.g.,
the X/Z or Y/Z planes) would be compromised. Depending on
the angular coverage of the projection views, the quality of the
features evident along distinct viewing directions may vary. In
experimental cases where the projections are dominated by more
than just a few orientations (or when there is a high molecular
symmetry), there may be only minor, if any, variations when viewing the map along any of the three directions. In the more severe
cases, an anisotropic distribution of projection orientations may
lead to apparent elongation of structural features within the map
along the Z-direction. This may affect the interpretation of the
map—sometimes severely—due to the appearance of artifactual
(low-resolution) density parallel to the dominant view [6]. In
some cases, an additional consequence of severe variations in directional resolution is that the refinement of individual projection
orientations could be affected, leading to orientation misassignment. Therefore, this may lead to additional overfitting and/or
artifacts during the refinement process.
Variations in directional resolution arise from preferred orientation of macromolecules within the vitrified ice layer, resulting in
incomplete sampling of orientations in Fourier space [6, 19, 20]. If
the macromolecules are in random orientations and approximately
uniformly distributed within the ice layer (this means that there is
no single dominant view), then the projections are also evenly
sampled, and we expect the directional resolution curves, described
164
Sriram Aiyer et al.
these individual 1D curves are compiled into a 3D array that we
term the 3D FSC. This 3D FSC can be visualized as an isosurface
density just like any other map within a visualization software (e.g.,
in Chimera) and at some threshold value. When projections are
evenly distributed within the Fourier transform and individual
lattice points are approximately equally sampled across any individual shell, the directional resolution should not vary with different
viewing angles. In such a scenario, the directional resolution is
isotropic. However, when projections are not evenly distributed,
there could be large variations in apparent structural features
depending on the viewing angle, and the directional resolution is
anisotropic. As a result, structural features might be elongated in
one direction, which could lead to misinterpretations of the density
and problems during derivation or refinement of the atomic model.
As we showed recently, this will also affect the global resolution
[18]. Careful examination of the 3D FSC, especially under conditions when anisotropy can be significant, can lead to a better
understanding of how experimental data is affected.
Due to the geometry of the imaging experiment, the direction
that is parallel to the electron beam shows the poorest resolution
for preferentially oriented samples. If the electron beam is assumed
to be along the Z direction, then the X/Y plane of Fourier space
should be best resolved, whereas resolution curves along Z (e.g.,
the X/Z or Y/Z planes) would be compromised. Depending on
the angular coverage of the projection views, the quality of the
features evident along distinct viewing directions may vary. In
experimental cases where the projections are dominated by more
than just a few orientations (or when there is a high molecular
symmetry), there may be only minor, if any, variations when viewing the map along any of the three directions. In the more severe
cases, an anisotropic distribution of projection orientations may
lead to apparent elongation of structural features within the map
along the Z-direction. This may affect the interpretation of the
map—sometimes severely—due to the appearance of artifactual
(low-resolution) density parallel to the dominant view [6]. In
some cases, an additional consequence of severe variations in directional resolution is that the refinement of individual projection
orientations could be affected, leading to orientation misassignment. Therefore, this may lead to additional overfitting and/or
artifacts during the refinement process.
Variations in directional resolution arise from preferred orientation of macromolecules within the vitrified ice layer, resulting in
incomplete sampling of orientations in Fourier space [6, 19, 20]. If
the macromolecules are in random orientations and approximately
uniformly distributed within the ice layer (this means that there is
no single dominant view), then the projections are also evenly
sampled, and we expect the directional resolution curves, described
164
Sriram Aiyer et al.