Re: [ccp4bb] how to convert matrix to angle

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CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Previous message:
Subject: Re: anisotropic displacement parameter matrix shelxl
From: Gerard Bricogne gb10 {- at -} GLOBALPHASING {- dot -} COM
Date: 2007-07-08

Next message:
Subject: Re: how to convert matrix to angle
From: Paul Emsley emsley {- at -} YSBL {- dot -} YORK {- dot -} AC {- dot -} UK
Date: 2007-07-08

Subject: Re: how to convert matrix to angle
From: "Douglas L {- dot -} Theobald" dtheobald {- at -} BRANDEIS {- dot -} EDU
Date: 2007-07-08

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:CCP4BB@JISCMAIL.AC.UK] 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: Kay.Diederichs@uni-konstanz.de Tel +49 7531 88 4049 Fax 3183
> Fachbereich Biologie, Universität Konstanz, Box M647, D-78457 Konstanz

CCP4bb navigation

CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Previous message:
Subject: Re: anisotropic displacement parameter matrix shelxl
From: Gerard Bricogne gb10 {- at -} GLOBALPHASING {- dot -} COM
Date: 2007-07-08

Next message:
Subject: Re: how to convert matrix to angle
From: Paul Emsley emsley {- at -} YSBL {- dot -} YORK {- dot -} AC {- dot -} UK
Date: 2007-07-08