X-Ray Diffraction: Understanding Reflection Symmetry

[alona]

hi,

i'm having trouble with a problem regarding X-ray crystallography. the question is as follows:

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In general, crystals can have various symmetry elements: rotation, translation, reflection, etc. however, you never find reflection (mirror) symmetry in protein crystals. why?

On the other hand, you can get mirror symmetry in the diffraction pattern. Why?

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i know the answer to the first part of the question - it's because proteins are made of L-amino acids only, which are not symmetrical, so can't reflect.

i have no idea why you can get mirror symmetry in the diffraction pattern. how can the diffraction image have a form of symmetry that the original crystal doesn't? i'd appreciate if someone could help me with this. thanks.

 

[Physics Monkey]

The key here is that the symmetry of the diffraction pattern is determined by the symmetry of the Bravais lattice without reference to the basis. In other words, while the proteins themselves are chiral, the way the proteins are distributed in space can still have reflection symmetry. The full crystal is determined by the Bravais lattice decorated with a basis, in this case chiral proteins; however, only the Bravais lattice determines the diffraction pattern. Note that the basis can affect the intensity of the spots or even cause some spots to vanish, so what "the diffraction pattern is symmetric" means is that the position of the spots is symmetric.