Symmetric Particles in Subtomogram Averaging (new pipeline)

Symmetric biomolecules really aren't (symmetric). At some limiting resolution, the symmetry will always be broken. Consider 3 examples:

• small rigid enzyme - symmetry breaking might be at the level of independent individual sidechain motion, may only impact at 3-5 Å resolution
• C4 ion channel - Each of the 4 subunits will somewhat independently bind modulators or be otherwise conformationally variable, while maintaining overall symmetry, may impact at the level of 6-12 Å resolution
• C8 nuclear pore complex - While ostensibly 8-fold (some parts D8) symmetric, in reality, the variations in separation of the inner and outer nuclear membranes, interactions with substrates, etc, require significant accommodations by the complex, resulting in large 20-40 Å resolution symmetry breaking

In canonical single particle reconstruction, you would simply impose the specified symmetry and hope for the best. Clearly, however, the structure resulting from a symmetrized average of non-identical or mispositioned components will not result in the best possible subunit resolution. We instead need a strategy to look at a single subunit at a time, and refine that, characterizing/classifying not entire symmetric particles, but on an individual subunit basis.

EMAN2 has 2 primary methods to permit this in the new subtomogram averaging pipeline (using e2spt_refine_new and related programs):

Approach 1 - re-extract particles centered on each oriented subunit

In this approach you begin with a normal symmetry-imposed refinement. Then, when you've done the best you can with the normal refinement, you use the resulting per-particle orientations to extract a new set of particles for each of the N subunits. ie - if you have N C4 particles, you will produce 4N smaller particles with no symmetry, and known initial orientations. These orientations could then be further refined or the 4N particles could be classified to produce self-similar subsets.

1. Run a normal refinement following the tutorial. Be sure to use e2spt_refine_new when presented with the option of the older programs.

2. The refinement will produce aliptcls3d_XX.lst and aliptcls2d_XX.lst files containing the particles with per-particle alignment data. The 3-D alignments are required for extraction of particles from the original

Approach 2 - replicate each particle N times and align with a mask

note about "subtraction" methods - In the mid 2000s, EMAN2 offered an experimental approach for single particle analysis (which still exists) for not just masking out the individual subunits from symmetric particles, but subtracting away the density for the other subunits. That is, if you had a C4 particle, when extracting a subunit, you would subtract away the density for 3 of the 4 subunits, ostensibly leaving behind only the density for the subunit you wish to consider. This idea later propagated into Relion where it is considered a standard method there. However, there is a logical flaw of sorts in this scheme. If the macromolecule was perfectly C4 symmetric, it would, indeed, be possible to subtract away the other subunits. However, in that case, there would be no reason to do so, since a C4 refinement would yield optimal results. If the symmetry is broken then any subtraction we do will leave behind artifacts wherever the symmetry is broken, and, indeed, these artifacts are the only thing which should interfere with the correct alignment of the particle in the first place, so in the end, subtraction doesn't really accomplish anything very useful, with some minor caveats.