To add a bit to what others have already said --
The formula that Kay gave ((a11 + a22 + a33 - 1) / 2) throws out 2/3
of the rotational information. A 3D rotation cannot be described
completely by a single angle: minimally three angles are actually
required. There are many different ways, of course, to represent a
3D rotation, and what Kay gave is one component of the "axis-angle"
representation. However, if you aren't interested per se in the axis
of rotation, the angle from that formula will be the minimum possible
angle required to rotate one domain/structure onto another -- and in
that sense it is somewhat more intuitively apprehensible than the
complete rotation. Note that, in general, a translation is also
required to completely specify the transformation necessary to
superimpose two domains, and thus using just a single angle is
ignoring 5/6 of the relevant information.
BTW, the corresponding axis of (unnormalized) rotation is given by
[a21-a12, a02-a20, a10-102] (ignoring the annoying singularities at
180 degrees).
If you use the most recent version of THESEUS to do your
superpositions, the angle-axis representation is given in the
transformations output file along with the matrix representation of
the rotation. And in general the rotation given by the maximum
likelihood method used by THESEUS will be different from that of a
conventional unweighted least-squares superposition (the ML rotation
is much less artifactually biased by regions of a domain, like mobile
loops, that differ in conformation between the two domains being
superpositioned).
http://www.theseus3d.org/
Cheers,
Douglas
On Jul 8, 2007, at 5:21 AM, Bernhard Rupp wrote:
Not that I want to open a can of worms here...
but could someone explain what is meant
with 'angle between domains'?
Thx, br
-----Original Message-----
From: CCP4 bulletin board [mailto:[EMAIL PROTECTED] On Behalf
Of Das,
Debanu
Sent: Saturday, July 07, 2007 7:51 PM
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] how to convert matrix to angle
Hi,
You can also use LSQKAB in CCP4 to get the angle between two similar
domains.
-Debanu.
-----Original Message-----
From: CCP4 bulletin board on behalf of Kay Diederichs
Sent: Sat 7/7/2007 7:30 AM
To: CCP4BB@JISCMAIL.AC.UK
Subject: Re: [ccp4bb] how to convert matrix to angle
Jiamu Du schrieb:
Dear all:
I want to calculate the rotation angle between two similar
domains. By
using Coot, I can superposr the two domain and get the rotation
matrix.
But how to convert this matrix to an angle. Is there any program can
calculate this ?
Thanks.
Jiamu Du,
If you have the rotation matrix
a11 a12 a13
a21 a22 a23
a31 a32 a33
then
(a11 + a22 + a33 - 1) / 2
is the cosine of the angle you're looking for.
HTH,
Kay
--
Kay Diederichs http://strucbio.biologie.uni-konstanz.de
email: [EMAIL PROTECTED] Tel +49 7531 88 4049 Fax 3183
Fachbereich Biologie, Universität Konstanz, Box M647, D-78457 Konstanz
