we have NCS rotation (158.56, 180, 0) - rotation matrix [R]
and we have two CS operators (P21) - rotation matrix (0 0 0) [1]
and (90 90 180) [2].
So, all symmetry related (for [R]) rotations are
[1][R][1] = [R] - (158.56, 180, 0)
[1][R][2] = [R][2] - ( 111.44 0.0 180.0)
[2][R][1] = [2][R] - ( 111.44 0.0 180.0)
[2][R][2] - (21.44, 0, 180)
Really we have two rotations, because
(158.56, 180, 0) and (21.44, 0, 180) are idendical.
There is nothing special.
If there is pure dimer one rotation is pure 2-fold axis
another is 2-fold axis with translation.
Alexei
On 23 Apr 2008, at 22:29, Derek Logan wrote:
> Thanks to everyone who helped with the self RF problem: Eleanor,
> Ian, Claudine, Pietro & Alexei.
>
> Eleanor wrote:
>
>> 1) It is a bit hard to find out how MOLREP defines its orthogonal
>> axes - many programs use X0 || a, Yo || b* and in P21 hence Zortho
>> is || to c*
>> If that is what Molrep does then your 2 fold is in the a c* plane,
>> 21 degrees or 111 degrees from c*.
>> The 2 peaks you see are symmetry equivalents.
>
> This was my interpretation. Glad we agree ;-) The documentation
> says "A parallel to X , Cstar parallel to Z"
>
>> As for the Patterson - what height are those peaks relative to
>> the origin?
>
> The peaks are u = 0.129, v = 0.473, w = 0.220 (20% of origin peak
> height) and u = 0.180, v = 0.500, w = 0.248 (19%). What I don't get
> is why there are two and only one strong 2-fold. 2 dimers in the AU
> gives 50% solvent, 1 dimer 75%. The crystals diffract to 2.3Å,
> which would tip the balance in favour of 50% solvent in my opinion.
>
>> With 2 dimers in the asymm unit and with the non-cryst 2-fold
>> perpendicular to b* you could have such translations between one
>> monomer and another.
>
> Would the 2-folds of both dimers have to be very similarly
> oriented? Maybe one peak masks the other at this resolution?
>
>> is there a model - easiest to solve it then analyse this sort of
>> stuff later!
>
> Believe me, we've been trying for a very long time! The problem is
> that it's a leucine rich repeat protein with under 30% sequence
> identity to any of the other LRR models out there. I think the
> failure of MR is down to a combination of a) the low homology, b)
> the pseudosymmetry, c) the nature of the LRR, which means you can
> get MR solutions that are out by one or more repeats. Maybe even
> the internal symmetry of the whole LRR structure can add to this
> pathology? We've had some solutions that looked almost right, but
> we can never see much more than what's already in the MR solution.
>
> Ian wrote:
>
>> The symmetry of the self-RF is explained in detail in the
>> documentation for POLARRFN, in fact I would advise you to use this
>> because you can then plot monoclinic space groups with the unique
>> b axis along the orthogonal Z axis (NCODE = 3) and then the
>> symmetry is *much* easier to interpret.
>
> The reason I started using Molrep was that POLARRFN always used to
> choke on these data. However that problem seems to have
> disappeared. Using ORTH 3 indeed gives a more interpretable plot,
> as you say.
>
>> According to polarrfn.doc the symmetry generated by a 2-fold along
>> b parallel to Z is (180-theta, 180-phi, kappa) so the peak in the
>> list (159,180,180) is the same as (21,0,180) which is a NCS 2-fold
>> that you can see just below centre. The peak (111,0,180) is thus
>> the same as (69,180,180) near the top which is another NCS 2-fold
>> perp to the first generated by the crystallographic 2-fold.
>
> Indeed, I see the peak (69, 180, 180) but I don't find it in the
> list in the log file from Molrep. I thought that list was supposed
> to be exhaustive. Also the plot is not well documented for Molrep.
> I wrote to the BB a while ago to ask what the contour levels were
> but no-one answered. By Googling I found a crystallisation paper
> where it was described as "from 0.5 sigma in steps of 0.5 sigma"
> but that information appears to have come by word of mouth. Also,
> is it just the "north hemisphere", as Claudine put it, that is
> plotted?
>
> Anyway, I feel somewhat wiser now...
>
> Derek
>
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