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On Jan 5 2007, Jenny wrote:
I heard that it's quite tricky for R32 and I wondered what's that.
I've lost the post that talked about the impact of high symmetry on molecular replacement, but it might be worth clarifying what was said.
For those who were at the recent CCP4 study weekend, Phil Evans discussed this point. When you are carrying out a translation search with the full symmetry methods in modern programs (fast CC search in AMoRe or Molrep, LLG search in Phaser), the model is complete for every translation, so symmetry doesn't have an effect on signal-to-noise. The difficulty with high crystallographic symmetry comes at the point of the rotation search, and it is the number of *primitive* symmetry operations that matters, not the lattice translations. Phil mentioned two ways of looking at this. One is in terms of the traditional Patterson overlap rotation function, which compares the observed and calculated Pattersons in a sphere around the origin. As the number of primitive symmetry operations increases, the number of intramolecular vector sets superimposed on each other around the origin also increases. Another way to look at it is in terms of the rotation likelihood target used in Phaser. This target considers what structure factors could be built up by adding the contributions of the symmetry-related molecules, with unknown relative phase. As the number of contributions increases, the uncertainty in their sum increases, reducing the signal-to-noise. The relative phases of contributions from molecules related by lattice translations are known, because their relative positions are known. So lattice translations don't affect the difficulty.
Actually, there's a third way to look at it, which might be the most intuitive. The rotation search can also be carried out by computing the correlation between the observed and calculated Patterson maps in P1. This could be done in our old program BRUTE, but is most familiar as the direct rotation function in XPLOR or CNS. The observed Patterson map has contributions from the vectors between all pairs of molecules. If there are N primitive symmetry operations, there are N^2 unique sets of vectors between molecules. Of these, N are intramolecular vector sets and can be predicted just knowing the orientation of the molecule. The rest (N^2-N) are intermolecular vector sets, which cannot be predicted until the translation is known and thus add noise to the rotation search. So the rotation search can in principle explain the fraction N/N^2 or 1/N of the vectors in the Patterson, which accounts nicely for the increasing difficulty with higher primitive symmetry.
Non-crystallographic symmetry has a similar effect, and what matters is the product of the number of NCS operations with the number of crystallographic symmetry operations. But NCS also makes the translation search more difficult, because you're only explaining a fraction of the data in all but the last translation search.
Getting back to R32, it shouldn't be intrinsically difficult. There are only 6 primitive symmetry operations, coming from the combination of the 3-fold and 2-fold operators, and the rest of the symmetry comes from lattice translations. So R32 shouldn't be any more difficult than, say, P32 or P6. We haven't noticed any differences in test cases.
I hope that helps! Randy Read
