Non-merohedral twinning: from minerals to proteins

Examples are presented of successful data-processing, phasing and refinement strategies for non-merohedral twins, covering the range from minerals to proteins.


S1.1. HKLF5 Format
An overlapped reflection is described by its two (or more) components. Therefore there are two (or more) lines in the HKLF5 data file. The indices h'k'l' are the indices derived with orientation matrix 2, while hkl is derived with orientation matrix 1. The absolute value of the integer number in the last column, batch number, defines the domain. A negative number means that it overlaps with all following reflections until the batch number is positive. F 2 represents the summed intensity.

S2.1.1.1 Output using default options in CELL_NOW
The following cells would appear to be plausible, but should be checked using XPREP because they are not necessarily the conventional cells.
FOM, % within 0.2, a..gamma, volume and lattice type for potential unit-cells:  It is not obvious from this table that cell 5 is a good choice, but rotating the others did not index enough of the remaining reflections. To force CELL_NOW to find only the known F-centred cubic cell, the cell search was restricted. Then it just finds the two twin components: S2.1.1.2 CELL_NOW Output Searching for vectors with 8.00 < d < 9.00 The following cells would appear to be plausible, but should be checked using XPREP because they are not necessarily the conventional cells.
FOM, % within 0.2, a..gamma, volume and lattice type for potential unit-cells:  Percentages of reflections in this domain that do not have: h=2n: 56.4, k=2n: 56.4, l=2n: 55.9, h=3n: 66.6, k=3n: 67.3, l=3n: 64.3% 392 reflections within tolerance assigned to domain 1, 392 of them exclusively; 335 reflections not yet assigned to a domain In the cubic crystal system, there are many symmetry equivalent twin laws. To show that this rotation of 144.5 ° is a proper rotation we applied a rotation of -90 ° around 0 1 0, which leads to a symmetry equivalent cell in Laue group m3 m. This operation was applied with the program GEMINI (Sparks, 2000).  -89.99998 The rotation between this cell and the first cell is a rotation of 180 ° around -2 -1 1

S2.2.1. Determination of the Cell Constants and the Twin Law
The following cells would appear to be plausible, but should be checked using XPREP because they are not necessarily the conventional cells.
FOM, % within 0.2, a..gamma, volume and lattice type for potential unit-cells:            The coordinates of Zr1/Ti2 and Zr2/Ti1 are related by the symmetry operator -x, y+0.5, 0.5-z describing a 2 1 axis. The coordinates of the two Zr atoms as well the two Ti atoms are related by x+0.5, y+0.5, z+0.25 describing an I-centring for a cell with a halved c axis.

S3.1.1. Cell Determination with CELL_NOW
The following cells would appear to be plausible, but should be checked using XPREP because they are not necessarily the conventional cells.
FOM, % within 0.2, a..gamma, volume and lattice type for potential unit-cells:  Here it is necessary to re-index the second component because, as the R int values indicate, the two components are indexed inconsistently. Note also that the systematic absences are the same for space group I23 and I2 1 3. SHELXD finds the six sulfur atoms using the anomalous differences, thereby confirming I2 1 3.    The other reflections that overlap with 3 1 46 again have several new overlaps. Therefore, adding step by step all twin-related reflections leads to ca. 90 % of the data starting with just one reflection Searching for vectors with 90.00 < d < 110.00, superlattice threshold = 10.0%

SPACE GROUP DETERMINATION
The following cells would appear to be plausible, but should be checked using XPREP because they are not necessarily the conventional cells.
FOM, % within 0.2, a..gamma, volume and lattice type for potential unit-cells:    This full sidechain tracing is in an early stage of development and is likely to get better.