Amplitude-only information from all molecules of known orientation in the unit cell, including any not related by crystallographic symmetry (whose positions are consequently unknown), is however used in the Fobs/Fcalc scaling, in the calculation of normalised structure factor amplitudes, and optionally in the subtraction of the transform of the intramolecular vector set.
The conventional crystallographic T2 function is in general the 3-dimensional sum function of the pairwise 2-dimensional T1 functions; however in polar space groups the crystallographic T2 function is also 2-dimensional. It is especially advantageous in high-symmetry space groups, where the smaller signal/noise ratio of the peaks in the T1 functions may cause difficulties.
TFFC works for all space-group symmetries containing only rotation and screw axes, and non-primitive lattice elements, provided the conventional settings in International Tables Vol. A are used (R3 must be indexed on hexagonal axes).
The partial T2 function (also called non-crystallographic, meaning obtained using structure factors from a partially known structure, which may or may not be related by non-crystallographic symmetry to the remaining unknown part) is also the 3-dimensional sum function of the pairwise partial T1 functions; however the partial T1 and T2 functions are always 3-dimensional. The program can also be used to calculate the individual T1 functions, but a satisfactory automatic method for analysing these functions has yet to be devised, and so they have to be analysed manually (hopefully this should never be necessary!).
The T2 Translation Function can be used to resolve a space group ambiguity, for example, I222/I212121 or P3121/P3221, where the systematic absence conditions do not distinguish the pairs, or for example P21212/P212121 where the identification of systematic absences is not always clear-cut.
Three important features which further improve the signal/noise ratio of the T2 function are the shell-scaling of the F(obs) and F(calc) values by the difference Wilson method, the use of normalised amplitudes (E values), and the subtraction of the transform of the intramolecular vector set from the transform of the Patterson function of the target structure.
The program works by calculating the Fourier coefficients of the Translation Function from the transform of the intermolecular vector set, and the Fast Fourier Transform (FFT) program is used to effect the transformation into real space. This method is about 3 orders of magnitude faster than a real space search, and the speed is also much less dependent on the fineness of the grid search.
IMPORTANT: The unit cell specified in SFALL must be the experimentally determined cell of the crystal whose structure is being determined, not some arbitrarily chosen cell as in the Rotation Function. This is because the aim is to match the inter-molecular vectors (not the intra-molecular ones). This is clearly not possible if the cells of the unknown and model structures are different.
If there is more than one molecule per asymmetric unit then the above procedure must be repeated for each molecule, using column labels of the form FCA1 PCA1 FCA2 PCA2 ... for the first molecule, FCB1 PCB1 FCB2 PCB2 ... for the second and so on. The files must then be column-merged into a single input reflection file (using CAD this operation can be done in a single run).
The output of TFFC is used as input to the P1 version of FFT. The program outputs two sets of Fourier coefficients; for the TO/O function two FFTs are necessary, using labels A and B for the TO function and AO and BO for the O function. It is not necessary to print any maps; instead specify binary map output in FFT and use the program MAPSIG to perform the division TO/O and analyse the results. For the T2 function only the labels A and B are used, only one FFT is done, but MAPSIG can still be used.
When computing the TO and O functions, the F000 terms must be entered manually into the FFT program; the required values are given at the end of the TFFC printer output (the two values are for the TO and O functions respectively). The volume V must also be given, but this acts only as an arbitrary scale, and any value (typically around 1000) which gives sensible magnitudes in the Translation Function map can be used.
Note that the reflection indices produced by TFFC are not the same as those read from the input reflection file. Consequently the S values calculated for these reflections are meaningless, and therefore it is important not to apply any resolution cutoffs in FFT. If resolution cutoffs are desired they must be applied by TFFC to the original indices.
FIND, LABIN, LIST, NONCRYST, PART, POINTGROUP, RESOLUTION, SELF, SHELL, SPACEGROUP, SYMMETRY, TITLE, VECTOR.
Only the first 4 characters of each keyword are significant. All keywords are optional, though normally one would specify LABIN to use other than the default file labels.
The keywords SPACEGROUP and SYMMETRY are mutually exclusive; one or the other is only required if the space group information in the reflection file header is incorrect. This may happen because the systematic absences do not unambiguously define the space group; the point group information defined by the rotation components of the symmetry matrices however must be correct. It is not then necessary to re-run SFALL & CAD, it is only necessary to specify the correct symmetry with either SPACEGROUP or SYMMETRY.
If the space group has screw-axis translations (ignoring non-primitive lattice translations), and an earlier program used the translation components to apply phase shifts, the SPACEGROUP option cannot be used. The SYMMETRY option must be used and the screw-axis translations then omitted.
The SYMMETRY option must also be used if the primitive General Equivalent Positions in symop.lib are in a different order from those originally specified. This can happen either because for some space groups different editions of International Tables have the equivalent positions in a different order, or because for some space groups with the same point group, the order of the rotation components may vary. When the SYMMETRY option is used, the order of equivalent positions must be identical with that used when the input file was prepared.
No problems should occur using the SPACEGROUP option if
1 2 222 3 312 321 4 422 6 622 23 432 The number of primitive g.e.p.'s to follow must be then : 1 2 4 3 6 6 4 8 6 12 12 24The default is to use the point group implied by the space group. The space/point group may be 1 (one equivalent position) only if the PART option is specified.
With this option NONCRYSTVECTOR. For example if NONCRYST is given as 4, then 3 runs of the program would be required:
Run 1 : VECTOR A Ax Ay Az FIND B Run 2 : VECTOR A Ax Ay Az VECTOR B Bx By Bz FIND C Run 3 : VECTOR A Ax Ay Az VECTOR B Bx By Bz VECTOR C Cx Cy Cz FIND D
The first translation vector for the A subunit could be determined by the crystallographic Translation Function, except in P1 where the first translation vector can be chosen arbitrarily. Note that the translations need not be determined in the order shown; it may be easier to start by fixing one of the other subunits, and then determine the other translations in a different order.
To calculate a T1 function, both the subunit label and the number of the equivalent position must be specified in VECTOR (of which there may only be one) and FIND; for example:
VECTOR A1 Ax Ay Az FIND B2
If NONCRYST = 0 or omitted, the program labels are:
H K L FP SIGFP FC1 PC1 FC2 PC2 ... where FP, SIGFP = Fobs, sigma(Fobs) FCn, PCn = Fcalc and phase of n'th asymmetric unit of model.
If NONCRYST > 0 the program labels are H K L FP SIGFP (Fobs, sigma(Fobs)), followed by NONCRYST*NUMGEP pairs of columns containing the partial Fcalc, phase contributions (NUMGEP = number of primitive g.e.p.'s).
For example, if NONCRYST = 4, NUMGEP = 2, the column labels
FCA1 PCA1 FCA2 PCA2 FCB1 PCB1 FCB2 PCB2 FCC1 PCC1 FCC2 PCC2 FCD1 PCD1 FCD2 PCD2i.e. the letters A,B,C,D refer to non-crystallographically related subunits and the numbers 1,2... refer to crystallographically related subunits.
In polar space groups, the translation vector for the crystallographic T function is limited to the plane perpendicular to the unique axis, so only one section need be calculated; also, all space groups have equivalent origins, which reduces the asymmetric unit of the Translation Function, e.g. in orthorhombic, these origin positions are at 0 and 1/2 in x, y and z, which reduces the asymmetric unit to 0 to 1/2 along each axis. The table below shows the asymmetric unit for each point group.
Note that in trigonal point groups it is not possible to calculate just one asymmetric unit by applying limits parallel to the cell edges. Consequently the ranges suggested actually enclose 3 equivalent origins.
pg2: y=0 section, 0 to 1/2 along x and z. Orthorhombic pg222: 0 to 1/2 along x, y and z. Trigonal pg3: z=0 section, 0 to 1 along x and y. pg312 and pg321: 0 to 1 along x and y, 0 to 1/2 along z.
In centred space groups, these asymmetric units may be reduced further. Note that although higher symmetry point groups have smaller asymmetric units (as a fraction of the unit cell) in the space group, they have larger asymmetric units in the Translation Function.
Tetragonal pg4: z=0 section, 0 to 1 along x,
0 to 1/2 along y (or vice versa).
pg422: x and y as for pg4, 0 to 1/2 along z. Hexagonal pg6: z=0 section, 0 to 1 along x and y. pg622: 0 to 1 along x and y, 0 to 1/2 along z. Cubic pg23/pg432: 0 to 1/2 along x, 0 to 1 along y and z
(or any other permutation).
For a given subunit, the total Translation Function is simply the sum of crystallographic and partial contributions, and the program MAPSIG can be used to do this summation (a minimum function could be used, but I have not tried this). In practice I have not found it necessary to do this summation; manual inspection of the peak lists generated from the separate maps is usually all that is necessary.
The A and B columns (real and imaginary components of the Fourier coefficient of the transform of the Translation Function) are used in a run of FFT in P1. The solution vector should appear as a single peak; the corresponding molecule is to be translated by this vector. The AO and BO columns are the transform of the Harada et al O (overlap) function.
TFFC (main subprogram)
Dimensions a working array (not used when PART option is selected). Calls CCPFYP and TFMAIN.
Initialises file titles,flags for Harker section test, sums for scaling.
Calls GETINP to set up input data, calls GENPGT (for partial T1 function only), reads MTZ file first time for resolution range, reads MTZ file second time for scale factor sums, putting Fobs^2 and Fcalc^2 into bins of constant d*^3, calculates maximum indices and scale factors. For crystallographic T function dimensions a number of complex arrays (one for each Harker section) and calls TFSGEN. For partial T function calls TFPART.
Calls MTZINI, opens HKLIN reflection file. Calls PARSER to read control data and checks it. Sets up input labels and calls GRASSN to do input file assignments.
Makes input MTZ file assignments.
Generates point group multiplication table.
Calculates reflection multiplicity and symmetry weight factor epsilon.
Generates equivalent reflection.
Reads MTZ file third time, applies scales using spline interpolation (FSPLIN). Accumulates translation and overlap Fourier coefficients in arrays. This is necessary because the FFT input routines only use the last coefficients read in for a particular hkl (to avoid having to worry about reflection multiplicity). Calls GWOPEN to open output MTZ file HKLOUT and writes structure factors using routine PUTREF.
Cubic spline interpolation.
General purpose output file (HKLOUT) open for MTZ.
Writes a structure factor to HKLOUT, accumulating minimum, maximum and sum statistics for data columns.
Calls GWOPEN to open output MTZ file HKLOUT. Reads MTZ file third time, applies scales using spline interpolation (FSPLIN). Calculates translation and overlap Fourier coefficients and writes structure factors using routine PUTREF.
# tffc hklin tffc_inp hklout tffc_out << eof TITL test TFFC P6522 hex pepsin. SPAC P6522 LABI FP=FOHEXPEP SIGFP=SIGHEXPEP eof # fft hklin tffc_out mapout tffc_out << eof LABI A=A B=B TITL T2 function for hex pepsin assuming P6522. AXIS Y,X,Z GRID 72 72 300 XYZL 0 1 0 1 0 .5 VF00 1000 eof # mapsig mapin tffc_out << eof eof #
# tffc hklin bbp_tf hklout tffc_out << eof TITL C222 Find subunit B1 using A1 known. SPAC C222 SHEL 150 NONC 2 VECT A 0.491 0.224 -0.002 LABI FP=FO SIGFP=SIGFO - FCA1=F1B1 PCA1=PC1B1 FCA2=F1B2 PCA2=PC1B2 - FCA3=F1B3 PCA3=PC1B3 FCA4=F1B4 PCA4=PC1B4 - FCB1=F2B1 PCB1=PC2B1 FCB2=F2B2 PCB2=PC2B2 - FCB3=F2B3 PCB3=PC2B3 FCB4=F2B4 PCB4=PC2B4 eof # fft hklin tffc_out mapout tffc_out << eof LABI A=A B=B TITL C222 Find subunit B1 using A1 known. AXIS Y,X,Z VF00 1000 GRID 192 208 96 XYZL 0 .5 0 .5 0 .5 eof # mapsig mapin tffc_out << eof eof #
# tffc hklin bbp_tf hklout tffc_out << eof TITL C222 Find subunit B1 using A1 known. SPAC C222 SHEL 150 NONC 2 VECT A 0.491 0.224 -0.002 PART LABI FP=FO SIGFP=SIGFO - FCA1=F1B1 PCA1=PC1B1 FCA2=F1B2 PCA2=PC1B2 - FCA3=F1B3 PCA3=PC1B3 FCA4=F1B4 PCA4=PC1B4 - FCB1=F2B1 PCB1=PC2B1 FCB2=F2B2 PCB2=PC2B2 - FCB3=F2B3 PCB3=PC2B3 FCB4=F2B4 PCB4=PC2B4 eof # fft hklin tffc_out mapout tffc_out << eof LABI A=A B=B TITL C222 (T2):find translation vector for molecule 1B using 1A known VF00 1000 GRID 192 208 96 XYZL 0 1 0 .5 0 1 eof # mapsig mapin tffc_out << eof eof #
#!/bin/csh -f # Calculate Translation Function (TFFC), # Map (FFT) and find peaks (PEAKMAX) # # goto FFT # goto PEAKMAX # goto PLUTO # TFFC: # tffc hklin ../mtz/i96v/cad_all2.mtz hklout ../mtz/i96v/tf_all2.mtz << eof TITL Barnase finding B1, A1 known POINTGROUP pg3 SYMMETRY X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z SHEL 150 NONC 3 VECT A 0.690 0.865 0.000 FIND B PART LABI FP=iv96_F SIGFP=iv96_SIGF - FCA1=FCP_A1 FCB1=FCP_B1 FCC1=FCP_C1 - PCA1=PHICP_A1 PCB1=PHICP_B1 PCC1=PHICP_C1 - FCA2=FCP_A2 FCB2=FCP_B2 FCC2=FCP_C2 - PCA2=PHICP_A2 PCB2=PHICP_B2 PCC2=PHICP_C2 - FCA3=FCP_A3 FCB3=FCP_B3 FCC3=FCP_C3 - PCA3=PHICP_A3 PCB3=PHICP_B3 PCC3=PHICP_C3 eof # exit # # Make a map with FFT, find peaks with PEAKMAX # FFT: # fft hklin ../mtz/i96v/tf_all2.mtz mapout map/tf_all2.map << eof RESO 100 1 LABIN A=A B=B TITLE TF all for C from ALMN ---> TFFC !SCALE Label Scale B-factor ! optional !NOCHECKS ! optional !SYMMETRY 1 !space-group name or number ! optional !FFTSYMMETRY 1 !space-group name or number ! optional AXIS Z X Y !Axis order fast, medium, slow GRID 200 200 200 !nx ny nz VF000 0 145300 XYZLIM 0 1 0 1 0 1 !xmin xmax ymin ymax zmin !BIAS bias [optional] !EXCLUDE keyword1 value1 keyword2 value2 . !PROJECTION !optional !RHOLIM rhomax [rhomin] !optional eof # PEAKMAX: # peakmax mapin map/tf_all2.map to peaks/tf_all2.peaks << eof output peaks threshold rms 3 numpeaks 20 eof # exit # NPO: npo mapin map/tf_all.map plot tf_all.plt << eof TITL Translation function, solution 2 from TFFC MAP CONTRS 1 TO 6 BY .08 SECTNS 0 PLOT eof # xplot84driver tf_all.plt # exit #