How are sym_expand/idx IDs assigned during symmetry expansion?


Can someone please explain to me how sym_expand/idx IDs are assigned to symmetry expanded particles?

I am working with a protein with D6 symmetry, I understand that after symmetry expansion I will have 12 idx IDs (0-11) associated with each sym_expand/src_uid.

My question is how are the idx IDs assigned across the protein?
Or more specifically, are the idx IDs assigned to all 6 subunits in one mirror plane 0-5 before moving to other side of the protein?


Hi @JJtheCryoEMguy!

For your particular (D6) case, here are the symmetry rotations applied to a coordinate axis. In each case, we’re looking down along the Z-axis of the un-rotated object (index 0). In order to support arbitrary point group symmetries, we generate symmetry-related rotations incrementally, which is why they do not appear in a simple order.

As you can see, indices 0, 1, 5, 7, 10, and 11 form the “top” plane, while the others are in the rotated “bottom” plane.

If you don’t mind, could I ask for what type of analysis you need to know which rotation corresponds to which symmetry expansion index?

Hi @rposert, thank you for the explanation and the diagram. It was very helpful.

If you don’t mind, could I ask for what type of analysis you need to know which rotation corresponds to which symmetry expansion index?

I am trying to understand how conformations are distributed across my particle to see if there is cooperation between subunits. To approach this, I had done 3D classification on symmetry expanded and signal subtracted particles. I am using the source ptcl IDs and the symm expansion index numbers from the meta data with respect to each class to see if there is any preference to where each class occurs in the particle (i.e. on the same side of the particle or randomly across it). I figured using the symmetry expansion ID would be an easy way to process the data with custom scripts, provided I knew how the index IDs were being assigned.

Does that make sense? Do you think this is a correct approach?

It’s certainly not a bad idea for a first analysis! It’s important to remember, though, that the symmetry index has a consistent relationship only to the pose of the original particle.

For instance, consider a C4 pseudosymmetric particle. It can be in four symmetry-related poses: A, B, C, or D. Symmetry index 0 will correspond to whichever of those four poses the initial (un-expanded) particle is in, and the others will be related to that pose by some rotation (for the sake of example, let’s say all symmetry indices are related by a 90° rotation).

This means that a particle with some symmetry-breaking feature in the expanded particles with indices 0 and 1 may be the same as a particle with symmetry breaking features in 0 and 3, if the first particle was in pose A and the second in pose D.

As long as you keep that in mind, I think your idea is sound!