Volumes, represented as a lexicographic string of density values arranged on a 3D grid, can be subjected to the same techniques of multivariate data analysis (MDA) and classification as earlier discussed for images in chapter 4. Again, the fundamental requirement is that they are perfectly aligned, so that in each case the lexicographic index of the array refers to the same point in space. Three-dimensional masking is used to focus the analysis on the relevant region of the molecule while discarding the surrounding densities.
These volumes can be multiple reconstructions of the same molecule from different single-particle data sets or from the same data set but with different starting conditions of a common-lines algorithm (Penczek et al., 1996). In the latter case, classification is used to find a core group of density maps most consistently reproduced. They can be single-particle reconstructions representing the same molecule in different experimental conditions or states, in which case it might be desirable to explore the similarity relationships between the density maps that could contain clues on the way the states evolve over time. They can also be separate tomographic reconstructions of several molecules, where the objective is to find those that are most consistently preserved (Walz et al., 1997b; Bohm et al., 2001). Finally, they can be pseudo-repeats of a 3D ordered structure, such as the insect flight muscle (Winkler and Taylor, 1999; Chen et al., 2002b; Pascual-Montano et al., 2002), representing the force-generating interaction between actin and myosin in different states. In this case, MDA and classification are able to group the different motifs, so that they can be separately averaged. The resulting density maps provide a view of the dynamically changing structure.
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