I have a ring-shaped protein sample. When I do homogeneous refinement with C1 symmetry, the particle distribution plot showed uneven distribution (figure 1), however if I do a subsequent homo refinement with C6 symmetry, the particle distribution looks very different with more even distribution (figure 2). I am puzzled by why this happens. In my understanding, when you impose symmetry, you are basically re-inserting each particles fourier transforms N times where N is the symmetry you impose and each insertion is aligned 360/N degrees relative to the original particle. But how does imposing symmetry affect particle distribution?

That C1 symmetry reconstruction is actually fairly even, just aligned (roughly) against the x-axis rather than the z-axis which is what symmetry aligns against. The reason they look so different is because of the Mercator projection - how the 2D plots distort the view at the “poles” of the map, over-emphasising the sampling spacing. It’s also why I talk about “equatorial/side” and “polar/top” views for projections/particles, although it’s only really applicable to symmetric objects… but it seems to help some students understand more easily.