It's more complicated than that, since the tricky thing is to distinguish between reflections related eg by a putative crystallographic two-fold and by a parallel non-crystallographic two-fold, which would give very similar intensity relationships. Pointless does try to score these alternative models, but it is not fool-proof. 

In the end, the best test is probably comparing refinements in different space groups (as is done by the Andrey Lebedev's Zanuda program, on the York University server), though it seems to me that in the limit you can't tell: how close does a non-crystallographic axis have to be to a crystal direction to be crystallographic, 1degree, 0.1 degrees, 0.01degrees?

Phil Evans

(incidentally, the algorithms used in Pointless are described in a paper due to appear in the Acta Cryst. D volume from the 2010 CCP4 Study Weekend, probably early next year. But I don't really know how best to calculate the probabilities)   


On 21 Oct 2010, at 21:03, Ethan Merritt wrote:

> On Thursday, October 21, 2010 11:38:55 am Jacob Keller wrote:
> 
>> 
>> "if the data really looks like P21--" what are the criteria for that?
> 
> This is a straightforward statistical question.
> In testing for a possible 2-fold, you want to know:
> 
> Do two random reflections related by the putative 2-fold agree with
> each other better than two random reflections not related by the
> putative 2-fold?
> 
> To make this test less sensitive to scaling, one can formulate it
> as a correlation coefficient.  Have a look at the paper describing
> `pointless`.
> 
>  P Evans (2006), Acta Cryst. D62: 72-82
> 
> Testing the for systematic absences indicating a screw axis can also
> be phrased as a statistical test, although generally there are a relatively
> small number of putative absences to inspect so the test is not all that
> strong.
> 
> 	Ethan
> 
> 
> 
> 
> 
>> I believe p1 can have good-as-perfect 90deg angles, no? 
> 
> Correct. The cell angles don't really enter into it.
> 
> 
> 
>> And also 
>> equal cell dimensions? So I don't think you will be able to tell from the 
>> positions of the spots on the detector, necessarily. Also, would it not be 
>> more rigorous to say "I can gain a lot by assuming these molecules are in 
>> p21?" Look, nobody thinks that every molecule in the crystal is identical, 
>> so that is truly a convenient assumption. The symmetry, I think, is a 
>> similar assumption at a different level.
>> 
>> By the way, I have always wondered whether anybody has looked into the 
>> degree of intermolecular differences possible given all of the parameters in 
>> our crystallographic models. In other words, would a microscopic observer 
>> look at the molecules in the crystal and see what looks like a crowd from a 
>> NYC street, or something more like an army formation? How much variety is 
>> there at the molecular lever, I wonder?
>> 
>>> True: but how do you judge that those differences are within or
>>> outside of experimental noise?
>> 
>> Agreed!
>> 
>>> What if by refining in P1 the parametrisation makes those side-chains
>>> different in the first place? A poorly defined Lys side-chain suddenly
>>> becomes two significantly different poorly defined side-chain?
>> 
>> I don't know--depends on last question I think.
>> 
>> Jacob
>> 
>> *******************************************
>> Jacob Pearson Keller
>> Northwestern University
>> Medical Scientist Training Program
>> Dallos Laboratory
>> F. Searle 1-240
>> 2240 Campus Drive
>> Evanston IL 60208
>> lab: 847.491.2438
>> cel: 773.608.9185
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>> 
> 
> -- 
> Ethan A Merritt
> Biomolecular Structure Center,  K-428 Health Sciences Bldg
> University of Washington, Seattle 98195-7742