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MR Tutorial Bath - Renin case study
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5. Case study 2 - mouse renin

Target:
Mouse renin/inhibitor complex (space group P21,
4 molecules/asymmetric unit).
Model:
Hexagonal pepsin (PDB code 5PEP).

5.1 Rotation function (AMORE / ROTFUN) with F's

5.1.1. AMoRe SORTFUN

Convert the reflection data file into the internal format used by the AMORE program.

#
amore  HKLIN mrenin  HKLPCK0 mrenin.hkl  <<EOD
TITLE  ** packing h k l F for mouse renin crystal **
SORT
LABIN  FP=FPmrenin  SIGFP=SPmrenin
EOD

5.1.2. AMoRe TABFUN

Compute a molecular Fourier transform for use in structure factor calculation by interpolation.

#
amore  XYZIN1 hexpep  XYZOUT1 hexpep_model  table1 hexpep.tab  <<EOD
TITLE  Produce table for hexagonal pepsin model.
TABFUN NOROTA                 ! No rotate for comparison.
CRYST  CELL 78.34 117.76 85.88 90 101.18 90
MODEL  1
SAMPLE 1  RESO 2.8            ! Beyond native resolution for interpolation.
EOD

5.1.3. AMoRe ROTFUN GENERATE

Compute structure factor amplitudes for the search model in space group P1 in a large rectangular cell.

5.1.4. AMoRe ROTFUN CLMN

Compute spherical harmonic coefficients for the target and model Pattersons.

5.1.5. AMoRe ROTFUN CROSS

Compute the cross-RF.

#
amore  HKLPCK0 mrenin.hkl  table1 hexpep.tab  HKLPCK1 hexpep.hkl  \
       CLMN0 mrenin.clmn  CLMN1 hexpep.clmn  MAPOUT mrenin_rotfun  <<EOD
ROTFUN
TITLE  Generate HKLPCK1 from pepsin model.
GENER  1  RESO 20 3  CELL 80 84 97
CLMN   CRYST  RESO 20 3  SHARP -20  SPHERE 35
CLMN   MODEL 1  RESO 20 3  SHARP -20  SPHERE 35
ROTATE CROSS  MODEL 1  BMAX 90  NPIC 20               ! Beta = 0-90.
EOD
\rm mrenin_rotfun.map

Note that here the Rotation function uses the default orthogonalisation convention (ORTH 1, with x || a and z || c*; this is also the standard PDB convention). Normally for monoclinic space groups the alternative convention (ORTH 3, with x || c and z || b*) would be used as it takes advantage of the 2-fold symmetry about the b axis. However in the current version (3.1) of Amore, there is a bug in the translation function which gives incorrect results with ORTH 3.

Peak list from ROTFUN.
a b g S
SOLUTIONRC 1 74.87 76.93 346.67 0.0000 0.0000 0.0000 8.7 0.0 1
SOLUTIONRC 1 68.82 76.47 346.99 0.0000 0.0000 0.0000 8.0 0.0 2
SOLUTIONRC 1 246.92 85.32 8.87 0.0000 0.0000 0.0000 6.0 0.0 3
SOLUTIONRC 1 244.00 86.00 8.50 0.0000 0.0000 0.0000 5.9 0.0 4
SOLUTIONRC 1 329.77 62.61 22.31 0.0000 0.0000 0.0000 5.2 0.0 5
SOLUTIONRC 1 155.01 67.65 314.16 0.0000 0.0000 0.0000 5.0 0.0 6
SOLUTIONRC 1 298.57 90.00 194.00 0.0000 0.0000 0.0000 4.9 0.0 7
SOLUTIONRC 1 348.33 76.05 198.50 0.0000 0.0000 0.0000 4.8 0.0 8
Rotation function of mouse renin (F's).

The table below shows values of DS/s for 2 peaks (the other 2 are related by the crystallographic 2-fold).

Resolution limits = 20-3Å Resolution limits = 8-3Å
Radius/ŠB = -20Ų B = 0
15 0.79 -0.54 0.95 -0.22
20 2.07 0.37 2.39 0.81
25 1.92 0.28 2.44 1.14
30 2.59 0.58 2.73 1.27
35 3.14 0.63 3.08 0.79
40 2.90 0.43 3.24 1.05

5.2 Rotation function (AMORE / ROTFUN) with E's

5.2.1. PDBSET

Modify the PDB header in the coordinate file.

#
pdbset  XYZIN hexpep  XYZOUT hexpep_rfcell  <<EOD
SPACEG P1
CELL   80 84 97
EOD

5.2.2. SFALL

Compute structure factor amplitudes in space group P1 for the search model in a large rectangular cell.

#
# Structure factors for hexagonal pepsin model in RF cell.
#
sfall  XYZIN hexpep_rfcell  HKLOUT hexpep_rfcell <<EOD
MODE   SFCALC XYZIN
SFSG   1
SYMM   1
RESO   20 3
LABOUT PHIC=PC
EOD

5.2.3. ECALC

Normalise the observed and calculated amplitudes.

#
ecalc  HKLIN mrenin  HKLOUT mrenin_ecalc  <<EOD
TITLE  ** Ecalc for mouse renin crystal**
LABIN  FP=FPmrenin  SIGFP=SPmrenin
EOD

# Calc E's for hexagonal pepsin model.
#
ecalc  HKLIN hexpep_rfcell  HKLOUT hexpep_ecalc  <<EOD
TITLE  ** Ecalc for hexagonal pepsin model**
LABIN  FP=FC
EOD

5.2.4. AMoRe SORTFUN

Convert the normalised observed and calculated reflection data files into the internal format used by the AMORE program.

#
amore  HKLIN mrenin_ecalc  HKLPCK0 mrenin_ecalc.hkl  <<EOD
TITLE  ** packing h k l E for mouse renin crystal **
SORT
LABIN  FP=E  SIGFP=E
EOD

amore  HKLIN hexpep_ecalc  HKLPCK0 hexpep_ecalc.hkl  <<EOD
TITLE  ** packing h k l E for hexagonal pepsin model **
SORT
LABIN  FP=E  SIGFP=E
EOD

5.2.5. AMoRe ROTFUN CLMN

Compute spherical harmonic coefficients for the target and model Pattersons.

5.2.6. AMoRe ROTFUN CROSS

Compute the cross-RF.

#
amore  HKLPCK0 mrenin_ecalc.hkl  HKLPCK1 hexpep_ecalc.hkl  \
       CLMN0 mrenin_ecalc.clmn  CLMN1 hexpep_ecalc.clmn  \
       MAPOUT mrenin_ecalc_rotfun  <<EOD
ROTFUN
TITLE  Rotation function with E's.
CLMN   CRYST  ORTH 3  RESO 20 3  SPHERE 35            ! ORTH code 3.
CLMN   MODEL 1  RESO 20 3  SPHERE 35
ROTATE CROSS  MODEL 1  NPIC 20                        ! Beta = 0-180.
EOD
Peak list from ROTFUN.
a b g S
SOLUTIONRC 1 61.50 20.45 113.50 0.00000 0.00000 0.00000 9.9 0.0
SOLUTIONRC 1 67.98 26.00 107.67 0.00000 0.00000 0.00000 8.3 0.0
SOLUTIONRC 1 111.50 156.50 286.50 0.00000 0.00000 0.00000 6.0 0.0
SOLUTIONRC 1 116.00 157.39 293.50 0.00000 0.00000 0.00000 5.7 0.0
SOLUTIONRC 1 103.13 88.06 166.43 0.00000 0.00000 0.00000 5.1 0.0
SOLUTIONRC 1 67.02 105.44 97.32 0.00000 0.00000 0.00000 5.0 0.0
SOLUTIONRC 1 70.09 116.84 97.53 0.00000 0.00000 0.00000 5.0 0.0
SOLUTIONRC 1 114.90 8.17 100.72 0.00000 0.00000 0.00000 4.9 0.0

Note that the Eulerian angles of the peaks obtained here are different from those obtained previously (see section 4.1.5.); this is because of the different orthogonalisation convention (ORTH 3) used.

Rotation function of mouse renin (E's).

Signal (correct-background) and signal/noise are shown for 2 molecules (A and C). The other 2 molecules (B and D) give resolved peaks only for radii >= 35Å.

Radius/Å s DS (A) DS/s (A) DS (C) DS/s (C)
15 3.3 1.7 0.5 -5.0 -1.5
20 2.2 5.7 2.5 0.1 0.0
25 1.7 4.6 2.8 2.5 0.5
30 1.3 4.4 3.4 1.3 1.0
35 1.1 4.5 4.1 0.6 0.6
40 0.9 3.6 4.1 0.7 0.8

5.2.7. POLARRFN

In the case of NCS, using E's compute and plot the self-Rotation function in terms of spherical polar angles. Then compute again in terms of Euler angles, and check for consistency with the cross-RF. The self-Rotation function computed in terms of Euler angles is more accurate, but that computed in terms of spherical polars is better for visualisation.

Note that the alternate orthogonalisation code (ORTH 3) for monoclinic space groups is used here. This gives a more easily interpretable self-Rotation function map, because the crystallographic 2-fold axis along b is then at w = 0° (see section 2.9.), with c at (w,f) = (90°,0°) and a* at (w,f) = (90°,90°).

#
polarrfn  HKLIN mrenin_ecalc  MAPOUT polarrfn  PLOT polarrfn  <<EOD
TITLE  Self Rotation function (spherical polars) of Mouse Renin with E's, R=35
SELF   35
RESO   20 3
CRYST  FILE 1  ORTH 3  SYMM P21
LABIN  FILE 1  F=E  SIGF=E
LIMITS 0 180 5  0 180 5  0 180 5                ! Same for all self-RF's.
MAP
NOPRIN
PLOT   10 5
FIND   2 20 RMS
EOD

if ($status) exit

pltdev  -i polarrfn.plo  -sta 37


#
amore  HKLPCK0 mrenin_ecalc.hkl  CLMN0 mrenin_ecalc.clmn  -
       MAPOUT mrenin_self  <<EOD
ROTFUN
TITLE  Self Rotation function (Euler angles) of Mouse Renin with E's, R=35
ROTATE SELF  NPIC 20
EOD

if ($status) exit

grep SOLUTIONRC mrenin_ecalc_rotfun.log >! mrenin_ecalc_rotfun.pkl

if ($status) exit

rfcorr MAPIN mrenin_self  PEAKS mrenin_ecalc_rotfun.pkl  <<EOD
TITLE  Mouse renin self/cross rotation function correlation.
SPACEG P2
ORTH   3
CHI    180
EOD
In the mouse renin case, the native Patterson demonstrates the existence of a NCS 2-fold parallel to the 21 axis:
Output from RFCORR.
PeakAlphaBetaGamma
161.5020.45113.50
267.9826.00107.67
3111.50156.50286.50
4116.00157.39293.50
5103.1388.06166.43
667.02105.4497.32
770.09116.8497.53
8114.908.17100.72
Serial #Peak #Peak(#Symm) Theta Phi Chi self-RF
1 3 4 ( 2) 2 81 179 78.75
2 1 2 ( 2) 3 87 179 51.59
3 2 3 ( 2) 90 180 179 39.46
4 2 3 ( 1) 90 90 180 39.46
5 1 3 ( 2) 90 179 174 37.41
6 1 3 ( 1) 87 89 179 37.41
7 1 4 ( 1) 89 89 179 32.41
8 1 4 ( 2) 89 179 178 32.41
9 2 4 ( 2) 90 179 176 25.68
10 2 4 ( 1) 88 89 179 25.68
Inter-vector angles:
Serial[i] Serial[j]
(Symm[j])		 Angle Serial[i] Serial[j]
(Symm[j])		 Angle Serial[i] Serial[j]
(Symm[j])		 Angle
1 2( 1) 2 1 2( 2) 5 1 3( 1) 90
1 3( 2) 90 1 4( 1) 88 1 4( 2) 89
1 5( 1) 90 1 5( 2) 89 1 6( 1) 89
1 6( 2) 86 1 7( 1) 89 1 7( 2) 87
1 8( 1) 90 1 8( 2) 89 1 9( 1) 90
1 9( 2) 89 1 10( 1) 86 1 10( 2) 90
2 3( 1) 90 2 3( 2) 90 2 4( 1) 86
2 4( 2) 87 2 5( 1) 90 2 5( 2) 90
2 6( 1) 90 2 6( 2) 84 2 7( 1) 88
2 7( 2) 86 2 8( 1) 90 2 8( 2) 89
2 9( 1) 90 2 9( 2) 89 2 10( 1) 85
2 10( 2) 89 3 4( 1) 90 3 4( 2) 90
3 5( 1) 1 3 5( 2) 1 3 6( 1) 89
3 6( 2) 89 3 7( 1) 89 3 7( 2) 89
3 8( 1) 1 3 8( 2) 1 3 9( 1) 0
3 9( 2) 1 3 10( 1) 90 3 10( 2) 90
4 5( 1) 89 4 5( 2) 89 4 6( 1) 3
4 6( 2) 2 4 7( 1) 2 4 7( 2) 1
4 8( 1) 89 4 8( 2) 89 4 9( 1) 90
4 9( 2) 90 4 10( 1) 2 4 10( 2) 3
5 6( 1) 90 5 6( 2) 90 5 7( 1) 90
5 7( 2) 90 5 8( 1) 0 5 8( 2) 1
5 9( 1) 0 5 9( 2) 1 5 10( 1) 90
5 10( 2) 90 6 7( 1) 2 6 7( 2) 4
6 8( 1) 90 6 8( 2) 90 6 9( 1) 90
6 9( 2) 90 6 10( 1) 5 6 10( 2) 1
7 8( 1) 90 7 8( 2) 90 7 9( 1) 89
7 9( 2) 89 7 10( 1) 3 7 10( 2) 1
8 9( 1) 1 8 9( 2) 1 8 10( 1) 89
8 10( 2) 89 9 10( 1) 90 9 10( 2) 90

5.3. Translation function (AMORE / TRAFUN) with F's

5.3.1. AMoRe TRAFUN

For the best RF solutions, compute the TF.

#
amore  HKLPCK0 mrenin.hkl  table1 hexpep.tab  MAPOUT mrenin_trafun  \
       TRAING_NR 30000 <<EOD
TRAFUN CB  RESO 20 3.5  PKLIM .25  NPIC 50
TITLE  Translation function
CRYST  SHARP -10
SOLUTIONRC    1   74.87   76.93  346.67  0.0000  0.0000  0.0000  9.4  0.0   1
SOLUTIONRC    1  111.18  103.53  166.99  0.0000  0.0000  0.0000  8.0  0.0   2
SOLUTIONRC    1  246.92   85.32    8.87  0.0000  0.0000  0.0000  6.0  0.0   3
SOLUTIONRC    1  296.00   94.00  188.50  0.0000  0.0000  0.0000  5.9  0.0   4
EOD
\rm mrenin_trafun.map

Note that a 2-fold crystallographic symmetry operator about the b axis (orthogonal y axis) has been applied to the Eulerian angles for molecules B and D (compare with the output from the Rotation function in section 4.1.5.). Although this is not essential, it is nevertheless convenient because it ensures that the set of protomer orientations chosen obeys the non-crystallographic 222 symmetry of the tetramer.

Sample output from AMORE/TRAFUN.
SOLUT_1 1 74.87 76.93 346.67 0.4167 0.0000 0.4904 11.1 57.6 1
SOLUT_1 1 74.87 76.93 346.67 0.3333 0.0000 0.2981 10.3 57.8 4
SOLUT_1 1 74.87 76.93 346.67 0.0938 0.0000 0.4904 9.8 57.9 6
SOLUT_2 1 111.18 103.53 166.99 0.3958 0.0000 0.0096 10.5 57.8 1
SOLUT_2 1 111.18 103.53 166.99 0.0104 0.0000 0.3462 9.3 58.4 6
SOLUT_2 1 111.18 103.53 166.99 0.4896 0.0000 0.1923 9.3 58.1 5
SOLUT_3 1 246.92 85.32 8.87 0.0729 0.0000 0.0673 9.0 58.2 2
SOLUT_3 1 246.92 85.32 8.87 0.4062 0.0000 0.0673 9.0 58.2 1
SOLUT_3 1 246.92 85.32 8.87 0.3125 0.0000 0.1827 8.5 58.4 6
SOLUT_4 1 296.00 94.00 188.50 0.4271 0.0000 0.4327 9.4 58.0 2
SOLUT_4 1 296.00 94.00 188.50 0.1875 0.0000 0.2404 8.7 58.5 4
SOLUT_4 1 296.00 94.00 188.50 0.1875 0.0000 0.3077 8.7 58.2 6
Translation function of mouse renin (F's).
Correlation coefficient
Molecule Correct Background
A 0.111 0.103
B 0.105 0.093
C 0.090 0.085
D 0.094 0.087

5.3.2. AMoRe TRAFUN 2

Fix the first molecule, compute the TF for the second; repeat for rest.

#
amore  HKLPCK0 mrenin.hkl  table1 hexpep.tab  MAPOUT mrenin_trafun  \
       TRAING_NR 30000 <<EOD
TRAFUN CB  NMOL 2  RESO 20 3.5  PKLIM .25  NPIC 50
TITLE  Translation function.  Fix A; find B.
CRYST  SHARP -10
SOLUT_1  FIX  1   74.87   76.93  346.67  0.4167  0.0000  0.4904 11.1 57.6   1
SOLUTIONRC    1  111.18  103.53  166.99  0.0000  0.0000  0.0000  8.0  0.0   2
EOD
\rm mrenin_trafun.map


#
amore  HKLPCK0 mrenin.hkl  table1 hexpep.tab  MAPOUT mrenin_trafun  \
       TRAING_NR 30000 <<EOD
TRAFUN CB  NMOL 3  RESO 20 3.5  PKLIM .25  NPIC 50
TITLE  Translation function.  Fix A and B; find D.
CRYST  SHARP -10
SOLUT_1  FIX  1   74.87   76.93  346.67  0.4167  0.0000  0.4904 11.1 57.6   1
SOLUT_2  FIX  1  111.18  103.53  166.99  0.8984  0.0213  0.0080 18.8 56.0   1
SOLUTIONRC    1  296.00   94.00  188.50  0.0000  0.0000  0.0000  5.9  0.0   4
EOD
\rm mrenin_trafun.map


#
amore  HKLPCK0 mrenin.hkl  table1 hexpep.tab  MAPOUT mrenin_trafun  \
       TRAING_NR 30000 <<EOD
TRAFUN CB  NMOL 4  RESO 20 3.5  PKLIM .25  NPIC 50
TITLE  Translation function.  Fix A, B and D; find C.
CRYST  SHARP -10
SOLUT_1  FIX  1   74.87   76.93  346.67  0.4167  0.0000  0.4904 11.1 57.6   1
SOLUT_2  FIX  1  111.18  103.53  166.99  0.8984  0.0213  0.0080 18.8 56.0   1
SOLUT_3  FIX  1  296.00   94.00  188.50  0.4227  0.9769  0.9295 22.5 54.8   1
SOLUTIONRC    1  246.92   85.32    8.87  0.0000  0.0000  0.0000  6.0  0.0   3
EOD
\rm mrenin_trafun.map

5.3.3. AMoRe FITFUN

For the best TF solution(s), do rigid-body refinements and choose the solution with the highest correlation coefficient.

#
amore  HKLPCK0 mrenin.hkl  table1 hexpep.tab  FITING_NR 50000  <<EOD
FITFUN NMOL 4  RESO 20 3
TITLE  Rigid body refinement.
REFSOL AL BE GA X Y Z BF
SOLUT_1       1   74.87   76.93  346.67  0.4167  0.0000  0.4904 11.1 57.6   1
SOLUT_2       1  111.18  103.53  166.99  0.8984  0.0213  0.0080 18.8 56.0   1
SOLUT_4       1  246.92   85.32    8.87  0.9038  0.0018  0.5704 27.4 54.3   1
SOLUT_3       1  296.00   94.00  188.50  0.4227  0.9769  0.9295 22.5 54.8   1
EOD
Sample output from AMORE/FITFUN.
  Scale, B-Fact, Correlation Coefficient, R-Fact
    0.20040E+01    26.834    48.589    50.694
    0.19908E+01    26.757    49.640    50.165
    0.19851E+01    26.844    50.399    49.725
    0.19806E+01    26.854    50.837    49.442

 FINAL POSITIONS
 SOLUTIONF     1   76.40   78.04  346.60  0.4206 -0.0007  0.4868 50.8 49.4   1
 SOLUTIONF     1  113.07  102.95  167.52  0.8980  0.0245  0.0083 50.8 49.4   2
 SOLUTIONF     1  250.63   85.32    8.82  0.9019  0.0022  0.5695 50.8 49.4   4
 SOLUTIONF     1  297.49   93.18  188.39  0.4229  0.9768  0.9281 50.8 49.4   3

5.3.4. PDBSET

Apply the optimised rotation matrix and translation vector to the model coordinates output by AMORE / TABFUN.

#
pdbset XYZIN hexpep_model  XYZOUT mrenin_mola <<EOD
SPACEG P21
CHAIN  A
ROTATE EULER   76.40   78.04  346.60
SHIFT  FRACT  0.4206 -0.0007  0.4868
EOD

pdbset XYZIN hexpep_model  XYZOUT mrenin_molb <<EOD
SPACEG P21
CHAIN  B
ROTATE EULER  113.07  102.95  167.52
SHIFT  FRACT  0.8980  0.0245  0.0083
EOD

pdbset XYZIN hexpep_model  XYZOUT mrenin_molc <<EOD
SPACEG P21
CHAIN  C
ROTATE EULER  250.63   85.32    8.82
SHIFT  FRACT  0.9019  0.0022  0.5695
EOD

pdbset XYZIN hexpep_model  XYZOUT mrenin_mold <<EOD
SPACEG P21
CHAIN  D
ROTATE EULER  297.49   93.18  188.39
SHIFT  FRACT  0.4229  0.9768  0.9281
EOD

5.4 Translation function (TFFC / FFT) using E's

5.4.1. PDBSET

For each molecule in the asymmetric unit apply the appropriate rotation matrix, calculated from the Eulerian angles of the peak(s) in the RF, to the model coordinates. Also modify the PDB header in the coordinate file.

#
pdbset XYZIN hexpep  XYZOUT hexpep_mola  <<EOD
CELL   78.34 117.76 85.88 90 101.18 90
SPACEG P1
ORTHOG 3
ROTATE EULER  61.50    20.45   113.50
EOD

pdbset XYZIN hexpep  XYZOUT hexpep_molb  <<EOD
CELL   78.34 117.76 85.88 90 101.18 90
SPACEG P1
ORTHOG 3
ROTATE EULER  247.98    26.00   107.67
EOD

pdbset XYZIN hexpep  XYZOUT hexpep_molc  <<EOD
CELL   78.34 117.76 85.88 90 101.18 90
SPACEG P1
ORTHOG 3
ROTATE EULER  111.50   156.50   286.50
EOD

pdbset XYZIN hexpep  XYZOUT hexpep_mold  <<EOD
CELL   78.34 117.76 85.88 90 101.18 90
SPACEG P1
ORTHOG 3
ROTATE EULER  296.00   157.39   293.50
EOD

Again, note that a 2-fold crystallographic symmetry operator about the b axis (orthogonal z axis) has been applied to the Eulerian angles for molecules B and D (compare with the output from the Rotation function in section 4.2.6.), in order to ensure that the set of protomer orientations chosen obeys the non-crystallographic 222 symmetry of the tetramer.

5.4.2. SFALL

Calculate structure factor amplitudes and phases for each molecule in the asymmetric unit.

#
# Structure factors for hexagonal pepsin models in TF cell.
#
sfall  XYZIN hexpep_mola  HKLOUT hexpep_mola  <<EOD
MODE   SFCALC XYZIN
SFSG   1
SYMM   1
RESO   20 3
LABOUT PHIC=PC
EOD

sfall  XYZIN hexpep_molb  HKLOUT hexpep_molb  <<EOD
MODE   SFCALC XYZIN
SFSG   1
SYMM   1
RESO   20 3
LABOUT PHIC=PC
EOD

sfall  XYZIN hexpep_molc  HKLOUT hexpep_molc  <<EOD
MODE   SFCALC XYZIN
SFSG   1
SYMM   1
RESO   20 3
LABOUT PHIC=PC
EOD

sfall  XYZIN hexpep_mold  HKLOUT hexpep_mold  <<EOD
MODE   SFCALC XYZIN
SFSG   1
SYMM   1
RESO   20 3
LABOUT PHIC=PC
EOD

5.4.3. CAD

Combine all the columns for the observed reflection data with those for the calculated molecules into a single file.

#
cad    HKLIN1 mrenin  HKLIN2 hexpep_mola  HKLIN3 hexpep_molb  \
       HKLIN4 hexpep_molc  HKLIN5 hexpep_mold  HKLOUT mrenin_cad  <<EOD
RESO   OVER 20 3
TITLE  COMBINING  mouse renin and rotated hexpep molecules A, B, C, D.
LABIN  FILE 1  E1=FPmrenin E2=SPmrenin
CTYPE  FILE 1  E1=F        E2=Q
LABIN  FILE 2  E1=FC       E2=PC
CTYPE  FILE 2  E1=U        E2=V
LABOUT FILE 2  E1=FCA      E2=PCA
LABIN  FILE 3  E1=FC       E2=PC
CTYPE  FILE 3  E1=U        E2=V
LABOUT FILE 3  E1=FCB      E2=PCB
LABIN  FILE 4  E1=FC       E2=PC
CTYPE  FILE 4  E1=U        E2=V
LABOUT FILE 4  E1=FCC      E2=PCC
LABIN  FILE 5  E1=FC       E2=PC
CTYPE  FILE 5  E1=U        E2=V
LABOUT FILE 5  E1=FCD      E2=PCD
END
EOD

5.4.4. TFFC

Compute the Fourier coefficients for the Translation functions.

#
tffc   HKLIN mrenin_cad  HKLOUT mrenin_mola  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
FIND   A
EOD

tffc   HKLIN mrenin_cad  HKLOUT mrenin_molb  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
FIND   B
EOD

tffc   HKLIN mrenin_cad  HKLOUT mrenin_molc  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
FIND   C
EOD

tffc   HKLIN mrenin_cad  HKLOUT mrenin_mold  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
FIND   D
EOD

5.4.5. FFT

Compute the Fourier transforms to get the Translation function maps.

#
fft    HKLIN mrenin_mola  MAPOUT mrenin_mola  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 .5  0 0  0 .5                    ! Limits for point group 2.
GRID   160 240 180
LABIN  A=A  B=B
EOD

fft    HKLIN mrenin_molb  MAPOUT mrenin_molb  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 .5  0 0  0 .5
GRID   160 240 180
LABIN  A=A  B=B
EOD

fft    HKLIN mrenin_molc  MAPOUT mrenin_molc  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 .5  0 0  0 .5
GRID   160 240 180
LABIN  A=A  B=B
EOD

fft    HKLIN mrenin_mold  MAPOUT mrenin_mold  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 .5  0 0  0 .5
GRID   160 240 180
LABIN  A=A  B=B
EOD

5.4.6. MAPSIG

Search the Translation function map for peaks; one peak should stand out from the rest with relative signal/noise > 1.

#
mapsig MAPIN mrenin_mola  PEAK_LIST mrenin_mola.pkl  <<EOD
EOD
\rm mrenin_mola.mtz mrenin_mola.map
Peak list.
tx ty tz S/s
1 27 9 15.0 0.0 31.0 0.314 0.094 0.000 0.172 6.11
2 10 6 42.3 0.0 32.5 0.210 0.265 0.000 0.181 4.09
3 41 9 1.4 0.0 8.8 0.178 0.009 0.000 0.049 3.47
4 7 7 57.5 0.0 29.9 0.189 0.360 0.000 0.166 3.67 
#
mapsig MAPIN mrenin_molb  PEAK_LIST mrenin_molb.pkl  <<EOD
EOD
\rm mrenin_molb.mtz mrenin_molb.map
Peak list.
1 21 9 64.1 0.0 63.4 0.346 0.400 0.000 0.352 7.04
2 6 6 50.7 0.0 69.3 0.204 0.317 0.000 0.385 4.16
3 7 7 24.4 0.0 11.7 0.181 0.153 0.000 0.065 3.68
4 11 7 36.5 0.0 61.8 0.161 0.228 0.000 0.343 3.29 
#
mapsig MAPIN mrenin_molc  PEAK_LIST mrenin_molc.pkl  <<EOD
EOD
\rm mrenin_molc.mtz mrenin_molc.map
Peak list.
1 30 9 1.9 0.0 48.6 0.292 0.012 0.000 0.270 5.96
2 7 7 25.2 0.0 70.1 0.169 0.157 0.000 0.390 3.45
3 10 7 78.5 0.0 7.5 0.189 0.491 0.000 0.042 3.85
4 11 8 46.4 0.0 60.3 0.167 0.290 0.000 0.335 3.39 
#
mapsig MAPIN mrenin_mold  PEAK_LIST mrenin_mold.pkl  <<EOD
EOD
\rm mrenin_mold.mtz mrenin_mold.map
Peak list.
1 17 8 46.0 0.0 32.0 0.305 0.287 0.000 0.178 6.03
2 11 6 76.2 0.0 73.5 0.233 0.476 0.000 0.408 4.60
3 7 7 44.9 0.0 71.1 0.197 0.281 0.000 0.395 3.90
4 27 8 73.2 0.0 32.5 0.176 0.458 0.000 0.181 3.49

5.4.7. TFFC, FFT, MAPSIG

In cases of non-crystallographic symmetry it is necessary to place all molecules relative to the same origin with non-crystallographic Translation functions.

#
tffc   HKLIN mrenin_cad  HKLOUT mrenin_molca  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
PART
VECT   C 0.012  0.000  0.270
FIND   A
EOD

if ($status) exit

fft    HKLIN mrenin_molca  MAPOUT mrenin_molca  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 1  0 1  0 1                      ! Limits for NC-TF in P cell.
GRID   160 240 180
LABIN  A=A  B=B
EOD

if ($status) exit

mapsig MAPIN mrenin_molca  PEAK_LIST mrenin_molca.pkl  <<EOD
EOD
\rm mrenin_molca.mtz mrenin_molca.map
Peak list.
tx ty tz S/s
1 173 27 15.2 109.0 31.7 1.026 0.095 0.454 0.176 9.07
2 41 26 27.0 207.0 133.0 0.724 0.169 0.863 0.739 6.39
3 46 26 122.0 222.0 121.0 0.683 0.762 0.925 0.672 6.03
4 33 26 68.0 196.0 156.0 0.682 0.425 0.817 0.867 6.03 
#
tffc   HKLIN mrenin_cad  HKLOUT mrenin_molcad  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
PART
VECT   C 0.012  0.000  0.270
VECT   A 0.095  0.454  0.176
FIND   D
EOD

if ($status) exit

fft    HKLIN mrenin_molcad  MAPOUT mrenin_molcad  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 1  0 1  0 1
GRID   160 240 180
LABIN  A=A  B=B
EOD

if ($status) exit

mapsig MAPIN mrenin_molcad  PEAK_LIST mrenin_molcad.pkl  <<EOD
EOD
\rm mrenin_molcad.mtz mrenin_molcad.map
Peak list.
1 188 27 46.1 3.9 32.4 2.339 0.288 0.016 0.180 11.56
2 47 26 153.6 123.0 121.5 1.697 0.960 0.513 0.675 8.39
3 151 21 152.8 111.7 123.3 1.634 0.955 0.465 0.685 8.08
4 82 27 45.5 230.2 32.2 1.507 0.285 0.959 0.179 7.45 
#
tffc   HKLIN mrenin_cad  HKLOUT mrenin_molcadb  <<EOD
TITLE  tffc on mouse renin
RESO   20 3
LABIN  FP=FPmrenin  SIGFP=SPmrenin
NONCRY 4
PART
VECT   C 0.012  0.000  0.270
VECT   A 0.095  0.454  0.176
VECT   D 0.288  0.016  0.180
EOD

if ($status) exit

fft    HKLIN mrenin_molcadb  MAPOUT mrenin_molcadb  <<EOD
TITLE  FFT of tffc map
XYZLIM 0 1  0 1  0 1
GRID   160 240 180
LABIN  A=A  B=B
EOD

if ($status) exit

mapsig MAPIN mrenin_molcadb  PEAK_LIST mrenin_molcadb.pkl  <<EOD
EOD
\rm mrenin_molcadb.mtz mrenin_molcadb.map
Peak list.
tx ty tz S/s
1 116 27 57.1 114.7 63.4 2.479 0.357 0.478 0.352 8.77
2 23 21 19.0 104.0 111.0 1.447 0.119 0.433 0.617 5.12
3 18 18 18.7 111.2 5.0 1.425 0.117 0.463 0.028 5.04
4 16 15 142.3 66.6 169.4 1.465 0.889 0.277 0.941 5.18
Translation function of mouse renin (E's).
Fix Find DS/s
- A 2.02
- B 0.49
- C 2.51
- D 1.43
C A 2.68
CA D 3.17
CAD B 3.65

Note that the fractional translation vectors obtained here are different from those obtained previously (section 4.3.3.) because the centroid of the model coordinates used had been shiftedto the origin.

5.4.8. PDBSET

Apply these translation vectors to the rotated model coordinates.

#
pdbset XYZIN hexpep_mola  XYZOUT mrenin_mola <<EOD
SPACEG P21
CHAIN  A
SHIFT  FRACT .095 -.546 .176
EOD

pdbset XYZIN hexpep_molb  XYZOUT mrenin_molb <<EOD
SPACEG P21
CHAIN  B
SHIFT  FRACT .357 -.522 .352
EOD

pdbset XYZIN hexpep_molc  XYZOUT mrenin_molc <<EOD
SPACEG P21
CHAIN  C
SHIFT  FRACT .012 1 .27
EOD

pdbset XYZIN hexpep_mold  XYZOUT mrenin_mold <<EOD
SPACEG P21
CHAIN  D
SHIFT  FRACT .288 1.016 .18
EOD

Note that unit cell shifts have been added to some of the fractional translation vectors in order to bring all 4 molecules together into a tetramer.

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