Re: dm-averaging

[Edward Berry <eaberry@lbl.gov>]

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> once again a question concerning a slightly complicated case of dm and
> ncs-averaging.

Here's how I understand the problem:

1. Since each of your operators has a transitional (screw?) component,
you have no proper symmetry. This means you must use a monomer mask:
If mask A covers the dimer and you use it for averaging with operator
A1->A2, it will be used also for A2->A1' which is not valid.
If there is intimate contact between the dimers then the protein will
get mangled a bit by inaccuracies of the mask at the contact. 
On the other hand the improper symmetry should make determining
the monomer mask much easier- NCS correlation will drop sharply 
outside the correct mask. I think CCP4 has a program to determine
NCS masks based on correlation.

2. Since you have 6 monomers you need 6 operators:
A1->A1 (1 0 0 0 1 0 0 0 1; 0 0 0)
A1->A2
A1->B1 =(A -> B)
A1->B2 =(A1->A2)x(A->B) 
A1->C1 =(A->C)
A1->C2 =(A1->A2)x(A->C)

Note that the way operator multiplication is usually expressed
the order is reversed- if XY goes from x to y and YZ from y to z
then XZ = YZ*XY (Multiply the first operator by the second ON THE LEFT)

----
I may be mis-interpreting your "transition component" as a screw
component. Any rotation operator whose axis does not pass through
the origin will have a translation component. If that translation
component is perpendicular to the rotation axis, symmetry will be
proper if the rotation is integer-fold (e.g. 2-fold), and the
operator A1->A2 will work for A2->A1. In this case you can use
a dimer mask, with the same six operators above. Averaging will
be two-fold redundant (you average point 1 with point 2 and also
point 2 with point 1) but there will be no distortion by a mask
border passing between intimate monomers.
-- 
Edward A. Berry, MailStop 3-250
Lawrence Berkeley National Laboratory
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e-mail: EABerry@lbl.gov