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

If CORRECT suggests	it could just as well be	Comment
1	-
3	4	screw axis extinctions let you decide
5	-
16	17, 18, 19	screw axis extinctions let you decide
21	20	screw axis extinctions let you decide
22	-
23	24	screw axis extinctions do not let you decide
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
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

Attention: this table was set up on February 15, 2015 and has been not verified by anyone. If you find an error 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

As the old REIDX= input has lost its importance, it is useful to keep in mind that 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 (see [1])

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

1. 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!).
2. 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 . 3₁ and 3₂ cannot be distinguished.
3. 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. 3₁ versus 3₂, or 6₂ versus 6₄) - see the table above!
  • twinning may make a low-symmetry space group look like a high-symmetry one
• 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.