menu
![[Figure 3]](hen5001fig3mag.jpg)
|
|
Figure 3
Concepts of 3D reconstruction, spatial frequency and resolution estimation in cryo-EM. (a) Left and middle – imaging a vitrified sample on a cryo-EM grid using electrons gives a 2D projection of the 3D object; because transmission EM is used, all internal features of the object are present in the corresponding 2D projection. Right – concept of 3D reconstruction from 2D projections using back-projection; this is the reverse process as compared with the data acquisition in the left panel. Three-dimensional reconstruction requires one to have viewing angles assigned (i.e. orientations of each particle view), e.g. as Euler angles. Three-dimensional reconstruction assumes unique particles (homogenous in terms of composition and conformation) and an equal distribution of particle orientations to avoid map distortions, otherwise appropriate measures need to be taken during image processing (e.g. structure sorting, focused refinements or correction of preferred particle orientations). Three-dimensional reconstruction results in a cryo-EM map that can be interpreted by building and refining an atomic model. (b) Relationship between the pixel size of an image and the highest spatial frequency (Nyquist frequency), which is 1/(2 times the pixel size). The sampling corresponds to the physical pixel size of the detector divided by the magnification. Resampling (or sub-sampling) reduces the number of pixels (and hence increases the pixel size) and corresponds to `binning' (on a detector) and `coarsening' during image processing. This is not the same as `rescaling', which changes the magnification. (c) Reference coordinate system for a spatial frequency distribution with typical annotations; low spatial frequencies correspond to low resolution (infinitely low at the origin on the left), and high spatial frequencies correspond to high resolution (limited by the pixel size; amplitude is abbreviated as Ampl.). The unit of spatial frequency is 1/Å; hence, to calculate the resolution one needs to take the inverse value. (d) Example of the effect of band-pass filtering drawn into the spectrum of spatial frequencies as in (c) with annotation of low-pass and high-pass filter values at the corresponding inflection points. Usage of band-pass filters avoids sharp frequency cuts, which lead to artefacts in Fourier space (Fourier ripples etc.) during image processing. While amplitudes are reduced within the pass (boundaries within the region defined by the two inflection points), they are in part still present outside that region. (e) Concept of FSC calculations using thin sliding windows of spatial frequency shells within which the correlation of amplitudes is calculated between two half maps (for this the obtained image data have been split into two halves and the two corresponding 3D reconstructions were refined independently), resulting in an FSC curve [units are those defined in panel (c)]. (f) Left – FSC curve calculated using a soft-edge mask (e.g. 7 or 9 pixels) as is normally done. Right – FSC curve using a sharp-edge mask, which leads to correlation artefacts at high spatial frequencies and thereby shifts the FSC curve to higher values, giving the false impression of a higher resolution estimation. Using a mask per se is necessary to remove noise outside the core 3D reconstruction and properly evaluate the resolution of the cryo-EM map. (g) A typical FSC curve as can be found in the PDB validation report associated to a given EMDB cryo-EM map deposition file. The resolution estimation indicated here uses both the 0.143 threshold (Rosenthal & Henderson, 2003  ) and the 1/2 bit criterion (van Heel & Schatz, 2005; its numerical value asymptotically approaches 0.1716; the collected information is measured in bits per voxel in Fourier space), these often give overall comparable resolution estimation values as also visible in this example. To obtain the estimated resolution, one has to take the inverse value of the spatial frequency [as in panel (c)] at the intersection point. The 0.5 criterion shown in the PDB validation report here is normally used only for map–model FSC calculations and evaluation of the quality of the derived atomic model. |
![[Figure 3]](hen5001fig3.jpg)
IUCrJ
ISSN: 2052-2525
CRYO | EM
Open 
access
access