Comparison of Common Lines Versus Random Conical Methods

Several macromolecules have been reconstructed with both random-conical and common-lines methods for initial angle assignment (though both using the same 3D projection matching approach in the refinement), and a comparison shows that the results are equivalent—if one abstracts from differences in filtration, representation, and quality of the data, which are not germane to the particular methods of angular assignment used. Examples for such comparisons of contemporaneous studies are the E. coli 70S ribosome (Frank et al., 1995a; Stark et al., 1995), calcium release channel (Radermacher et al., 1994a,b; Serysheva et al., 1995), and a ribosomal release complex (Klaholz et al., 2003; Rawat et al., 2003).

Since the common-lines method is based on the presence of multiple views covering the whole angular space, it can be seen as complementary to the random-conical method, which exploits a different situation: the presence of a few preferred views, or even a single one.

Common-lines methods require a minimum number of views to succeed— otherwise the initial reconstruction becomes so crude that it cannot be used in the refinement, and, at any rate, not enough data are present, according to the premise, to fill the angular range as required for a meaningful reconstruction.

In contrast, the random-conical method works in both extremes of angular prevalence—with projections showing a single view, as well as a large range of different views. In the latter case, subsets of particles falling in different views can be handled one at a time, but only a few, most populous subsets need be used (see Penczek et al., 1994; Radermacher et al., 2001).

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