Tianyang Liu asked on the ChimeraX mailing list how to take a C2 symmetric map with symmetry axis that does not align with x, y, or z axes and make a new map so the symmetry axis aligns with the z axis. To do this you resample the map on a new 3d grid where the z-axis is parallel the symmetry axis. This resampling is going to reduce the quality of the map, so I don’t advice it. Instead you the cryoEM single-particle reconstruction software should put the symmetry axis on the z-axis if you want to preserve map quality. But here is an example how to do the resampling in ChimeraX if you want to.

In this example I make the map from atomic model PDB 7qa1 which has symmetry axis approximately along the xy diagonal. I find the symmetry axis by making two copies of the map, rotating one copy 180 degrees about the approximate axis and fitting it to the first copy. Once I know the axis direction I tilt one of the copies to make the axis along z, then I center it at 0,0,0 and resample it on a new grid at a slightly finer grid spacing. Here are the commands I used. It is a rather tedious process – there is no special ChimeraX command to do this realignment.

```
open 7qa1
molmap #1 3 gridSpacing 0.8
close #1
volume copy #2
turn 1,1,0 180 model #2
fit #2 in #1
> Axis -0.72099508 -0.69293944 0.00101434
turn 0.69293944,-0.72099508,0 89.942 models #2 coordinateSystem #1
volume new size 256,256,256 gridSpacing 0.5 origin 0,0,0
volume #3 showOutlineBox true
volume #3 originIndex 127.5,127.5,127.5
measure center #2
> Center of mass xyz scene coordinates for 7qa1 map 3 = (8.81, -11.79, -28.81)
move -8.81,11.79,28.81 models #2 coordinateSystem #3
volume resample #2 onGrid #3
save aligned.mrc models #4
```

The rotation by 89.942 degrees was from acos(0.00101434), the arc-cosine of the z component of the symmetry axis unit vector z component. The tilt is done about axis -vy,vx,0 in the xy plane which is perpendicular to the symmetry axis vx,vy,vz.

Original map with symmetry axis along xy diagonal. |
New map with symmetry axis along z. |

Tom Goddard, May 22, 2023