[Chimera-users] Measure rotation using "measure rotation" and "match"

[Elaine Meng]

Dear Hui-Ting,
You really should send questions to chimera-users at cgl.ucsf.edu (CC’d here) instead of to me directly, since other people may be able to give better answers.

In this case, I’m not certain that I understand what you are trying to do.  First, your question, and then I will try to answer below:

> On Apr 10, 2018, at 3:47 AM, Chou, Hui-Ting <chouh at janelia.hhmi.org> wrote:
> 
> Dear Elaine,
> I am trying to measure the rotation angle and shift of the domain movement, but don’t quite understand the output values when I run “measure rotation” and “match”. I fit a pdb file to two different EM maps and saved them separately (but saved relatively to the same map). When I opened these two pdb files and run “measure rotation #9 #10”. The rotation angle is 10.36 degree and the shift is 1.39 angstrom. The Reply Log shows--  
> Position of prop_fit4.9A_relative4.9Amap.pdb (#10) relative to prop_fit14A_relative4.9Amap.pdb (#9) coordinates:
>   Matrix rotation and translation
>      0.98376605  -0.01263314   0.17901049 -36.94403456
>      0.01042163   0.99985738   0.01328910  -3.85711966
>     -0.17915284  -0.01120778   0.98375741  42.31539129
>   Axis  -0.06809615   0.99561826   0.06408739
>   Axis point 215.26774421   0.00000000 225.37339748
>   Rotation angle (degrees)  10.36217664
>   Shift along axis   1.38741058
>  
> But when I run “match showmatrix true #9 #10”. It gave me two rotation angles and shifts for “the motion of #9 in #10 coordinate system” and “motion of #9 original coordinates in #10 coordinate system”. How do I obtain the actual rotation and shift from these two matrices? Should I use the values calculated from “measure rotation” or “match”?  And could I measure the rotation angle and shift from two atomic coordinates with a specific rotation axis?
> 
> Executing match ['#9', '#10'], no iteration
> Motion of #9 in #10 coordinate system
> Matrix rotation and translation
> 0.97764856 0.13202668 -0.16362225 13.44032867
> -0.15552155 0.97782730 -0.14023843 73.46708163
> 0.14147909 0.16255069 0.97650445 -62.31730866
> Axis 0.58548705 -0.58995806 -0.55601655
> Axis point 447.68302710 0.00000000 23.93534493
> Rotation angle (degrees) 14.98575215
> Shift along axis -0.82390335
> Motion of #9 original coordinates in #10 coordinate system
> Matrix rotation and translation
> 0.93081946 0.14002215 -0.33759285 62.65401058
> -0.19045400 0.97420342 -0.12105775 75.31116754
> 0.31193334 0.17697881 0.93347528 -89.61097572
> Axis 0.37852984 -0.82494928 -0.41973067
> Axis point 314.38283856 0.00000000 122.06207432
> Rotation angle (degrees) 23.18345231
> Shift along axis -0.79900536
> RMSD between 2428 atom pairs is 0.001 angstroms
>  
> I failed to find the answers online, so it would be greatly appreciated If you could spare time to drop few lines or suggest me where to find the related document on the UCSF Chimera website!
>  
> Thank you very much!
> Best,
> Hui-Ting

It depends on whether you want the relationship of two sets of coordinates in the positions when you open them, or after matching them (superimposing their atoms).  “measure rotation” gives you the relative position without matching, “match” gives you the relative position after they are matched.  

However, I would expect “measure rotation” to give you only identity matrix when you reopen the saved PDB files and don’t move them relative to each other. As I understand it, it  knows nothing about the structures in the files, it only cares about whether they were moved relative to one another since opening.  So that part of your question is a mystery me.

If the 2 PDB files are similar or the same structures in 2 different fitted positions and you want to know how the 2 fitted positions relate to each other, I believe it would make sense to use the “match” result, but I don’t know why it gives two sets of results.  Since “measure rotation” did not give an identity matrix, however, I’m suspicious of the situation (it suggests you moved one relative to the other after opening the files).  I might start over in a new Chimera session and just open those two PDB files again and try “measure rotation” without moving one relative to the other, and then “match."

I hope this helps,
Elaine
-----
Elaine C. Meng, Ph.D.                       
UCSF Chimera(X) team
Department of Pharmaceutical Chemistry
University of California, San Francisco