My understanding is that with tetrahedral, typically a 2-fold is along each axis (X, Y, and Z) and the 3-fold axes are across the cube diagonals. Similar to this image:
This convention allows for one to easily address the D2/C2 symmetry that is inherently present in T symmetry. While it still requires a rotation to center the C3 symmetry on an axis, CryoSPARC’s current method still only allows for a single C3 axis on X, Y, or Z, and requires rotations to reach the other three.
I’m by no means a symmetry expert here, so I could be wrong, but I was wondering if this placement was intentional, and if so, what the rationale was for it?
Thanks for the post! I believe our convention for tetrahedral symmetry (3 fold axis on Z) is consistent with RELION’s conventions. (Note that this isn’t true for all symmetry groups — in particular, our convention for Dn symmetry places the two fold axis along Y, rather than X). We’d like to document our symmetry conventions better, and we’ve made a note to describe this on our guide.
Could you describe your rationale for preferring the indicated convention? Do you mean that, if T symmetry is implemented with the 2fold axis along Y, then the inherent D1 group inside the T group is already aligned?
Another thought — Since the D1 (equivalent to C2) group, comprising a single 2-fold rotation axis, is effectively contained within the T group, you could use Volume Alignment Tools with the tetrahedral volume but specify a symmetry group of D1 to obtain a rotated output volume with the two fold axis along Y.
I’m trying to examine symmetry breaking features along a 3-fold axis, and most of the software I’m used to using places it as described in my original post. By placing the 2-folds along X, Y, and Z, it lets me easily address the two different major subgroups (C3 and D2). With the 3-fold on Z, at most I can address a single 3-fold, but still need rotations to get to the other 3. With 2-folds on X, Y, and Z, I can address all the 2-fold symmetry in the particle with no rotations. That said, my PI was a crystallographer and so many of our tools are coming from that domain.
This is ultimately what I wound up doing.
I think if RELION chose that convention, while the convention doesn’t make a lot of sense to me, CryoSPARC sticking to it does.
I hope it is ok to revive this old discussion but the first post explains my problem better than I can. I am trying to symmetrize my monomer fit into a tetrahedral cryosparc map with chimera. Unfortunately, since the axis are oriented as described in the first post this is not possible. Neither T,222 nor T,z3 works (I can only use C3 getting only 2 of the missing 11 subunits).
I have another tetrahedral map which I had to mirror to get the handedness right and this one now has chimeras T,z3 symmetry. Does anyone know how I can transform my normal tetrahedral map to follow the chimera tetrahedral convention?
