Background: Twinned crystals require special consideration during analysis, as they contain a mixture of two or more orientations of a lattice in what is apparently a single crystal. In some space groups, merohedral twinning (a form of twinning in which reflections from the twin components that make up the crystal overlap each other) is not uncommon. This type of twinning is more easily overlooked than other forms of twinning because the diffraction patterns show no abnormalities. In the case of merohedral twinning the intensity of each diffraction spot is actually the sum of the unrelated intensities of the twin components:
If this type of twinning were ignored during model building and refinement, up to 50% of the scattering matter would not be taken into account.
The bacteriorhodopsin crystals discussed below were grown from a cubic lipid phase matrix (Landau & Rosenbusch, PNAS, 1996). The crystals belong to space group P63 with a=b=61 Å, c=108 Å and contain two trimers per unit cell, offset by 1/2 in c.
1) Evidence that our (Luecke et al., Science, June 1998) crystals are strongly merohedrally twinned.
a. Two programs (SHELXS-92 and DATAMAN/GEMINI) were employed in an initial attempt to determine whether our observed data sets had twinning. These programs attempt to detect a deviation in the probability distribution of diffraction intensities due to twinning. Neither program indicated the presence of twinning. In other words, both programs failed to detect the nearly perfect merohedral twinning indicated by other criteria (see point b below). We are in the process of preparing a separate manuscript that will discuss the technical aspects of this discrepancy.
b. Despite 1a, it became obvious that every one of our crystals was strongly twinned, for the reasons outlined in our manuscript (Luecke et al.), namely,
ii) the occurrence of very strong two-fold axes in the a/b plane of the self-rotation function (Fig. 1 of Luecke et al. Science paper and Illustration 1e below),
iii) the fact that we find two nearly equally strong solutions to the cross rotation search with the EM models which are related by a two-fold rotation in the a/b plane,
iv) the fact that refining the structure with the program SHELXL-97 with a provision for de-twinning drastically reduces both the R and Rfree factors.
2) Evidence that substantially twinned crystals were used unknowingly by Pebay-Peyroula et al. (Science, September 1997).
a. We understand that the same approach we used in 1a was used by Pebay-Peyroula et al. with their observed structure factors, and it was on this basis that significant twinning in their crystals was ruled out.
b. After submitting our manuscript, we obtained a copy of the refined atomic coordinates from Pebay-Peyroula et al. Based on their model we detected strong twinning in Pebay-Peyroula et al.'s observed diffraction data, as described in the following:
In summary, Illustration 1 contains self-rotation function (SRF) maps based on the following:
As expected, Illustrations 1a and 1b (based on EM models) show very little two-fold symmetry in the a/b plane [phi=0º; kappa=180º] since space group P63 does not have two-fold symmetry in the a/b plane.
In contrast, Illustration 1c reveals strong (8 sigma) two-folds at [psi=0,30,60,90º; phi=0º; kappa=180º], indicating novel two-fold axes which due to the lack of any crystallographic two-fold axes in the a/b plane for space group P63 indicate the presence of non-crystallographic symmetry. And since there is no significant internal two-fold symmetry in the bacteriorhodopsin monomer, we interpret these two-fold axes as originating from the fact that strong twinning was overlooked in Pebay-Peyroula et al.'s crystals and consequently the XPLOR minimizer was forced to refine a non-twinned model against data from a twinned crystal. We believe that the two-fold symmetry in the a/b plane in Illustration 1c is due to twinning in Pebay-Peyroula et al.'s diffraction data, the signature of which has effectively been stored in their model and can be revealed in the manner described.
Illustration 1d shows the self-rotation function for our model, refined as described in our manuscript, and does not show two-folds in the a/b plane, similar to Illustrations 1a and 1b produced from the EM models.
Finally, Illustration 1f demonstrates that when one incorrectly refines our SHELXL model (used for Illustration 1d) with XPLOR in the same fashion as Pebay-Peyroula et al. refined their model, i.e. non-twinned model against twinned Fobs, one obtains a signature of two-folds in the a/b plane that is very similar to the one observed in Illustration 1c. This graph demonstrates that when the structure factors contain strong twinning, after incorrect refinement even a monomeric atomic model will retain traces of twinning of data it was refined against.
From the above evidence it seems an unavoidable conclusion that, like us, Pebay-Peyroula et al. had strongly twinned crystals. Since Pebay-Peyroula et al. did not take twinning into account, and thus effectively did not account for about 50% of the scattering matter in their crystals, their structural analysis is incorrect.
Of course, the most direct test for twinning in Pebay-Peyroula et al.'s crystals and thus their original structure factors (Fobs) would be based on their original data. Twinning of their crystals will be indicated by fact that:
ii) the self-rotation function for kappa=180º of their Fobs shows unexplained strong peaks at [psi=0,30,60,90º; phi=0º] in addition to the expected crystallographic peak at [psi=90º; phi=90º],
iii) their cross-rotation search with the EM model yielded not one but two solutions which are related by a two-fold rotation in the a/b plane.
Addendum (September 1998):
After the release of the preliminary structure in January of 1998 by Pebay-Peyroula, the Protein Data Bank has recently (September 1998) released the final model (1AP9). The coordinate file now contains the following passage:
Other links related to twinning: