When an isomorphous difference Patterson is calculated, GraphEnt will plot
the normal probability diagram of the input data, together with a
reference dotted line of gradient 1.0 and zero intercept12.
The usage of the normal probability plots for accessing the usefulness (or otherwise) of
a putative derivative is well documented and will not be discussed here
(see Howell, P.L. & Smith, G.D. (1992),
J. Appl. Cryst., 25, 81-86, and Abrahams, S.C. & Keve, E.T. (1971),
Acta Cryst., A 27, 157-165). If you scaled your (macromolecular)
data using the program
scaleit from the CCP4 suite, then although you have not seen the plot, you have seen
the variation of its gradient and intercept versus resolution (using the program
xloggraph on the .log file written by scaleit).
The reason for repeating the calculation here, is that the normal probability
plot can also be used to select suspect data that do not fit an otherwise linear trend.
The important thing is that the selection is not performed on the basis of just the magnitude
of the difference (ie
|| FPH| - | FP||, as happens in scaleit), but on the basis of
both the observed amplitudes and their standard deviations. The normal probability plot
together with the ``large contributions to 
'' table (files
CHIcontributions.dat and CHIcontributions.ps),
which is produced after the calculation is over, should allow you to justifiably select
outliers13.
This is achieved as follows : GraphEnt will write out an ASCII file (named Normplot_tails.dat which contains the hkl indeces for all reflections that comprise the tails of the plot. These points are shown in the graphics window with a different colour. If some of these points deviate significantly from the rest of the plot, then they are candidates for rejection (note that some deviation from linearity will always be present near the tails. What you are looking for is an outstanding deviation.)
You can then match what you see in the plot with what is written in the
Normplot_tails.dat, decide which reflections to exclude, write their indeces in an
ASCII file with the name REJECT.HKL,
and then re-run the program using the MAXENT_AUTO.IN file
after adding the keyword REJECT (see page ![[*]](cross_ref_motif.gif)
). Because this sounds
quite complicated, I will now give a detailed example to show how it works :
We start with just one .mtz file containing data for a putative derivative :
crystal2 ~/test crystal2 ~/test d total 260 -rw-r--r-- 1 glykos sys 262300 Dec 16 15:45 from_scaleit.mtz crystal2 ~/test crystal2 ~/test mtzdump hklin from_scaleit.mtz ########################################################## ########################################################## ########################################################## ### CCP PROGRAM SUITE: MTZDUMP VERSION 3.5: 18/06/98## ########################################################## ............... OVERALL FILE STATISTICS for resolution range 0.001 - 0.245 ======================= Col Sort Min Max Num % Mean Mean Resolution Type Column num order Missing complete abs. Low High label 1 ASC -46 35 0 100.00 -11.3 18.0 35.81 2.02 H H 2 NONE 0 11 0 100.00 4.0 4.0 35.81 2.02 H K 3 NONE 0 31 0 100.00 12.3 12.3 35.81 2.02 H L 4 NONE 4.4 902.0 3 99.96 92.65 92.65 35.81 2.02 F FP 5 NONE 0.6 26.2 3 99.96 3.34 3.34 35.81 2.02 Q SIGFP 6 NONE 8.7 956.3 3500 51.49 137.07 137.07 18.78 2.50 F FPH 7 NONE 1.2 41.5 3500 51.49 7.95 7.95 18.78 2.50 Q SIGPH 8 NONE -73.2 72.3 3718 48.47 0.29 7.29 18.78 2.51 D DPH 9 NONE 0.0 66.8 3718 48.47 11.85 11.85 18.78 2.51 Q SIGDPH No. of reflections used in FILE STATISTICS 7215 LIST OF REFLECTIONS =================== ............... MTZDUMP: Normal termination of mtzdump Times: User: 0.2s System: 0.1s Elapsed: 0:03 crystal2 ~/test crystal2 ~/test
Then, we run GraphEnt on the centrosymmetric [010] projection :
crystal2 ~/test
crystal2 ~/test GraphEnt h0l 10 3 from_scaleit.mtz
___________________________________________________________________________________________________________________________
### ### ####### #
## ## # # #
# # # # #### ### ### # # ## ### ######
# # # # # # # # # # ## # #
# # # # # # #### # # #
# # # ##### # # # # # #
# # # # # # # # # # #
# # # # # # # # # # # #
### ### #### # ### ### ####### ### ### ###
Gull, S.F. & Daniell, G.J. (1978), Nature, 272, 686-690
Collins, D.M. (1982), Nature, 298, 49-51
NMG
___________________________________________________________________________________________________________________________
- Assuming that input is a .mtz file. Interpreting ...
..............................................
- Now trying lambda = 0.010000
.............................................
- Initial value for lambda set to 1000.000000
___________________________________________________________________________________________________________________________
- MAXENT starts here
Chi**2 : 1593.822 R : 1.0000 Lambda : 1000.00000 Nobs : 366
Chi**2 : 1588.187 R : 0.9992 Lambda : 1000.00000 Nobs : 366
........................................................................................
Chi**2 : 365.790 R : 0.5621 Lambda : 945.19320 Nobs : 366
803 cycles in 74 seconds, giving an average of 0.092 seconds per cycle.
___________________________________________________________________________________________________________________________
CONVERGENCE ACHIEVED.
The final R-factor between the observed
and calculated amplitudes is 0.5621040
........................................
Normal termination ? (100 seconds)
Now we have all these files :
crystal2 ~/test d total 652 -rw-r--r-- 1 glykos sys 68 Dec 16 15:51 CHIcontributions.dat -rw-r--r-- 1 glykos sys 37224 Dec 16 15:51 CHIcontributions.ps -rw-r--r-- 1 glykos sys 31101 Dec 16 15:49 MAXENT_AUTO.IN -rw-r--r-- 1 glykos sys 30595 Dec 16 15:48 MAXENT_FROM_MTZ.in -rw-r--r-- 1 glykos sys 103 Dec 16 15:48 MAXENT_FROM_MTZ_ANOMALOUS.in -rw-r--r-- 1 glykos sys 10365 Dec 16 15:48 Normal_probability.ps -rw-r--r-- 1 glykos sys 825 Dec 16 15:48 Normplot_tails.dat -rw-r--r-- 1 glykos sys 132176 Dec 16 15:50 conventional.map -rw-r--r-- 1 glykos sys 262300 Dec 16 15:45 from_scaleit.mtz -rw-r--r-- 1 glykos sys 132176 Dec 16 15:51 maxent.map crystal2 ~/test
Both CHIcontributions.dat and Normplot_tails.dat point to problems with reflections 0,0,11 and -12,0,8 :
crystal2 ~/test
crystal2 ~/test
crystal2 ~/test more CHIcontributions.dat
0 0 11 55.19882
-12 0 8 59.04416
crystal2 ~/test
crystal2 ~/test
crystal2 ~/test more Normplot_tails.dat
0 0 6 -2.99385 -30.69588
2 0 4 -2.64107 -28.07780
-12 0 8 -2.46310 -26.91301
0 0 11 -2.34000 -25.43124
-4 0 8 -2.24461 -22.29077
0 0 7 -2.16611 -21.85669
4 0 10 -2.09905 -18.73302
-16 0 5 +2.04028 +10.47118
8 0 6 +2.09905 +10.55087
4 0 4 +2.16611 +10.55754
-8 0 9 +2.24461 +11.08962
6 0 3 +2.34000 +11.90654
4 0 6 +2.46310 +12.23197
-16 0 10 +2.64107 +12.45890
2 0 6 +2.99385 +13.12762
crystal2 ~/test
crystal2 ~/test
The normal probability plot suggests that all seven reflections in the lower left-hand side corner are suspect. Its somewhat sigmoidal shape suggests the presence of non-normally distributed (systematic) errors :
Let's repeat the calculation but with these seven reflections excluded from the calculation. The first step is to create a file with the name REJECT.HKL whose first three columns contain the indeces of the reflections to be excluded :
crystal2 ~/test
crystal2 ~/test cp Normplot_tails.dat REJECT.HKL
crystal2 ~/test ed REJECT.HKL
crystal2 ~/test more REJECT.HKL
0 0 6 -2.99385 -30.69588
2 0 4 -2.64107 -28.07780
-12 0 8 -2.46310 -26.91301
0 0 11 -2.34000 -25.43124
-4 0 8 -2.24461 -22.29077
0 0 7 -2.16611 -21.85669
4 0 10 -2.09905 -18.73302
crystal2 ~/test
crystal2 ~/test
Then, we edit the file MAXENT_AUTO.IN and we add the keyword REJECT :
crystal2 ~/test crystal2 ~/test ed MAXENT_AUTO.IN crystal2 ~/test more -20 MAXENT_AUTO.IN REJECT CELL 94.14900 24.17000 64.31901 90.00000 130.36700 90.00000 SPACEGROUP 1 MAP_FORMAT CCP4 DIFF_PATT PERMUTATION 3 1 2 GRID 128 256 1 GRACYCLES 80 GRATWOWINDOWS REFLECTIONS -30 0 9 89.88602 3.43968 123.75751 12.84017 -30 0 10 126.17858 3.93975 110.84611 10.25688 -30 0 11 38.71215 5.14720 36.43570 15.66436 -30 0 12 165.68549 4.99690 154.67838 7.42726 -30 0 13 38.65771 4.30664 43.59790 16.74030 -30 0 14 158.72888 4.75254 159.23166 5.49528 -30 0 15 86.40644 3.25414 84.79811 15.51947 -30 0 16 150.11438 4.57498 146.66685 5.11194 -30 0 17 132.07582 4.08662 164.78131 5.11169 -30 0 18 21.89952 8.06613 23.18951 10.87039 ................................................................................. crystal2 ~/test crystal2 ~/test
... and we run it again, but this time giving as input the MAXENT_AUTO.IN file :
crystal2 ~/test
crystal2 ~/test GraphEnt MAXENT_AUTO.IN
___________________________________________________________________________________________________________________________
### ### ####### #
## ## # # #
# # # # #### ### ### # # ## ### ######
# # # # # # # # # # ## # #
# # # # # # #### # # #
# # # ##### # # # # # #
# # # # # # # # # # #
# # # # # # # # # # # #
### ### #### # ### ### ####### ### ### ###
Gull, S.F. & Daniell, G.J. (1978), Nature, 272, 686-690
Collins, D.M. (1982), Nature, 298, 49-51
NMG
___________________________________________________________________________________________________________________________
Keyword REJECT : 7 reflections specified in REJECT.HKL.
Keyword CELL : Cell dimensions set to 94.15 24.17 64.32 90.00 130.37 90.00
Keyword SPACEGROUP : space group number set to 1
Keyword MAP_FORMAT : CCP4 map file selected.
Keyword DIFF_PATT : Difference Patterson map run [h k l FP sig(FP) FPH sig(FPH)].
Keyword PERMUTATION : Permutation set to 3 1 2
Keyword GRID : Grid set to 128 256 1
Keyword GRACYCLES : Plot every 80 cycles.
Keyword GRATWOWINDOWS : Will keep conventional map plot.
Keyword REFLECTIONS : start reading reflections.
Reflection rejected : -12 0 8
Reflection rejected : -4 0 8
Reflection rejected : 0 0 6
Reflection rejected : 0 0 7
Reflection rejected : 0 0 11
Reflection rejected : 2 0 4
Reflection rejected : 4 0 10
___________________________________________________________________________________________________________________________
...........................................................................................................................
Normal termination ? (32 seconds)
NOTE WELL : Because the normal probability plot is calculated with
data expanded to P1, each point on the plot may actually correspond to a
superposition of several symmetry-equivalent reflections. When you reject
data, you MUST reject all symmetry equivalent reflections that are present
in your P1 data set. Failure to do so will show-up in your maps as absence
of the expected symmetry elements. Now : under normal circumstances the
Normplot_tails.dat file will contain all symmetry equivalent reflections,
except if these are near the assumed linear part of the plot. In this case,
I'm afraid that you will have to manually add the indeces of the missing
equivalents in the REJECT.HKL file (sorry).
(| FP312|) = 14,
| FPH312| = 183,
(| FPH312|) = 120, and assume for the sake of argument that
the rmsd of the observed differences is 20 e-. Then, we can ignore the fact that
the measurement of
| FPH312| is loosy, and reject this reflection as ``highly
improbable''. This is of course nonsense : the standard deviation of the difference
| FPH312| - | FP312| is 134 e-, which means that with
the observed difference of 80 e- we can not even say at the 50% significance
level that the amplitudes
| FP312| and
| FPH312| are indeed different. The
trouble is that if you include the reflection in your Fourier synthesis, it
will probably make a mess out of your map because in the case of the conventional synthesis
you treat all differences as if having zero standard deviation. Needless to say that the
maxent map not only is insensitive to such differences, but that you should actually
avoid rejecting anothing until you are certain that for some reason the standard
deviations are wrong.