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*To*: ccp4 <ccp4bb@dl.ac.uk>*Subject*: summary dm-averaging*From*: Jan Abendroth <Jan.Abendroth@uni-koeln.de>*Date*: Wed, 24 Nov 1999 08:49:38 +0100*Organization*: Uni Koeln - Biochemie*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 *** Dear all, thanks a lot for all the reply concerning my question on dm-averaging. Due to the proposals in the last week here is a short summary: MY QUESTION: > Within the the asymmetric unit of my crystal there are six copies of the > protomer grouped as three dimers A (consisting of A1 and A2), B and C. > I could determine the following symmetry operators: > inter-dimer: A -> B > B -> C > intra-dimer: A1 -> A2 (from subunit 1 of dimer A to subunit 2 of dimer 1) > B1 -> B2 > C1 -> C2 > > All symmetry operators are 2-folds with a transition-component. None of > them falls on a crystallographic axis. SORRY FOR THIS CONFUSING STATEMENT. I MENT THAT THE OPERATOR CONSISTS OF THE 3X3 MATRIX AND A VECTOR. > > For the symmetry operations A -> B, A -> B and A1 -> A2 I use A as mask, > for B1 -> B2 i use B as mask and for C1 -> C2 C as mask. > > The question: > Are these symmetry operations enough to cover the whole symmetry? > Or do I have to specify the operations A -> C, A1 -> B1, A1 -> B2 ,... > seperately? REPRESENTATIVELY FOR ALL THE ANSWERS THE SUGGESTION FROM KEWIN COWTAN: > The following fundamental principle should be applied... > > YOU ONLY NEED ONE MASK FOR `dm'. IF YOU HAVE MORE THAN ONE MASK YOU > ARE DOING SOMETHING WRONG (unless you are an expert and are solving a > very specific problem, in which case you know all about it). > > What you need to do is supply one mask, which covers A1, and the > operators which map A1-A1(*), A1-A2, A1-B1, A1-B2, A1-C1, A1-C2. > > If your dimer rotations are self-inverse, then you mask could equally > well cover A instead of A1. > > If all 6 ncs ops form a closed group, then you could use a haxamer mask. > > (*)-the identity. > HOW TO GENERATE THE SYMMETRY OPERATOR FROM A1-B2 IF YOU JUST KNOW THE OPERATORS A-B AND B1-B2? (A1-B2) = (B1-B2)x(A-B): multiply the matrices, take the right order! As all symmetry operators X consist of a 3x3 matrix M AND a vector t for the multiplication you have to multiply the augmented 4x4 matrices: (m11 m12 m13 t1) X= M + t => (m21 m22 m23 t2) (m31 m32 m33 t3) ( 0 0 0 1) Take maple or a lot of paper to calculate the multiplication. THE RESULT nicely smoothed averaged and phase extended maps!!!!!!!! Thanks again Jan -- ------------------------------ Jan Abendroth Institut fuer Biochemie Universitaet Koeln Zuelpicher Strasse 47 D-50674 Koeln Tel: +49-(0)221 470 6455 (Labor) 6445 (Buero) Fax: +49-(0)221 470 5092

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