Density Thresholding

Domains of proteins are often compact, but divided from other domains by a trough of density. Depending on resolution, this dip in density often helps in the delineation of the domains, by the application of a density threshold that is above the density of the trough.

In principle, molecules consisting of materials with different electron-scattering densities can be divided into their components by application of an appropriate density threshold. A typical example is RNA and protein, a mixture in which RNA stands out on account of its higher scattering density due to the high content of phosphorus atoms. For example, the ribosome embedded in ice is a three-component system, in which three kinds of density transitions are realized: those at the boundaries ice-protein, ice-RNA, and protein-RNA (K├╝hlbrandt, 1982; Frank et al., 1991). Low-resolution density maps pose a problem, since the sharp density steps are washed out, making the determination of the precise boundary uncertain (Frank et al., 1991). The same situation arises in all visualizations of RNA by cryo-EM, as in spliceosomal components (Stark et al., 2001) and RNA polymerase II (Craighead et al., 2002).

This problem can be discussed in terms of the density histogram (figure 6.9), which is a display of the number of voxels in which a certain density is realized, versus the correponding density value. For a high-resolution density map, the density histogram of the ribosome in the above example would consist of three well-separated peaks: one for water (very high because of the large volume within the box around the particle), one for protein, and one for RNA (Zhu et al., 1997).1 However, low resolution will cause each of the peaks to spread and overlap with its neighbor. It is easy to see in the example shown that there are only few small density ranges where the identity of the density mass can be determined with certainty. For example, densities above the density identified as dRNA can only originate from RNA, meaning that the mass obtained by eliminating all density below that density value (i.e., by application of a density threshold) is solely RNA. However, this process has not only eliminated protein and water, but a large part of the RNA, as well. Similarly, there is no density range allowing pure protein to be isolated, since there exists a low-density tail of RNA, mostly originating from boundaries where RNA directly borders water and causes all

'Note that in Zhu et al. (1997), the legends of two key figures showing histograms were erroneously switched: the legend of figure 11 belongs to figure 12 and vice versa.

density values intermediate between water and RNA to be seen in the low-resolution map.

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