REINDEXING (CCP4 GENERAL) NAME REINDEXING INFORMATION ABOUT CHANGING

                           Reindexing (CCP4: General)

NAME

   reindexing - information about changing indexing regime

  Contents

     * General Remarks
     * A real monoclinic example
     * Lookup tables
     * Changing hand
     * Pictures

  General Remarks

   It is quite common to find that the diffraction from subsequent
   crystals for a protein do not apparently merge well. There are many
   physical reasons for this, but before throwing the data away it is
   sensible to consider whether another indexing regime could be used. For
   illustrations and examples see HKLVIEW-examples below. For
   documentation on re-indexing itself, and some hints, see also REINDEX.

   For orthorhombic crystal forms with different cell dimensions along
   each axis you can usually recognise if the next crystal is the same as
   the last and see how to transform it (remember to keep your axial
   system right-handed!).

   In P1 and P21 there are many ways of choosing axes, but they should all
   generate the same crystal volume. Use MATTHEWS_COEF or some other
   method to check this - if the volumes are not the same, or at least
   related by integral factors, you have a new form. If they are the same
   it is recommended to plot some sections of the reciprocal lattice; you
   can often see that the patterns will match if you rotate in some way
   (see HKLVIEW-examples below). A common change in P21 or C2 where the
   twofold axis will be constant, is that a*new = a*old + c*old, and c*new
   must be chosen carefully. One very confusing case can arise if the
   length of (a*+nc*) is almost equal to that of a* or nc*, but it should
   be possible to sort out from the diffraction pattern plots.

   Confusion arises mostly when two or more axes are the same length, as
   in the tetragonal, trigonal, hexagonal or cubic systems. In these cases
   any of the following definitions of axes is equally valid and likely to
   be chosen by an auto-indexing procedure. The classic description of
   this is that these are crystals where the Laue symmetry is of a lower
   order than the apparent crystal lattice symmetry.

   real axes:       (a,b,c)    or (-a,-b,c)    or (b,a,-c)    or (-b,-a,-c)
   reciprocal axes: (a*,b*,c*) or (-a*,-b*,c*) or (b*,a*,-c*) or
   (-b*,-a*,-c*)

   N.B. There are alternatives where other pairs of symmetry operators are
   used, but this is the simplest and most general set of operators. For
   example: in P4i (-a,-b,c) is equivalent to (-b,a,c), or in P3i
   (-a,-b,c) is equivalent to (-b,a+b,c). N.B. In general you should not
   change the hand of your axial system; i.e. the determinant of the
   transformation matrix should be positive, and only such transformations
   are discussed here.

   The crystal symmetry may mean that some of these systems are already
   equivalent:
   For instance, if (h,k,l) is equivalent to (-h,-k,l), the axial system
   pairs [(a,b,c) and (-a,-b,c)] and
   [(b,a,-c) and (-b,-a,-c)] are indistinguishable. This is the case for
   all tetragonal, hexagonal and cubic spacegroups.
   If (h,k,l) is equivalent to (k,h,-l), the axial system pairs [(a,b,c)
   and (b,a,-c)] and
   [(-a,-b,c) and (-b,-a,-c)] are indistinguishable. This is true for
   P4i2i2, P3i2, P6i22 and some cubic spacegroups.
   If (h,k,l) is equivalent to (-k,-h,-l), the axial system pairs [(a,b,c)
   and (-b,-a,-c)] and
   [(-a,-b,c) and (b,a,-c)] are indistinguishable. This is only true for
   P3i12 spacegroups.
   See detailed descriptions below.

  A real monoclinic example

   Two datasets from the same crystal with apparently the same cell
   dimensions:

          run1 55.76 84.62 70.96 90 112.71 90
          run2 56.04 85.11 71.57 90 113.15 90

   However, the Rmerge from Scala was around 40% Viewing the k = constant
   sections in HKLVIEW showed that the diffraction patterns were rotated
   with respect to each other. A reindexing transformation of -h, -k, h+l
   was inferred. In terms of the real-space cell, the new axes are
   constructed as follows:

   cell axes transformation

   Some basic trigonometry shows the new cell dimensions to be:

          run1 (reindexed) 55.76 84.62 71.33 90 113.42 90

   The new dimensions are slightly closer to those of run2. The previous
   similarity is shown to be a coincidence.

   Note the transformation -h, -k, h+l preserves the hand, i.e. the
   corresponding matrix has a determinant of +1.

  Lookup tables

   Here are details for the possible systems:
     * All P4i and related 4i space groups:
       (h,k,l) equivalent to (-h,-k,l) so we only need to check:

       real axes:       (a,b,c)    and (b,a,-c)
       reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
       i.e. check if reindexing (h,k,l) to (k,h,-l) gives a better match
       to previous data sets.

          space group number space group point group crystal system
                  75             P4          PG4       TETRAGONAL
                  76             P41         PG4       TETRAGONAL
                  77             P42         PG4       TETRAGONAL
                  78             P43         PG4       TETRAGONAL
                  79             I4          PG4       TETRAGONAL
                  80             I41         PG4       TETRAGONAL

     * For all P4i2i2 and related 4i2i2 space groups:
       (h,k,l) is equivalent to (-h,-k,l) and (k,h,-l) and (-k,-h,-l) so
       any choice of axial system will give identical data.

          space group number space group point group crystal system
                  89            P422        PG422      TETRAGONAL
                  90            P4212       PG422      TETRAGONAL
                  91            P4122       PG422      TETRAGONAL
                  92           P41212       PG422      TETRAGONAL
                  93            P4222       PG422      TETRAGONAL
                  94           P42212       PG422      TETRAGONAL
                  95            P4322       PG422      TETRAGONAL
                  96           P43212       PG422      TETRAGONAL
                  97            I422        PG422      TETRAGONAL
                  98            I4122       PG422      TETRAGONAL

     * All P3i and R3:
       (h,k,l) not equivalent to (-h,-k,l) or (k,h,-l) or (-k,-h,-l) so we
       need to check all 4 possibilities:

     real axes:       (a,b,c)    and (-a,-b,c)    and (b,a,-c)    and (-b,-a,-c)
     reciprocal axes: (a*,b*,c*) and (-a*,-b*,c*) and (b*,a*,-c*) and
   (-b*,-a*,-c*)
       i.e. reindex (h,k,l) to (-h,-k,l) or (h,k,l) to (k,h,-l) or (h,k,l)
       to (-k,-h,-l).
       N.B. For trigonal space groups, symmetry equivalent reflections can
       be conveniently described as (h,k,l), (k,i,l) and (i,h,l) where
       i=-(h+k). Replacing the 4 basic sets with a symmetry equivalent
       gives a bewildering range of possibilities!.

          space group number space group point group crystal system
                 143             P3          PG3        TRIGONAL
                 144             P31         PG3        TRIGONAL
                 145             P32         PG3        TRIGONAL
                 146             R3          PG3        TRIGONAL

     * All P3i12:
       (h,k,l) already equivalent to (-k,-h,-l) so we only need to check:

       real axes:       (a,b,c)    and (b,a,-c)
       reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
       i.e. reindex (h,k,l) to (k,h,-l) which is equivalent here to
       reindexing (h,k,l) to (-h,-k,l).

          space group number space group point group crystal system
                 149            P312        PG312       TRIGONAL
                 151            P3112       PG312       TRIGONAL
                 153            P3212       PG312       TRIGONAL

     * All P3i21 and R32:
       (h,k,l) already equivalent to (k,h,-l) so we only need to check:

       real axes:       (a,b,c)    and (-a,-b,c)
       reciprocal axes: (a*,b*,c*) and (-a*,-b*,c*)
       i.e. reindex (h,k,l) to (-h,-k,l).

          space group number space group point group crystal system
                 150            P321        PG321       TRIGONAL
                 152            P3121       PG321       TRIGONAL
                 154            P3221       PG321       TRIGONAL
                 155             R32        PG32        TRIGONAL

     * All P6i:
       (h,k,l) already equivalent to (-h,-k,l) so we only need to check:

       real axes:       (a,b,c)    and (b,a,-c)
       reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
       i.e. reindex (h,k,l) to (k,h,-l).

          space group number space group point group crystal system
                 168             P6          PG6       HEXAGONAL
                 169             P61         PG6       HEXAGONAL
                 170             P65         PG6       HEXAGONAL
                 171             P62         PG6       HEXAGONAL
                 172             P64         PG6       HEXAGONAL
                 173             P63         PG6       HEXAGONAL

     * All P6i2:
       (h,k,l) already equivalent to (-h,-k,l) and (k,h,-l) and (-k,-h,-l)
       so we do not need to check.

          space group number space group point group crystal system
                 177            P622        PG622      HEXAGONAL
                 178            P6122       PG622      HEXAGONAL
                 179            P6522       PG622      HEXAGONAL
                 180            P6222       PG622      HEXAGONAL
                 181            P6422       PG622      HEXAGONAL
                 182            P6322       PG622      HEXAGONAL

     * All P2i3 and related 2i3 space groups:
       (h,k,l) already equivalent to (-h,-k,l) so we only need to check:

       real axes:       (a,b,c)    and (b,a,-c)
       reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
       i.e. reindex (h,k,l) to (k,h,-l).

          space group number space group point group crystal system
                 195             P23        PG23         CUBIC
                 196             F23        PG23         CUBIC
                 197             I23        PG23         CUBIC
                 198            P213        PG23         CUBIC
                 199            I213        PG23         CUBIC

     * All P4i32 and related 4i32 space groups:
       (h,k,l) already equivalent to (-h,-k,l) and (k,h,-l) and (-k,-h,-l)
       so we do not need to check.

          space group number space group point group crystal system
                 207            P432        PG432        CUBIC
                 208            P4232       PG432        CUBIC
                 209            F432        PG432        CUBIC
                 210            F4132       PG432        CUBIC
                 211            I432        PG432        CUBIC
                 212            P4332       PG432        CUBIC
                 213            P4132       PG432        CUBIC
                 214            I4132       PG432        CUBIC

  Changing hand

   Test to see if the other hand is the correct one:
   Change x,y,z for (cx-x, cy-y, cz-z)
   Usually (cx,cy,cz) = (0,0,0).

   Remember you need to change the twist on the screw-axis stairs for P3i,
   P4i, or P6i!

   P2[1] - to P2[1]; For the half step of 2[1] axis, the symmetry stays
   the same.

   P3[1] - to P3[2]
   P3[2] - to P3[1]

   P4[1] to P4[3]
   (P4[2] - to P4[2]: Half c axis step)
   P4[3] -to P4[1]

   P6[1] to P6[5]
   P6[2] - to P6[4]
   (P6[3] - to P6[3])
   etc.

   In a few non-primitive spacegroups, you can change the hand and not
   change the spacegroup by a cunning shift of origin:

   I4[1]
          (x,y,z) to (-x,1/2-y,-z)

   I4[1]22
          (x,y,z) to (-x,1/2-y,1/4-z)

   F4[1]32
          (x,y,z) to (3/4-x,1/4-y,3/4-z)

   Plus some centric ones:

   Fdd2
          (x,y,z) to (1/4-x,1/4-y,-z)

   I4[1]md
          (x,y,z) to (1/4-x,1/4-y,-z)

   I4[1]cd
          (x,y,z) to (1/4-x,1/4-y,-z)

   I4bar2d
          (x,y,z) to (1/4-x,1/4-y,-z)

PICTURES

   Full size versions of the example pictures can be viewed by clicking on
   the iconised ones.

             HKLVIEW Barnase pH6 A P3[2] data set indexed h,k,l
    HKLVIEW Barnase pH6 indexed -h-kl The same P3[2] data set, reindexed
                                   -h,-k,l
    HKLVIEW Barnase pH6 indexed -k-hl The same P3[2] data set, reindexed
                                   -k,-h,l
     HKLVIEW Barnase pH6 indexed kh-l The same P3[2] data set, reindexed
                                   k,h,-l
            HKLVIEW Hipip h2l Monoclinic data set, HKLVIEW h,2,l
       HKLVIEW Hipip reindexed The same monoclinic data set, reindexed
                                  -h,-k,h-l

AUTHORS

   Eleanor Dodson, University of York, England
   Prepared for CCP4 by Maria Turkenburg, University of York, England
   Some additional material from Martyn Winn, Daresbury Lab.
Tags: reindexing (ccp4:, to reindexing, reindexing, about, information, changing, (ccp4, general)