FASTRAN

FASTRAN calculates a modified version of the Harada-Lifchitz's fast translation function [1]. The translation function is defined by the following formulae: 
Eq. 1.	 TO( t ) = sum[ Io'(h) Im:m(h, t ) ] / sum[ Io'(h) Io'(h) ]
Eq. 2.   TC( t ) = sum[ Io'(h) Im:a(h, t ) ] / sum[ Io'(h) Io'(h) ]
Eq. 3.   O²( t ) = sum[ (Im:m(h, t ) + Im:a(h, t ))² ] / sum[ Io'(h) Io'(h) ]
Eq. 4.   O( t )  = sum[ (Ic,m(h, t ) + Im:a(h, t ) + Ic,a(h)) ] / sum[ Io(h) ]
Eq. 5.   T( t )  = [ TO( t ) + TC( t ) ] / sqrt[ O²( t ) ]
Eq. 6.   T'( t ) = [ TO( t ) + TC( t ) ] / O( t )
where 
Eq. 7.   Io'(h)          = Io(h) - [ Iself_vector(h) + Ic,a(h) ] 	
Eq. 8.   Im:m(h, t )     = |Fc(h, t )|² - Iself_vector(h)    
Eq. 9.   Im:a(h, t )     = F*c,a(h) Fc(h, t ) + Fc,a(h) F*c(h, t )
Eq. 10.  Fc(h, t )       = sum[ TFc,m(Sh)
                         = sum[ Fc,m(hR) exp( i2pihT +i2pihRt )
Eq. 11.  Iself_vector(h) = sum[ |Fc,m(hRj)|² ]
{Sj(Rj,Tj), j=1,nsym} are the symmetry operators of the crystal and their rotation/translation components, t is the translation vector in real space, Fc,m's are structure factors calculated with the single search model, and Fc,a's are structure factors calculated from a known structural fragment with all the symmetry operators.

The calculated and observed intensities are scaled such that 

Eq. 12.  f= { sum[ Iself_vector(h) ] + sum[ Ic,a(h) ] } / sum[ Io(h) ]
where f is the structural fraction of the search model (plus the known structural fragment, if any) in the asymmetric unit.

The Equations of TO( t ), TC( t ) and T( t ) can be simplified as 

Eq. 13.  TO( t ) = < Pobs.,m:m&m:a | Pcalc.,m:m( t ) > 
Eq. 14.  TC( t ) = < Pobs.,m:m&m:a | Pcalc.,m:a( t ) > 
Eq. 15.  T( t )  = < Pobs.,m:m&m:a | Pcalc.,m:m&m:a( t ) > /
          sqrt[ < Pobs.,m:m&m:a | Pobs.,m:m&m:a > 
                < Pcalc.,m:m&m:a( t ) | Pcalc.,m:m&m:a ( t ) > ]
where < | > indicates an integral over the unit cell, P indicates the vector density of a Patterson map at position u, and t is the translation vector in real space. Theoretically, the value of T( t ) should be within [-1.0,1.0]. The truncation of the coefficient series may causes deviation from the true correlation value, especially when high resolution data is used in the translation function calculation. The relative height of peaks of the function T( t ) may be more useful.

Either T( t ) or T'( t ) can be used in a translation function search.

Ideally, the high resolution limit of the output files should be dmin/4 for T( t ) and dmin/2 for T'( t ), where dmin is the input high resolution limit. This idea situation will often not be reached because of the limitation of the maximum index. By the way, the low resolution limit of the output is infinite. In other words, the C(000) coefficient is important for the value of correlation to be reasonable.

To report bugs, please contact

Cai X.-J. Zhang at chk@uoxray.uoregon.edu

Input files

Two or three structure factor (amplitude) files of HKL/TNT format [2]are expected as the input.

Output file

The output files have HKL/TNT format, containing the fast translation function coefficients, which can be used as the input for the program FOURIER in the TNT package [2] for map calculation.

Commands

FASTRAN uses key-word leading, free format input cards. A key-word can be abbreviated as long as there is no ambiguity caused.

The following are the available commands. The commands marked with a star (*) are mandatary to the program, and those without star are optional.

CELL*, FC*, FC_A, FC_B, FO*, INCLUDE, O_C, O2_C, RESOLUTION*, SCALE, SYMMETRY*, TO_C, TC_C and !comment.
CELL a, b, c, alpha, beta, gamma
CELL inputs the cell parameters.
FC file_name
FC defines the HKL/TNT file name of the calculated structure factors for the search fragment. When the {Fc} are calculated, the model cell parameters must be the same as those of the observed crystal cell but all non-identity symmetry operators should be removed, except for those which correspond to any centering (if present) in the real crystal [3]. The model should be at a correct orientation (i.e. the solution of the rotation function).
FC_A file_name
FC_A defines the HKL/TNT file name of the calculated structure factors of a known structural fragment (rotationally, and translationally positioned). When the {Fc} are calculated, the model cell parameters and the symmetry operators should be the same as those of the real crystal. See Eq. 2 and 7.
FC_B file_name
FC_B defines the HKL/TNT file name of the calculated structure factors of a structural fragment, of which the orientation (but not the position) is known. The intra-molecular vectors of the this fragment will be subtracted from the observed Patterson function. The {Fc} are calculated with the correctly oriented fragment. Other conditions are the same as those of FC input. (See Eq. 7).
FO file_name
FO inputs the HKL file name of the observed structure factors (amplitude).
INCLUDE file_name
INCLUDE defines an input parameter file, which may contain any of the input cards, including INCLUDE card itself. For example, the symmetry operators can be input from a separate file for convenience.
O_C file_name, [low_resolution_limit]
O_C defines the output file name of O( t ) coefficients in HKL/TNT format, which, after Fourier transform in space group P1, will yield the function O( t ). The default low_resolution_limit is the same low resolution limit in RESOLUTION card. For the O( t ) function to work well as an overlap function, lower resolution data may be helpful.
O2_C file_name
O2_C defines the output file name of O2( t ) coefficients in HKL/TNT format, which, after Fourier transform in space group P1, will yield the function O2( t ).
RESOLUTION dmin, dmax
RESOLUTION defines the resolution limits of both {Fo} and {Fc} used in the calculation.
SCALE scale, f
Scale is multiplied on each of the output coefficients to make sure that they fit in the TNT/HKL format ('HKL ',3I4,F8.3,3F8.1) without lost of accuracy. f is the structural fraction of the search model, plus the know or partially-known fragment if any, in one asymmetric unit. The default is (1.0, 1.0).
SYMMETRY symmetry_operator
SYMMETRY inputs the symmetry operator in the international table format. For a centered space group, only the symmetry operators associated with one origin are needed. The origin shifts may be included in the structure factor calculation.
TO_C file_name
TO_C defines the output file name of TO( t ) coefficients to make a map, in P1 space group, of TO( t ).
TC_C [file_name]
TC_C defines the output file name of TC( t ) coefficients to make a map, in P1 space group, of TC( t ). If there is no file name specified following the TC_C key-word, the coefficients will be written to the file specified with the TO_C card.
!comment
Any input line starting with a semicolon (;) or an exclamation mark (!) will be ignored.

Examples

The following examples are of the T4 lysozyme wild type crystal. The space group is P3221.

(1) An example of a VAX/VMS command file to run FASTRAN with a single search model. This run calculates coefficients for TO( t ) in the file a.hkl and O( t ) in b.hkl. Because there is no input of known structure fragment, the function TC( t ), which measures the agreement between known-model and observed vectors cannot be calculated. The program FOURIER is a TNT program which simply calculates two P1 Fourier maps from the coefficients in a.hkl and b.hkl. FOURIER also creates the map of TO( t ) / O( t ). 

	$ RUN MRCHK_ROOT:[EXE]FASTRAN
	cell       61.2, 61.2, 96.8, 90., 90., 120. 
	symm       x,y,z
	symm       -y,x-y,z+2/3
	symm       y-x,-x,z+1/3
	symm       y,x,-z
	symm       -x,y-x,-z+2/3
	symm       x-y,-y,-z+1/3
	resolution 4., 8.
	FO         Fobs.HKL
	FC         Fmodel.HKL
	TO_c       a.hkl
	O_c        b.hkl 
	scale      1., 1.
	$ 
	$ RUN tnt_util:FOURIER
	cell       61.2, 61.2, 96.8, 90., 90., 120. 
	resolution 2.2   1.e32 
	FILE       TO_c  a.hkl  FORMAT HKL 
	FILE       O_c   b.hkl  FORMAT HKL 
	PUNCH a.map MAP SOURCE TO_c GRID 60 60 96 LAYOUT 0 60 0 60 0 96 
	PUNCH b.map MAP SOURCE  O_c GRID 60 60 96 LAYOUT 0 60 0 60 0 96 
	FILE       TO_m  a.map  FORMAT MAP 
	FILE       O_m   b.map  FORMAT MAP
	PUNCH t.map MAP DIVIDE TO_m O_m GRID 60 60 96 LAYOUT 0 60 0 60 0 96 
	$
(2) An example VAX/VMS command file of the fast translation function with a single search model plus information of the known structure fragment. 
	$ RUN MRCHK_ROOT:[EXE]FASTRAN
	cell       61.2, 61.2, 96.8, 90., 90., 120. 
	symm       x,y,z
	symm       -y,x-y,z+2/3
	symm       y-x,-x,z+1/3
	symm       y,x,-z
	symm       -x,y-x,-z+2/3
	symm       x-y,-y,-z+1/3
	resolution 4., 8.
	FO         Fobs.HKL
	FC         Fmodel.HKL
	FC_a       Fmodel_a.HKL
	TO_c       a.hkl
	TC_c
	O_c        b.hkl 
	scale      1., 1.
	$ 
	$ RUN tnt_util:FOURIER
	cell       61.2, 61.2, 96.8, 90., 90., 120. 
	resolution 2.2 1.e32 
	FILE      TOC_c  a.hkl  FORMAT HKL 
	FILE        O_c  b.hkl  FORMAT HKL 
	PUNCH a.map MAP SOURCE TOC_c GRID 60 60 96 LAYOUT 0 60 0 60 0 96 
	PUNCH b.map MAP SOURCE O_c  GRID 60 60 96 LAYOUT 0 60 0 60 0 96 
	FILE     TOC_m   a.map  FORMAT MAP 
	FILE       O_m   b.map  FORMAT MAP
	PUNCH t.map MAP DIVIDE TO_m O_m GRID 60 60 96 LAYOUT 0 60 0 60 0 96 
	$
In this case, an FC_A file of coefficients from a correctly oriented and translated fragment, Fmodel_a.hkl has been given so that the vectors which correspond to this partial solution can be removed from the observed data.

Three coefficient files are produced, a.hkl, b.hkl and c.hkl. The program FOURIER in the TNT package [2], as shown, calculates the P1 maps from these coefficient files and manipulates them so that a map of the function T( t ) (Eq. 6) is produced. Theoretically, this function measures the agreement between all vectors which are functions of t in the calculated Patterson map and the corresponding vectors of the observed Patterson map, while removing vectors which are not functions of t (namely the intra-molecular vectors and those vectors between copies of the known fragment).

References

1. Harada, Y., Lifchitz A. and Berthou J. (1981) A Translation Function Combining Packing and Diffraction Information: An Application to Lysozyme (High-Temperature Form). Acta Cryst. A37, 398-406.

2. Tronrud, D. et. al. (1987). TNT refinement package. Acta Cryst. A43, 489-503.

3. Zhang, X-J and Matthews W.B. (1994). Enhancement of the Method of Molecular Replacement by Incorporation of Known Structural Information. Acta Cryst. D50, 675-686.

Copyright 1995, Cai X.-J. Zhang, All Right Reserved.