Re: [ccp4bb] proper or improper ncs?
Hi, everybody, In addition to all comments, just as a pleasure to remind an old-fashion "no computer" way to calculate the rotation angle. The trace of a rotation matrix (the sum of its diagonal elements) is always equal to 2*cos(kappa)+1. Calculate it yourself for kappa = 180° and compare with the trace of the Francis's matrix. ROTA 1: -0.5444 -0.22020.8094 ROTA 2:0.8330 -0.02780.5526 ROTA 3: -0.09910.97510.1985 One can easily reject (still without a computer) other "crystallographic" angles. Best regards, Sasha Urzhumtsev -Message d'origine- De : CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] De la part de Ian Tickle Envoyé : mardi 21 février 2012 15:13 À : CCP4BB@JISCMAIL.AC.UK Objet : Re: [ccp4bb] proper or improper ncs? Francis, It's very easy to spot a 2-fold rotation or screw because the matrix must be symmetric (or nearly so)**. Your matrix very obviously is not (i,e, A12 ne A21, A13 ne A31 etc). ** Proof: A rotation matrix is orthogonal, which implies inverse = transpose: A^-1 = A~. A 2-fold rotation is proper which implies AA = I or A^-1 = A. Take these together and you get A = A~ i.e. A is symmetric. Surprising how many people aren't aware of this! Cheers -- Iann On 21 February 2012 13:47, Francis E Reyes wrote: > Hi all > > This structure has the following ncs (output via > phenix.simple_ncs_from_pdb) OPERATOR 1 > CENTER: 18.3443 -55.4605 23.0986 > > ROTA 1: 1. 0. 0. > ROTA 2: 0. 1. 0. > ROTA 3: 0. 0. 1. > TRANS: 0. 0. 0. > > OPERATOR 2 > CENTER: 37.0405 -23.8676 -14.9388 > > ROTA 1: -0.5444 -0.2202 0.8094 > ROTA 2: 0.8330 -0.0278 0.5526 > ROTA 3: -0.0991 0.9751 0.1985 > TRANS: 45.3456 -78.7231 53.0085 > > > It looks two-foldish but I'm not sure if it's proper or improper. (I'm trying > to rationalize the lack of peaks on the self rotation maps). > > > Any help would be appreciated. > > F > > > > - > Francis E. Reyes M.Sc. > 215 UCB > University of Colorado at Boulder
Re: [ccp4bb] proper or improper ncs?
I've had a couple of requests for the jiffy program that interpreted the transformation, so here's the FORTRAN source code for decomp.f, for anyone who is interested. It's very simple, so all you should need to do is something like: gfortran decomp.f -o decomp to get an executable (or replace gfortran by g77 or f77, as appropriate). Put the matrix and vector into a file (say matvec.dat), then: decomp < matvec.dat It takes a matrix and vector as four lines on standard input, then decomposes the transformation into a rotation around an axis, a point on the axis, and a translation parallel to the axis. Regards, Randy decomp.f Description: Binary data On 21 Feb 2012, at 14:01, Randy Read wrote: > Hi, > > I'm sure there's a way to do this in CCP4, but using some little jiffy > programs I've collected over the years... > > That's a 133 degree rotation around an axis defined by the unit vector > 0.290647, 0.624977, 0.724519, and there's a small screw component of about > 2.4A along the axis, so it's an improper rotation. > > On the other hand, if you combine a crystallographic symmetry operator with > that transformation, you might still find that it's equivalent to a proper > rotation. > > Regards, > > Randy Read > > On 21 Feb 2012, at 13:47, Francis E Reyes wrote: > >> Hi all >> >> This structure has the following ncs (output via phenix.simple_ncs_from_pdb) >> OPERATOR 1 >> CENTER: 18.3443 -55.4605 23.0986 >> >> ROTA 1:1.0.0. >> ROTA 2:0.1.0. >> ROTA 3:0.0.1. >> TRANS: 0.0.0. >> >> OPERATOR 2 >> CENTER: 37.0405 -23.8676 -14.9388 >> >> ROTA 1: -0.5444 -0.22020.8094 >> ROTA 2:0.8330 -0.02780.5526 >> ROTA 3: -0.09910.97510.1985 >> TRANS:45.3456 -78.7231 53.0085 >> >> >> It looks two-foldish but I'm not sure if it's proper or improper. (I'm >> trying to rationalize the lack of peaks on the self rotation maps). >> >> >> Any help would be appreciated. >> >> F >> >> >> >> - >> Francis E. Reyes M.Sc. >> 215 UCB >> University of Colorado at Boulder > > -- > Randy J. Read > Department of Haematology, University of Cambridge > Cambridge Institute for Medical Research Tel: + 44 1223 336500 > Wellcome Trust/MRC Building Fax: + 44 1223 336827 > Hills RoadE-mail: rj...@cam.ac.uk > Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk -- Randy J. Read Department of Haematology, University of Cambridge Cambridge Institute for Medical Research Tel: + 44 1223 336500 Wellcome Trust/MRC Building Fax: + 44 1223 336827 Hills RoadE-mail: rj...@cam.ac.uk Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk
Re: [ccp4bb] proper or improper ncs?
Francis, It's very easy to spot a 2-fold rotation or screw because the matrix must be symmetric (or nearly so)**. Your matrix very obviously is not (i,e, A12 ne A21, A13 ne A31 etc). ** Proof: A rotation matrix is orthogonal, which implies inverse = transpose: A^-1 = A~. A 2-fold rotation is proper which implies AA = I or A^-1 = A. Take these together and you get A = A~ i.e. A is symmetric. Surprising how many people aren't aware of this! Cheers -- Iann On 21 February 2012 13:47, Francis E Reyes wrote: > Hi all > > This structure has the following ncs (output via phenix.simple_ncs_from_pdb) > OPERATOR 1 > CENTER: 18.3443 -55.4605 23.0986 > > ROTA 1: 1. 0. 0. > ROTA 2: 0. 1. 0. > ROTA 3: 0. 0. 1. > TRANS: 0. 0. 0. > > OPERATOR 2 > CENTER: 37.0405 -23.8676 -14.9388 > > ROTA 1: -0.5444 -0.2202 0.8094 > ROTA 2: 0.8330 -0.0278 0.5526 > ROTA 3: -0.0991 0.9751 0.1985 > TRANS: 45.3456 -78.7231 53.0085 > > > It looks two-foldish but I'm not sure if it's proper or improper. (I'm trying > to rationalize the lack of peaks on the self rotation maps). > > > Any help would be appreciated. > > F > > > > - > Francis E. Reyes M.Sc. > 215 UCB > University of Colorado at Boulder
Re: [ccp4bb] proper or improper ncs?
Hi Francis, a quick insertion of your rotation matrix into CONVROT (by Alexandre Urzhumtsev) gives the following equivalent polar rotation angles (definition as in X-PLOR/CNS or Rossmann, 1962): phi,psi,kappa : 111.86 128.68 133.38 291.86 51.32 226.62 For a proper two-fold, a kappa of 180 degrees would be expected. This looks (very) improper to me. Best regards, Dirk. Am 21.02.12 14:47, schrieb Francis E Reyes: Hi all This structure has the following ncs (output via phenix.simple_ncs_from_pdb) OPERATOR 1 CENTER: 18.3443 -55.4605 23.0986 ROTA 1:1.0.0. ROTA 2:0.1.0. ROTA 3:0.0.1. TRANS: 0.0.0. OPERATOR 2 CENTER: 37.0405 -23.8676 -14.9388 ROTA 1: -0.5444 -0.22020.8094 ROTA 2:0.8330 -0.02780.5526 ROTA 3: -0.09910.97510.1985 TRANS:45.3456 -78.7231 53.0085 It looks two-foldish but I'm not sure if it's proper or improper. (I'm trying to rationalize the lack of peaks on the self rotation maps). Any help would be appreciated. F - Francis E. Reyes M.Sc. 215 UCB University of Colorado at Boulder -- *** Dirk Kostrewa Gene Center Munich Department of Biochemistry Ludwig-Maximilians-Universität München Feodor-Lynen-Str. 25 D-81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de ***
Re: [ccp4bb] proper or improper ncs?
Hi, I'm sure there's a way to do this in CCP4, but using some little jiffy programs I've collected over the years... That's a 133 degree rotation around an axis defined by the unit vector 0.290647, 0.624977, 0.724519, and there's a small screw component of about 2.4A along the axis, so it's an improper rotation. On the other hand, if you combine a crystallographic symmetry operator with that transformation, you might still find that it's equivalent to a proper rotation. Regards, Randy Read On 21 Feb 2012, at 13:47, Francis E Reyes wrote: > Hi all > > This structure has the following ncs (output via phenix.simple_ncs_from_pdb) > OPERATOR 1 > CENTER: 18.3443 -55.4605 23.0986 > > ROTA 1:1.0.0. > ROTA 2:0.1.0. > ROTA 3:0.0.1. > TRANS: 0.0.0. > > OPERATOR 2 > CENTER: 37.0405 -23.8676 -14.9388 > > ROTA 1: -0.5444 -0.22020.8094 > ROTA 2:0.8330 -0.02780.5526 > ROTA 3: -0.09910.97510.1985 > TRANS:45.3456 -78.7231 53.0085 > > > It looks two-foldish but I'm not sure if it's proper or improper. (I'm trying > to rationalize the lack of peaks on the self rotation maps). > > > Any help would be appreciated. > > F > > > > - > Francis E. Reyes M.Sc. > 215 UCB > University of Colorado at Boulder -- Randy J. Read Department of Haematology, University of Cambridge Cambridge Institute for Medical Research Tel: + 44 1223 336500 Wellcome Trust/MRC Building Fax: + 44 1223 336827 Hills RoadE-mail: rj...@cam.ac.uk Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk
[ccp4bb] proper or improper ncs?
Hi all This structure has the following ncs (output via phenix.simple_ncs_from_pdb) OPERATOR 1 CENTER: 18.3443 -55.4605 23.0986 ROTA 1:1.0.0. ROTA 2:0.1.0. ROTA 3:0.0.1. TRANS: 0.0.0. OPERATOR 2 CENTER: 37.0405 -23.8676 -14.9388 ROTA 1: -0.5444 -0.22020.8094 ROTA 2:0.8330 -0.02780.5526 ROTA 3: -0.09910.97510.1985 TRANS:45.3456 -78.7231 53.0085 It looks two-foldish but I'm not sure if it's proper or improper. (I'm trying to rationalize the lack of peaks on the self rotation maps). Any help would be appreciated. F - Francis E. Reyes M.Sc. 215 UCB University of Colorado at Boulder
