# Space group determination

## The 65 space groups in which proteins composed of L-amino acids can crystallize

The mapping of numbers and names is:

****** LATTICE SYMMETRY IMPLICATED BY SPACE GROUP SYMMETRY ****** BRAVAIS- POSSIBLE SPACE-GROUPS FOR PROTEIN CRYSTALS TYPE [SPACE GROUP NUMBER,SYMBOL] aP [1,P1] mP [3,P2] [4,P2(1)] mC,mI [5,C2] oP [16,P222] [17,P222(1)] [18,P2(1)2(1)2] [19,P2(1)2(1)2(1)] oC [21,C222] [20,C222(1)] oF [22,F222] oI [23,I222] [24,I2(1)2(1)2(1)] tP [75,P4] [76,P4(1)] [77,P4(2)] [78,P4(3)] [89,P422] [90,P42(1)2] [91,P4(1)22] [92,P4(1)2(1)2] [93,P4(2)22] [94,P4(2)2(1)2] [95,P4(3)22] [96,P4(3)2(1)2] tI [79,I4] [80,I4(1)] [97,I422] [98,I4(1)22] hP [143,P3] [144,P3(1)] [145,P3(2)] [149,P312] [150,P321] [151,P3(1)12] [152,P3(1)21] [153,P3(2)12] [154,P3(2)21] [168,P6] [169,P6(1)] [170,P6(5)] [171,P6(2)] [172,P6(4)] [173,P6(3)] [177,P622] [178,P6(1)22] [179,P6(5)22] [180,P6(2)22] [181,P6(4)22] [182,P6(3)22] hR [146,R3] [155,R32] cP [195,P23] [198,P2(1)3] [207,P432] [208,P4(2)32] [212,P4(3)32] [213,P4(1)32] cF [196,F23] [209,F432] [210,F4(1)32] cI [197,I23] [199,I2(1)3] [211,I432] [214,I4(1)32]

## Space group selected by XDS: ambiguous with respect to enantiomorph and screw axes

In case of a crystal with an unknown space group (SPACE_GROUP_NUMBER=0 in XDS.INP), XDS (since version June 2008) helps the user in determination of the correct space group, by suggesting possible space groups compatible with the lattice symmetry of the data, and by calculating the R_{meas} for these space groups.

XDS (or rather, the CORRECT step) makes an attempt to pick the correct space group automatically: it chooses that space group which has the highest symmetry (thus yielding the lowest number of unique reflections) and still a tolerable R_{meas} compared to the R_{meas} the data have in any space group (which is most likely a low-symmetry space group - often P1).

In many cases the automatic choice is the correct one, and re-running the CORRECT step is then not necessary. However, neither the correct enantiomorph nor screw axes (see below) are determined automatically by XDS.

### Space groups to consider based on CORRECT suggestion

Bravais type | Laue group | If CORRECT suggests | it could just as well be | Comment |
---|---|---|---|---|

aP | -1 | 1 | - | |

mP | 2m | 3 | 4 | screw axis extinctions let you decide |

5 | - | The pointless article discusses why I2 should not be used. | ||

16 | 17, 18, 19 | screw axis extinctions let you decide. The pointless article discusses why CCP4's 1017 (P2_{1}22), 2017 (P22_{1}2), 2018 (P2_{1}22_{1}) , 3018 (P22_{1}2_{1}) are not needed and should not be used.
| ||

21 | 20 | screw axis extinctions let you decide | ||

22 | - | |||

23 | 24 | screw axis extinctions do not let you decide because the I centering results in h+k+l=2n and the screw axis extinction 00l=2n is just a special case of that.
| ||

75 | 76, 77, 78 | screw axis extinctions let you decide, except between 76/78 enantiomorphs | ||

89 | 90, 91, 92, 93, 94, 95, 96 | screw axis extinctions let you decide, except between 91/95 and 92/96 enantiomorphs | ||

79 | 80 | screw axis extinctions let you decide | ||

97 | 98 | screw axis extinctions let you decide | ||

143 | 144, 145 | screw axis extinctions let you decide, except between 144/145 enantiomorphs | ||

146 | - | |||

149 | 151, 153 | screw axis extinctions let you decide, except between 151/153 enantiomorphs | ||

150 | 152, 154 | screw axis extinctions let you decide, except between 152/154 enantiomorphs | ||

155 | - | |||

168 | 169, 170, 171, 172, 173 | screw axis extinctions let you decide, except between 169/170 and 171/172 enantiomorphs | ||

177 | 178, 179, 180, 181, 182 | screw axis extinctions let you decide, except between 178/179 and 180/181 enantiomorphs | ||

195 | 198 | screw axis extinctions let you decide | ||

196 | - | |||

197 | 199 | screw axis extinctions do not let you decide because the I centering results in h+k+l=2n and the screw axis extinction 00l=2n is just a special case of that.
| ||

207 | 208, 212, 213 | screw axis extinctions let you decide, except between 212/213 enantiomorphs | ||

209 | 210 | screw axis extinctions let you decide | ||

211 | 214 | screw axis extinctions let you decide |

If you find an error in the table please send an email to kay dot diederichs at uni-konstanz.de !

## Space group selected by user

Even in case the space group selected by XDS should be incorrect, the resulting list (in CORRECT.LP) should give the user enough information to pick the correct space group herself. The user may then put suitable lines with SPACE_GROUP_NUMBER=, UNIT_CELL_CONSTANTS= into XDS.INP and re-run the CORRECT step to obtain the desired result. (The REIDX= line is no longer required; XDS figures the matrix out.)

## Influencing the selection by XDS

### keywords and parameters

The automatic choice is influenced by a number of decision constants that may be put into XDS.INP but which have defaults as indicated below:

- MAX_CELL_AXIS_ERROR= 0.03 ! relative deviation of unconstrained cell axes from those constrained by lattice symmetry
- MAX_CELL_ANGLE_ERROR= 3.0 ! degrees deviation of unconstrained cell angles from those constrained by lattice symmetry
- TEST_RESOLUTION_RANGE= 10.0 5.0 ! resolution range for calculation of R
_{meas} - MIN_RFL_Rmeas= 50 ! at least this number of reflections are required
- MAX_FAC_Rmeas= 2.0 ! factor to multiply the lowest R
_{meas}with to still be acceptable

The user may experiment with adjusting these values to make the automatic mode of space group determination more successful. For example, if the crystal diffracts weakly, all R_{meas} values will be high and no valid decision can be made. In this case, I suggest to use e.g.

TEST_RESOLUTION_RANGE= 50.0 10.0

### dealing with alternative indexing

There are two ways to have XDS choose an indexing consistent with some other dataset:

- using REFERENCE_DATA_SET= ! see also REFERENCE_DATA_SET
- using UNIT_CELL_A-AXIS=, UNIT_CELL_B-AXIS=, UNIT_CELL_C-AXIS= from a previous data collection run with the same crystal

One can also manually force a specific indexing, using the REIDX= keyword, but this is error-prone.

## Screw axes

The current version makes no attempt to find out about screw axes. It is assumed that the user checks the table in CORRECT.LP entitled "REFLECTIONS OF TYPE H,0,0 0,K,0 0,0,L OR EXPECTED TO BE ABSENT (*)", and identifies whether the intensities follow the rules

- a two-fold screw axis along an axis in reciprocal space (theoretically) results in zero intensity for the odd-numbered (e.g. 0,K,0 with K = 2*n + 1) reflections, leaving the reflections of type 2*n as candidates for medium to strong reflections (they don't
*have*to be strong, but they*may*be strong!). - similarly, a three-fold screw axis (theoretically) results in zero intensity for the reflections of type 3*n+1 and 3*n+2, and allows possibly strong 3*n reflections . 3
_{1}and 3_{2}cannot be distinguished. - analogously for four-fold and six-fold axes.

Once screw axes have been deduced from the patterns of intensities along H,0,0 0,K,0 0,0,L , the resulting space group should be identified in the lists of space group numbers printed in IDXREF.LP and CORRECT.LP, and the CORRECT step can be re-run. Those reflections that should theoretically have zero intensity are then marked with a "*" in the table. In practice, they should be (hopefully quite) weak, or even negative.

## Notes

- There is still the old Wiki page Old way of Space group determination
- To prevent XDS from trying to find a better space group than the one with the lowest R
_{meas}(often P1), you could just use MAX_FAC_Rmeas= 1.0 - Space group determination is not a trivial task. There is a number of difficulties that arise -
- ambiguity of hand of screw axis (e.g. 3
_{1}versus 3_{2}, or 6_{2}versus 6_{4}) - see the table above! - twinning may make a low-symmetry space group look like a high-symmetry one

- ambiguity of hand of screw axis (e.g. 3
- only when the structure is satisfactorily refined can the chosen space group be considered established and correct. Until then, it is just a hypothesis and its alternatives (see the table) should be kept in mind.