Re: [ccp4bb]: Self rotation function interpretation

["Eleanor J. Dodson" <ccp4@ysbl.york.ac.uk>]

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Andrew Gulick wrote:
> 
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> 
> Greetings all,
> 
> I was wondering if anyone could offer any suggestions in interpretting
> the following self rotation function.  My space group is P2(1) with
> beta=91.8.  I expect two molecules in the AU.
> Running through CCP4i MOLREP, the output peak list looks like:


 In discussing any monoclinic space group you must know the
orthogonalisation code 

Do you have the Z axis parallel to be, or the default in P21 , parallel
to c*?

 The first peak is the origin - yes..
But the directon of the cryst 2 fold depends on your orthogonalisation..


 Solutions 2 and 3 here are almost the same - if beta = 0.0, you can add
Alpha + Gamma;
ir 
>  Sol_RF  3   107.50    0.00   72.50    0.00    0.00 -180.00     5527.     11.13
is identical to:
>  Sol_RF  3   180.0    0.00    0.00    0.00    0.00 -180.00     5527.     11.13


 Both represent 2 fold rotations around the Z axis, whatever that is, 
which is ~ 2 degrees
off that for soln_2 

 > 
>              alpha    beta   gamma   theta    phi    chi        Rf    Rf/sigma
> 
>  Sol_RF  1   330.00    0.00   30.00    0.00    0.00    0.00    0.1278E+05 25.73
> 
>  Sol_RF  2   180.00    4.28    0.00  177.86    0.00  180.00    0.1003E+05 20.21
> 
>  Sol_RF  3   107.50    0.00   72.50    0.00    0.00 -180.00     5527.     11.13
> 
>  Sol_RF  4    56.40  177.66  123.60   88.83   56.40  180.00     1263.      2.54
> 
......
> 
> My interpretation is that the first solution Sol_RF 1 is the origin and Sol_RF 2 is the
> crystallographic
> two-fold.  This would suggest that Sol_RF 3 is the non-crystallographic 2-fold, but I can't make
> sense of
> the alpha,beta,gamma compared to the theta,phi,chi representations.


 I just trust the mathematics! it is VERY hard to visualise Eulerian
angles, unless they happen to be simple..

> 
> Running the self rotation function with AMORE gives the following peak list:
> Best Solution:   359.999     0.000     0.000   100.000
> 
>  SELF:: Self Rotation Function   1
> 
>                   ALPHA    BETA   GAMMA     Omega     Phi   Kappa      DC_X   DC_Y   DC_Z  CC_P
> 
>  SOLUTIONRS      360.00    0.00    0.00      0.00  999.00    0.00     0.000  0.000  1.000 100.0
> 
>  SOLUTIONRS      180.00    4.13    0.00      2.07 -180.00  180.00    -0.036  0.000  0.999  82.3


 Exactly the same result as soln_2 above
> 
>  SOLUTIONRS      540.00    0.00    0.00      0.00  999.00  180.00     0.000  0.000  1.000  52.9
> 
>  SOLUTIONRS      180.00    0.00    0.00      0.00  999.00  180.00     0.000  0.000  1.000  52.9
> 


 alpha = 540 = 180+360 so is identical - the problem is in the Amore
peak picking..

If omega is 0.0 or 180, then phi is indeterminate - and it is listed as
999 as a marker..

I think/hope this is described in the documentation..

> Again, I'm a little confused by some of the angles, (alpha=540?  phi= 999?) and if the
> first and second peaks are the origin and crystallographic 2-fold, this doesn't appear
> to have found a non-crystallographic 2-fold.


 The origin and the crystallographic symmetry operators MUST have the
same peak height, so soln 2 is not crystallographic.. The worry is
whether irt is a shoulder ofthe cryst peak..

But till you say what the ortho code is that is not possible to
determine.

 For Z along b the cryst 2 fold has omega = 0, phi indeterminate, chi =
180 and should have a peak height of 100.

 If the Z is along c* as it prob. is,  then your solution 2 is a NCS
two-fold and 3 and 4 are shoulders of that peak ( see omega is only
2degrees off the axis..)

Have you done an hklview and looked at the hol h1l etc sections - can
you see any two foldness there?

And what is beta - I would guess 94 degrees...

Eleanor