[3dem] protein crystals

[Henning Stahlberg]

Hi,
In general a 2D crystal with any higher order symmetry such as P3 symmetry will give you a (P3) symmetric projection map when imaged without tilt, but the projection map of such a crystal from a slightly tilted direction will not have any symmetry. This already applies for single-layered 2D crystals, and also applies to multi-layered 2D crystals or 3D crystals. For true 3D crystals, there might be other (e.g., orthogonal) views where other symmetries can be found in projection. But this doesn't apply to 2D crystals. 
If a structure has a screw axis, such as P312 or P321, then the structure is also P3 symmetric, and the same as above applies.

Philip, I think you are right: If you have a non-P3 symmetry crystal, but place three layers of such a crystal on top of each other, rotated each by 120 degrees with respect to each other, but centered onto the same point of origin, then the non-tilted projection map can well show P3 symmetry, even though none of the layers itself had that symmetry. In this case, processing that object under P3 symmetry would be wrong. 

Besides this, there are possible other sources of a fake P3 symmetry appearance:
Hexagonally closest packing is a common way for proteins to squeeze together in a membrane. At low resolution, one sometimes gets the impression to have P3 or even P6 symmetry in such a case. But the low resolution might not allow conclusions anyway.
Another way to get apparent symmetries is when the crystal is fragmented, so that different ares in the 2D crystal have differently oriented lattice vectors. If, for example, you are dealing with a P2 symmetry crystal that has as lattice vectors a=100A, b=100A, and an included angle of gamma=120deg, and this crystal has cracks after which the lattice orientation changes so that the new b becomes the old a vector, then the overall appearance of such a crystal can be P3, even though the local areas aren't P3 symmetric. 

All the best,

Henning.

 
Henning Stahlberg, PhD
Prof. for Structural Biology, C-CINA, Biozentrum, University Basel
Mattenstrasse 26 | D-BSSE | WRO-1058 | CH-4058 Basel | Switzerland
http://c-cina.org | Tel. +41-61-387 32 62



On Dec 20, 2013, at 3:26 PM, Philip Köck wrote:

> Yes, maybe. I was thinking in that direction.
> 
> I get the impression that the software for 2D crystallography (mrc, 2dx, crisp etc.)
> doesn't seem to allow for such a case. Is that true?
> 
> Philip
> 
> 
> -----Original Messages-----
> 
> HI Philip,
> 
> could you have a screw axis, which in projection looks like it's 3-fold?
> 
> Mike
> ________________________
> 
> Hej Philip,
> 
> En tunn p31-kristall?
> 
> Merry Xmas,
> 
> Martin Lindahl
> 
> 
> On Dec 20, 2013, at 8:44 AM, Philip Köck <Philip.Koeck at ki.se> wrote:
> 
>> Hi everybody.
>> 
>> Is it possible that a very thin (membrane) protein crystal, consisting 
>> of maybe two or three layers of proteins in there respective lipid 
>> membranes, could exhibit for example a p3 symmetry in zero degree projection when the crystal as a 3-dimensional object doesn't have this symmetry?
>> In other words only the central slice of the Fourier transform parallel to the crystal plane would have 3-fold symmetry, but not a non-central slice.
>> 
>> Thanks and Merry Christmas,
>> 
>> Philip
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