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*To*: ccp4bb@dl.ac.uk*Subject*: Re: [ccp4bb]: NCS analysis*From*: Edward Berry <eaberry@lbl.gov>*Date*: Thu, 03 Feb 2000 10:52:16 -0800*Organization*: Lawrence Berkeley Laboratory*References*: <200002030929.JAA17796@dlpx1>*Sender*: owner-ccp4bb@dl.ac.uk

*** For details on how to be removed from this list visit the *** *** CCP4 home page http://www.dl.ac.uk/CCP/CCP4/main.html *** Trixie Wagner, Ph.D. wrote: > > I am working on the structure of a tetramer with non-crystallographic 222 > > symmetry. It is not difficult to determine the three two-fold axes > > separately by superimposing dimers, but > > a) they are not necessarily perpendicular to each other and/or might not > > intersect in one point and > > b) from the direction cosines of the axes you cannot conclude where > > exactly to put the two-folds with respect to the tetramer (i.e. > > where the origin of the 222 system is located). > > For a), I don't know of such a program. It should be a fairly simple exercize in geometry to write a program that simultaneously minimizes rmsd for the three operators as a function of 8 parameters: x,y,z at the origin of the 2,2,2 system, x,y,z of a vector parallel to the first axis, and x,y of a vector parallel to the second axis (z being fixed by the requirement for perpendicularity, as is the third vector) b) if your derived operators were perfect 2-fold operators, points on each axis can be found as the midpoint between a point and the point generated from that point by the operator: 0,0,0 -> t1,t2,t3 and the point t1/2, t2/2, t3/2 is on the axis. Operating on another point and likewise taking the midpoint gives a second point on the axis, from which the equation for the line defining the axis can be derived. Repeating this for the other two axes and solving for the intersection of the three lines gives the origin of the system. Because the operators will not be perfect proper 2-folds, the point located thus will not be on the axis, but will be much closer than the starting point. Operate on it again. If it were on the axis, it would be unmoved or only moved along the axis by the screw component of the operator. If it is slightly off the axis, the midpoint between it and the the point generated from it by the operator will be much closer to the axis. This can be repeated until convergence (distance moved in each step is constant and in constant direction- along the axis) to give a point on the axis. Applying your direction cosines, or finding another point on the axis, then gives the equation of the line along the axis. Someone may have an equation for the least-squares closest point between three non-intersecting lines, or be able to derive one. To get back to CCP4, the points should be atoms and you can preform the successive operations with #!/bin/csh -f pdbset xyzin point1.pdb xyzout point2.pdb <<eof transform (ODB) lsq1.o end eof To get the most accurate operators lsqi.pdb, determine them for the whole tetramer, not dimers. Find the operator to take dimer AB to CD as the operator to take tetramer ABCD to tetramer CDAB. This should give a very nearly proper 2-fold with no screw, since operating twice has to bring everything back where it started. Ed

**References**:**[ccp4bb]: NCS analysis***From:*M.D.Winn@dl.ac.uk (M.D.Winn)

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