A bit late but I didnt answer in time.
This is one of the cases where I still wheel out ALMN to do the self
rotation. It generates ALL symmetry peaks and allows you to select which
axis you want to take as the polar axis. (ncode = 1 c*, ncode = 2 a*,
ncode = 3 b* and so on)
And the program output also makes an attempt to explain what it is doing!
A script
#!/bin/csh -f
#
almn \
hklin /y/people/ccp4/projects/mao/maon5_all_scaleit1.mtz \
MAPOUT /y/work/ccp4//almn.map \
<<eof
SELF 3 25
RESO 10 3.5
TITL Jean
CRYS file 1 orth 1 flim 1 10000000000000
LABI FILE 1 F=F_natlo
LIMIT 0 180 5 1 ! Beta limit 90 because of symmetry
! If in doubt set Beta limit 180..
FIND 5 40
NOPR
MAP
END
eof
Dirk Kostrewa wrote:
Dear CCP4ers,
I've asked you about symmetry in stereographic projections of
self-rotation functions, because I have in a monoclinic space group
with beta=97 a peak for a NCS 7-fold axis at Phi=83, Psi=90,
Kappa=51.4. In this self-rotation function, calculated with GLRF, the
monoclinic b-axis is oriented from south-pole to north-pole. Thus,
with Psi=90, the 7-fold lies in the a,c-plane, and I was wondering
wether it points along the c-axis by some symmetry element, since
83=180-97. Pierre Rizkallah pointed to the fact that the self-rotation
function is calculated in Patterson space which has an inversion
centre, and Ian Tickle has pointed me to the POLARRFN documentation
that discusses some of these symmetries. From this, I can, in my case,
construct the following symmetry-equivalent positions:
(1) Original Peak: Phi, Psi, Kappa --->
83, 90, 51.4
(2) General equivalent position: 180+Phi, 180-Psi, -Kappa --->
263, 90, -51.4
(3) Crystallographic Dyad || Poles: 180+Phi, Psi, Kappa --->
263, 90, 51.4
(4) (3) combined with (2): Phi, 180-Psi, -Kappa --->
83, 90, -51.4
Thus, none of these combinations gives a Phi-angle of 97 degrees.
However, meanwhile Liang Tong, the author of GLRF, explained to me,
that in his convention, a positive Phi angle goes from +X (=a) to -Z
(=-c*), which means that Phi=83 points really along the (-)c-axis
(thus confirming my initial hypothesis).
7-fold
/
/
/
b-------------- a
/|
/ |
/ |
/ |
c c*
So, many thanks to all of you who replied and helped me to solve this
puzzle!
I would still be interested in a textbook or paper discussing symmetry
in stereographic projections, though ...
Best regards,
Dirk.
Am 22.11.2007 um 14:40 schrieb Dirk Kostrewa:
Dear CCP4ers,
does any of you have a good reference describing the symmetry of
crystallographic stereographic projections? There is a lot of
literature describing rotational symmetry in Eulerian angular space,
but I'm not aware of any for polar angles. In particular, I've
calculated a self-rotation function for a crystal in space group C2
with a monoclinic beta-angle of 97 degrees in a convention where Phi
is the angle from the x-axis (=a-axis) and Psi is the angle from the
monoclinic b-axis. I get a beautiful peak for a seven-fold rotation
axis at Phi=83 degrees and Psi=90 degrees. I think that the
seven-fold NCS-axis should point along the crystallographic c-axis,
but then I would expect Phi=97 and Psi=90. Presumably, there must be
a symmetry with the term Phi' = 180-Phi, but I would like to _know_
it. I would be grateful for any pointer to a good reference
describing symmetry in crystallographic stereographic projections,
also for future cases.
Best regards,
Dirk.
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: [EMAIL PROTECTED]
*******************************************************
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: [EMAIL PROTECTED]
*******************************************************
