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4. MIRAS case study - Porphobilinogen deaminase

Six heavy-atom derivatives of porphobilinogen deaminase (PBGD), an enzyme of 313 amino-acids found ubiquitously in the haem and chlorophyll biosynthetic pathways, and which crystallises in space group P21212 were collected to 3Å resolution. Four of the derivatives appeared to have usable anomalous data (the anomalous data from the other two were rejected because of data collection problems).

4.1. Suggested procedure for derivative-native scaling

#
fhscal  HKLIN pbgd  HKLOUT pbgd_fhscal  <<EOD
LABIN  FP=FNAT     SIGFP=SIGFNAT                                         -
       FPH1=FPTCL  SIGFPH1=SIGFPTCL  DANO1=DANPTCL  SIGDANO1=SIGDANPTCL  -
       FPH2=FUAC   SIGFPH2=SIGFUAC   DANO2=DANUAC   SIGDANO2=SIGDANUAC   -
       FPH3=FUF    SIGFPH3=SIGFUF    DANO3=DANUF    SIGDANO3=SIGDANUF    -
       FPH4=FUS    SIGFPH4=SIGFUS                                        -
       FPH5=FPCMBS SIGFPH5=SIGFPCMBS DANO5=DANPCMBS SIGDANO5=SIGDANPCMBS -
       FPH6=FYBCL  SIGFPH6=SIGFYBCL
BIAS   1    ! Compensate for over-estimation of weak reflections.
EOD

Note that the BIAS factor, which compensates for over-estimation of the square of the isomorphous difference for weak reflections, particularly at high resolution, should only be used if it is known that the standard deviations of the amplitudes are reliable.

4.2. Example of manual Patterson interpretation

The w=0, v=½ and u=½ Harker sections of the isomorphous difference Pattersons for the uranyl fluoride derivative of PBGD are shown. For better resolution, click on the pictures.

w=0
v u

There is an obvious peak on each section respectively at:

( 2x, 2y, 0) = (51/120, 37/108, 0/72)
(½+2x, ½, 2z) = (9/120, 54/108, 24/72)
(½, ½+2y, 2z) = (60/120, 17/108, 24/72)

which can readily be interpreted as arising from a site with the coordinates:

(x, y, z) = (25.5/120, 18.5/108, 12/72)

The sampling grid, in this case 120x108x72 over a complete unit cell, has been chosen so that the separation between grid points = high resolution cutoff / 4 (=0.75Å).

There is also a second rather less obvious site, using the Harker vectors:

(2x, 2y, 0) = (0/120, 53/108, 0/72)
(½+2x, ½, 2z) = (60/120, 54/108, 16/72)
(½, ½+2y, 2z) = (60/120, 1/108, 16/72)

Remember, the coordinates of the second site can only be unambiguously assigned by using the cross vectors between it and the first site. Eventually five uranyl fluoride sites were found, but the remaining three are not easy to find by manual methods. Incidentally, the uranyl fluoride derivative turned out to be the best of the six used.

4.3. Suggested procedures for automatic heavy-atom Patterson search

4.3.1. SHELXS-86 script to run Patterson search

If necessary, first convert the reflection file to SHELX format.

#
mtz2various  HKLIN pgbd_fhscal  HKLOUT ufsx.hkl  <<EOD
OUTPUT SHELX
LABIN  FP=FNAT  SIGFP=SIGFNAT  FPH=FUF  SIGFPH=SIGFUF
EOD

if ($status) exit

cat  <<EOD  >ufsx.ins
TITL PBGD UF isodif Patterson
CELL 1.5418 88.0 75.9 50.5 90 90 90
LATT -1
SYMM -X,-Y,Z
SYMM .5-X,.5+Y,-Z
SYMM .5+X,.5-Y,-Z
SFAC N
SFAC U 0 0 0 0 0 0 0 0 86 0 0 100 5 238
UNIT 100 12
OMIT 0
PATT 10 25 5
HKLF 3
EOD
shelxs-86  ufsx
Sample output from SHELXS-86

In this example, the first site in the list of possible heavy atom positions, found by the program from the Harker vectors alone, is the one previously found manually, but with hand inversion, together with one of the symmetry transformations of the space group (-x,-y,z). Then the program finds the other sites using cross vectors; in this case the 2nd, 3rd and 5th sites in the second list are also correct. If the first site in the list of possibles had been wrong, then the program has an option to enter a site manually, as indicated by the message.

POSSIBLE HEAVY ATOM POSITIONS FOR  PBGD UF isodif Patterson
X Y Z 1/MULT R(PAT) RE(HA) SELFMF
.213.170.8361.0000.200.29935.4
.787.825.1641.0000.200.30023.0
.068.000.8831.0000.200.30123.1
.000.000.1170.5000.200.30141.5
.930.000.1171.0000.200.30124.4
.000.185.8881.0000.200.30124.5
.000.814.1121.0000.200.30125.3
.000.239.8921.0000.200.30216.5
.000.756.1081.0000.488.3014.9
** IT WILL NOW BE ASSUMED THAT THE FIRST ATOM IN THE ABOVE LIST IS A CORRECT
 HEAVY ATOM.  IF THIS IS NOT TRUE, THE REST OF THE OUTPUT WILL BE WORTHLESS.
 IN SUCH A CASE, RERUN THE JOB WITH A DIFFERENT ATOM FROM THE ABOVE LIST
 INSERTED BETWEEN THE PATT AND HKLF INSTRUCTIONS

 PATTERSON MINIMUM FUNCTIONS AND DISTANCES FOR  PBGD UF isodif Patterson


     X     Y     Z   1/MULT  SELF  CROSS-VECTORS
   .213  .170  .836  1.0000  52.7
                            41.92
   .314  .184  .893  1.0000  21.2  24.9
                            41.04  9.37
   .319  .312  .661  1.0000    .9  22.9  13.6
                            42.69 16.78 15.23
   .466  .224 1.177  1.0000    .0  21.0    .4    .0
                            34.54 23.25 19.83 28.45
   .497  .257 1.388  1.0000  25.6  20.9  10.1   9.0    .0
                            36.94 22.83 30.25 21.28 11.29
   .256  .190  .890  1.0000    .0  14.1    .0   1.2    .0    .0
                            39.55  4.91  5.13 15.82 23.58 27.07
   .464  .227 1.470  1.0000    .0  11.5   5.2    .0    .0    .0    .0
                            35.09 27.96 25.32 17.22 14.80  5.54 28.16
   .322  .325 1.016  1.0000    .0  10.8    .0   4.0   5.0    .0    .0    .0
                            40.04 17.68 12.40 17.95 16.84 24.82 13.34 27.09
   .312  .178  .782  1.0000    .0   7.2    .0   8.4    .0    .0    .0    .0    .0
                            42.65  9.13  5.60 11.92 24.32 26.40  7.43 21.00 16.27
   .213 -.002  .577  1.0000    .4   6.4    .0    .0   1.0    .0    .0    .0    .0    .0
                            37.56 18.43 23.03 18.79 28.91 26.12 21.83 25.91 24.59 19.19
   .370  .228  .836  1.0000    .0   6.3    .0   7.0    .5    .0   4.1    .0    .0    .0    .0
                            41.46 14.50  6.64 11.76 19.16 25.31 10.82 20.23 12.45  6.93 25.79
   .179  .170  .664  1.0000   6.6   6.3    .4    .0    .8    .0    .0    .0    .0    .0    .0   5.3
                            40.68  9.18 16.60 16.43 21.95 17.15 13.37 21.58 24.76 13.18 14.06 19.45

4.3.2. SHELXS-86 script to run direct methods phasing

#
cat  <<EOD  >ufsx.ins
TITL PBGD UF direct methods
CELL 1.5418 88.0 75.9 50.5 90 90 90
LATT -1
SYMM -X,-Y,Z
SYMM .5-X,.5+Y,-Z
SYMM .5+X,.5-Y,-Z
SFAC N
SFAC U 0 0 0 0 0 0 0 0 86 0 0 100 5 238
UNIT 100 4
TREF 50 400
SUBS 6 160
PLAN 10
HKLF 3
EOD
shelxs-86  ufsx

For the UF derivative this produced the same result as the Patterson search. However whereas Patterson searches produced at least one correct site for all six PBGD derivatives, direct methods worked for only four derivatives. The SHELXS-86 documentation points out that the direct methods phasing is expected to work best in high symmetry space groups, while the Patterson search is the best method for low symmetry or polar space groups.

4.3.3. FFT / VECSUM / PEAKMAX script to run symmetry function

#
fft  HKLIN pbgd_fhscal  MAPOUT ufdpa  <<EOD
TITL UF FH scaled native 3A isodif Patterson.
PATT
BIAS  1
LABI  F1=FUF SIG1=SIGFUF F2=FNAT SIG2=SIGFNAT
FFTS  2
GRID  120 108 72
XYZL  0 1 0 .5 0 1
VF00  151291.53       ! V factor from FHSCAL output.
EOD

if ($status) exit

vecsum  MAPIN ufdpa  MAPOUT vecsum1  <<EOD
Uranyl fluoride symmetry minimum.
2 1 3
0 30 0 27 0 18
50 .2 1.1 0 0 0
-1 1 3 3 0 3 0 3
-X,-Y,Z
½-X,½+Y,-Z
½+X,½-Y,-Z
1 2 3
1 1 1
EOD

if ($status) exit

peakmax  MAPIN vecsum1  <<EOD
THRESH RMS 2
NUMPEAKS 20
OUTPUT NONE
EOD
Output from PEAKMAX:
Order Number Site Height Grid location Fractional coordinates Orthogonal coordinates
1 6 6 36.05 3.46 26 19 12 0.21340 0.17168 0.16489 18.78 13.03 8.33
2 3 3 31.22 3.00 0 0 9 0.00000 0.00000 0.11806 0.00 0.00 5.96
3 1 1 31.22 3.00 0 0 9 0.00000 0.00000 0.11806 0.00 0.00 5.96
4 2 2 26.00 2.50 0 27 8 0.00000 0.25000 0.10981 0.00 18.98 5.55
5 7 7 22.96 2.21 11 27 16 0.09173 0.25000 0.22003 8.07 18.98 11.11
6 8 0 22.34 2.15 26 18 18 0.22018 0.16664 0.25000 19.38 12.65 12.63
7 4 4 21.95 2.11 8 0 9 0.07022 0.00000 0.11842 6.18 0.00 5.98
8 5 5 20.84 2.00 22 19 12 0.18374 0.17935 0.16031 16.17 13.61 8.10

4.3.4. VECSUM / PEAKMAX script to run superposition function

#
vecsum  MAPIN ufdpa  MAPOUT vecsum2  <<EOD
Uranyl fluoride superposition with 1 site.
2 1 3
0 60 0 54 0 72
50 .2 1.1 0 0 0
-1 1 3 3 0 3 1 3
-X,-Y,Z
½-X,½+Y,-Z
½+X,½-Y,-Z
1 2 3
1 1 1
26 19 12
EOD

if ($status) exit

peakmax  MAPIN vecsum2  <<EOD
THRESH RMS 2
NUMPEAKS 20
OUTPUT NONE
EOD
Output from PEAKMAX:
Order Number Site Height Grid location Fractional coordinates Orthogonal coordinates
1 10 10 37.13 5.06 26 19 12 0.21288 0.17173 0.16523 18.73 13.03 8.34
2 15 15 22.94 3.12 38 35 25 0.31561 0.32158 0.34106 27.77 24.41 17.22
3 17 17 21.96 2.99 0 26 28 0.00000 0.24387 0.38709 0.00 18.51 19.55
4 22 22 21.96 2.99 60 28 44 0.50000 0.25613 0.61291 44.00 19.44 30.95
5 30 30 21.08 2.87 35 19 60 0.28768 0.17199 0.83935 25.32 13.05 42.39
6 2 2 20.48 2.79 38 20 8 0.31375 0.18469 0.10975 27.61 14.02 5.54
7 24 24 17.34 2.36 26 18 48 0.21658 0.16600 0.66058 19.06 12.60 33.36
8 20 20 17.24 2.35 25 19 37 0.21237 0.17317 0.51793 18.69 13.14 26.16
9 5 5 17.09 2.33 60 0 9 0.50000 0.00000 0.12157 44.00 0.00 6.14
10 31 31 17.09 2.33 0 54 63 0.00000 0.50000 0.87843 0.00 37.95 44.36
11 13 13 17.07 2.32 27 35 24 0.22247 0.32861 0.33359 19.58 24.94 16.85
12 8 8 17.07 2.32 26 11 12 0.21472 0.10160 0.16868 18.90 7.71 8.52
13 33 33 16.99 2.31 60 0 64 0.50000 0.00000 0.89342 44.00 0.00 45.12
14 3 3 16.99 2.31 0 54 8 0.00000 0.50000 0.10658 0.00 37.95 5.38
15 16 16 16.76 2.28 0 0 27 0.00000 0.00000 0.37710 0.00 0.00 19.04
16 23 23 16.76 2.28 60 54 45 0.50000 0.50000 0.62290 44.00 37.95 31.46
17 9 9 16.32 2.22 34 11 12 0.28572 0.10138 0.17087 25.14 7.69 8.63
18 14 14 16.18 2.20 33 36 24 0.27855 0.33592 0.33218 24.51 25.50 16.77
19 19 19 15.56 2.12 26 36 29 0.21561 0.33373 0.40170 18.97 25.33 20.29
20 7 7 15.50 2.11 34 18 11 0.28077 0.17000 0.15587 24.71 12.90 7.87

4.3.5. VECSUM script to check Harker & cross vectors

#
vecsum  MAPIN ufdpa  <<EOD
Uranyl fluoride check all vectors for 2 sites.
2 1 3
0 60 0 54 0 72
50 .2 1.1 0 0 0
0 1 3 3 0 3 -2 3
-X,-Y,Z
½-X,½+Y,-Z
½+X,½-Y,-Z
1 2 3
1 1 1
26 19 12
38 35 25
EOD
Output:
HARKER VECTORS FROM SITE 1
TO SITE 1 -X,-Y,Z UVW = 52 37 0 VALUE = 411 M
TO SITE 1 ½-X,½+Y,-Z UVW = 9 54 48 VALUE = 463 Q
TO SITE 1 ½+X,½-Y,-Z UVW = 60 16 48 VALUE = 585 Z
CROSS VECTORS FROM SITE 1
TO SITE 2 X,Y,Z UVW = 12 15 13 VALUE = 233 8
TO SITE 2 -X,-Y,Z UVW = 55 54 13 VALUE = 366 I
TO SITE 2 ½-X,½+Y,-Z UVW = 4 38 36 VALUE = 402 L
TO SITE 2 ½+X,½-Y,-Z UVW = 72 0 36 VALUE = 377 J
HARKER VECTORS FROM SITE 2
TO SITE 2 -X,-Y,Z UVW = 44 39 0 VALUE = 299 D
TO SITE 2 ½-X,½+Y,-Z UVW = 104 54 23 VALUE = 170 3
TO SITE 2 ½+X,½-Y,-Z UVW = 60 16 49 VALUE = 566 X
NO OF HARKER VECTOR MISSES=0HITS=6
NO OF CROSS VECTOR MISSES=0HITS=4

The script below shows what happens if a wrong site is added:

#
vecsum  MAPIN ufdpa  <<EOD
Uranyl fluoride check all vectors for 3 sites - last one wrong
2 1 3
0 60 0 54 0 72
50 .2 1.1 0 0 0
0 1 3 3 0 3 -3 3
-X,-Y,Z
½-X,½+Y,-Z
½+X,½-Y,-Z
1 2 3
1 1 1
26 19 12
38 35 25
98 73 47
EOD
Output:
HARKER VECTORS FROM SITE 1
TO SITE 1 -X,-Y,Z UVW = 52 37 0 VALUE = 411 M
TO SITE 1 ½-X,½+Y,-Z UVW = 9 54 48 VALUE = 463 Q
TO SITE 1 ½+X,½-Y,-Z UVW = 60 16 48 VALUE = 585 Z
CROSS VECTORS FROM SITE 1
TO SITE 2 X,Y,Z UVW = 12 15 13 VALUE = 233 8
TO SITE 2 -X,-Y,Z UVW = 55 54 13 VALUE = 366 I
TO SITE 2 ½-X,½+Y,-Z UVW = 4 38 36 VALUE = 402 L
TO SITE 2 ½+X,½-Y,-Z UVW = 72 0 36 VALUE = 377 J
TO SITE 3 X,Y,Z UVW = 72 54 34 VALUE = 174 4
TO SITE 3 -X,-Y,Z UVW = 116 17 35 VALUE = 115 .
TO SITE 3 ½-X,½+Y,-Z UVW = 55 0 13 VALUE = 181 4
TO SITE 3 ½+X,½-Y,-Z UVW = 108 37 59 VALUE = 97 .
HARKER VECTORS FROM SITE 2
TO SITE 2 -X,-Y,Z UVW = 44 39 0 VALUE = 299 D
TO SITE 2 ½-X,½+Y,-Z UVW = 104 54 23 VALUE = 170 3
TO SITE 2 ½+X,½-Y,-Z UVW = 60 16 49 VALUE = 566 X
CROSS VECTORS FROM SITE 2
TO SITE 3 X,Y,Z UVW = 60 38 23 VALUE = 191 5
TO SITE 3 -X,-Y,Z UVW = 105 0 22 VALUE = 143 1
TO SITE 3 ½-X,½+Y,-Z UVW = 75 16 0 VALUE = 66 .
TO SITE 3 ½+X,½-Y,-Z UVW = 0 54 0 VALUE = 356 I
HARKER VECTORS FROM SITE 3
TO SITE 3 -X,-Y,Z UVW = 76 39 0 VALUE = 299 D
TO SITE 3 ½-X,½+Y,-Z UVW = 104 54 49 VALUE = 170 3
TO SITE 3 ½+X,½-Y,-Z UVW = 60 16 49 VALUE = 566 X
NO OF HARKER VECTOR MISSES =0HITS=9
NO OF CROSS VECTOR MISSES =3HITS=9
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