The algorithm method used for the 3d-reconstruction.
a method of data collection and reconstruction used for single particles,
typically used initially in a project, to obtain a first low-resolution
reconstruction of the macromolecule [Radermacher et al., 1987]. Two images
of the same specimen field are collected, one with untilted grid, the
other with the grid tilted by 50 to 60 degrees. Any set of particles
presenting the same view in the untilted-specimen image form a
random-conical projection set in the associated tilted-specimen image.
Helical reconstruction is used when the protein of interest forms a
natural helix. Since the helix is a recurring structure with a very
well defined pattern, the repeating pattern of the helix can be
exploited to solve the structure. In this case, no alignment of the
particles is needed, since the individual positions of subunits within
the helix are clearly defined by the shape of the helix. Two common
examples of structures solved by helical reconstruction are TMV and
Icosahedral reconstructions also take advantage of internal symmetry
and repetition to generate a detailed three-dimensional structure from
the data set. In this case, the symmetry is icosahedral (twenty-one sided).
Many viruses exhibit icosahedral symmetry in their capsid proteins,
and this method has been used to solve their structures.
Electron crystallography is similar to x-ray crystallography in that it
exploits the repeating pattern found within a crystal to generate a
structure. Just as with x-ray crystallography, difraction patterns are
generated and are used to define an electron density map. However, it
differs in that the crystal used is a two-dimensional sheet as opposed
to three three-dimensional crystals of x-ray crystallography.
Another reconstruction method searches for the intersection of any two
projections in Fourier space. The Fourier transform of the experimental
projections all form slices around a common core in Fourier space.
Therefore, the intersection of these projections are unique (unless the
projections perfectly overlap), and their relative orientation can be
found when three or more projections are used. A principal problem with
this method is that the handedness of the image is lost. This, however,
can later be corrected by visual examination of the model with other
known structural information.
As its name implies, back projection is the inverse function of projection.
When an n-dimensional object is projected, each projection is an n-1
dimensional sum of its density along the projection axis. Therefore, a
sphere would have circles as its projections. A cube, on the other hand,
would produce either squares, diamonds, or other intermediate parallelograms
depending on the direction of projection. The actual shape, of course,
depends on the orientation from which the projection was made. The reverse
function is called back projection and regenerates the original object.