Ed

The crystal size form factor will change the intensity of each spot so that instead of being a sharp maximum it will have a sinx/x behaviour. This will occur for each spot independently of resolution. There is a very good illustration of this in the paper referred to by Ethan where the sin(x)/x type fringes join up the spots so one can count the number of unit cells.



One doesn't see this normally because either one has lots of blocks of different sizes or, if there is just one block, the coherent length of the incident beam is smaller than the block size. Even if one satisfied the coherence condition, a very high resolution detector would be required (matched to the necessary beam divergence) for a normal size crystal.



I had a paper in 1999 describing some of these effects. I used the term sinc(x) as an alternative to sin(x)/x. This got changed to sine in the editing process but wasn't visible on the low resolution fax used to send the proofs (the old days!). I couldn't be bothered to produce a correction but have been waiting for 13 years for someone to point out this error. A small prize was waiting but it is too late now.



Of relevance to the initial question, one has to distinguish between short range and long range disorder. It is true that larger molecules will not pack as well as Crambin. There was some discussion of this at the CCP4 study weekend with issues such as the number of contacts between protein molecules as a function of their surface area. However, if the larger molecules maintain order over several unit cells, diffraction spots will still occur to high resolution. The reason that crystals of these larger molecules generally don't diffract to high resolution could be due to

1. The lack of contact between molecules and the larger solvent volumes mean that both the solvent and the protein (perhaps affected by the disordered solvent) will have short range disorder (i.e. not correlated between unit cells). This will lead to increased B factors.

2. Fewer strong contacts will lead to a variety of effects such as variation in unit cell size, smaller number of unit cells per block or angular variation between blocks. This longer range disorder will lead to increased spot sizes so that the spot eventually disappears below the background. James Holton has demonstrated that the background is the limiting factor for high resolution data collection.

3. The structure factors are lower for large unit cells. This will mean they will be harder to detect, particularly if there is a high background.



Well at least at the end there were some attempted answers to the original post.



Cheers

  Colin



-----Original Message-----

From: Ed Pozharski [mailto:[log in to unmask]] 

Sent: 10 January 2012 16:09

To: Nave, Colin (DLSLtd,RAL,DIA)

Cc: ccp4bb

Subject: Re: [ccp4bb] Sub-angstrom resolution



On Tue, 2012-01-10 at 09:04 +0000, Colin Nave wrote:

> Yes, I think Ed's analysis is a bit misleading.



I apologize if I misled anyone.  Re-reading my post, I can see that it lacked precision.  Indeed, in a perfect monocrystal all the molecules are lined up perfectly, so I should have emphasized rather that the culprit is the decay of correlation between atomic positions.  It is still a bit counterintuitive that a crystal can diffract beyond the resolution seemingly allowed by possible bragg planes.  Shouldn't the "crystal size" formfactor introduce something akin to sinx/x that will drive intensity rapidly down past the "bragg limit"?  Oh well.



On a second thought, maybe the unit cell size does not matter directly.

What matters perhaps is how quickly the disorder accumulates over distance, and that should be more pronounced for larger molecules.  Thus the problem is that larger molecules cannot pack as well as, say, crambin.



On empirical side, the largest molecule currently in the PDB with d<1A is 3ju4, 0.98A and ~75kDa.



See the distribution of sizes of "subangstrom" structures here.



http://tinyurl.com/8yhbcvk



BTW, the 3ju4 is reported on EDS as "unreliable".  Shall comment in the other thread.



Cheers,



Ed.



--

Oh, suddenly throwing a giraffe into a volcano to make water is crazy?

                                                Julian, King of Lemurs