Hi @olibclarke,
The symmetry option is just there to remind people that if they have symmetry, they should generally always perform symmetry expansion before 3D Var. If you put in a symmetry other than C1, the job will fail with an error message that says to use symmetry expansion.
3D Var is computing eigenvectors of the 3D covariance of the particle images, assuming fixed poses that come from the input. When there is “symmetry” in a particle, this only applies to the consensus structure - any variability mode can break the symmetry. However, the variability mode (assuming the underlying symmetry is a true symmetry) should naturally occur in all symmetric versions of itself.
In this sense there are two kinds of variability modes: modes that are changes/motion within just a single subunit, and modes where there are changes/motion across the entire particle in a coordinated fashion. The first kind are modes where each particle image contains information about multiple positions along the mode (since each subunit is in potentially a different position along that mode). The second kind are modes where each particle image contains information about only one position along the mode (since the entire particle is in only one position) but due to the symmetry, the image could be used as information for all symmetric copies of that same mode.
So for the first kind of mode, symmetry expansion is best. In this case it’s also fine to create a mask around a single subunit, but this is not necessary (since using the subunit mask will make it impossible to find motions across the entire particle). For the second kind of mode, using symmetry expansion will mean that there are many copies of the same mode that can be found (i.e. imaging a symmetric molecule bending along its entire length, in one direction. There are equivalent copies of that mode where the molecule bends in the symmetric versions of that one direction). Symmetry expansion makes sure that every particle counts for each one of these copies, rather than just the single one with which the particle is arbitrarily aligned in the input poses.
The above is still somewhat of a work in progress, and there are other cases (pseudosymmetry?) that should be considered. It would be great to hear your thoughts!