The slow translation function is defined by the following equation:
Eq. i. Ct(T)= sum[(Fo(h) - <Fo>)(TFc(h) - <TFc>)]
/ sqrt{ sum[(Fo(h) - <Fo>)²] sum[(TFc(h) - <TFc>)²]}
where the brackets (<>) indicate an average over all reflections, and
Eq. i-a. TFc(h)= sum[ TFc,m(Sjh)]The summation is over all the symmetry operators of the crystal {Sj,j=1,nsym}, Fc,m's are structure factors calculated with the single search model, and T is the translation operator. The value of Ct(T) should be between
[-1.0, 1.0].
The fast translation function is defined by the following equation:
Eq. ii. Tij(T)= <Po | TPm,si,sj>where the brackets (<|>) indicate the integral over one crystallographic unit cell of the two enclosed functions, T is the translation operator, Po is the Patterson function corresponding to the observed intensity, and Pm,si,sj is the set of vectors from one symmetry (si) related molecule to another (sj). Usually, several independent Tij(T) between different pairs of symmetry operators are required to solve a translation function problem. The required number of Tij is the number of independent non-unitary symmetry operators of the space group.
To report bugs, please contact
Cai X.-J. Zhang at chk@uoxray.uoregon.edu100.0.
The x (i.e. a
direction) changes fastest, y second, and z slowest
(sections).
(2) For the fast translation function, the output file is a HKL/TNT format file containing the fast translation function coefficients, which can be used as the input for the TNT program FOURIER for map calculation.
In the following, the commands marked with a star (*) are mandatary to the program, those without star are optional. Alphabetical order is used for each of the three classes of commands in the following.
CELL*, FC*, FC_A, FO*, RESOLUTION*, SYMMETRY*, TF; ATOM, GRID*, LAYOUT*, LIST, ORIGIN, PACK; and FAST*.
CELL a, b, c, alpha, beta, gamma, convention_number
FC file_nameCELLinputs the cell parameters. If the packing-search option is used, a convention may be specified to define the orthogonal (xyz) coordinate system relative to the crystal (abc) coordinate system. The convention is an integer code from1to8. The same code is used in the programs ALMN and ROTFUN.
FC defines the HKL/TNT file name of the calculated
structure factors.
When the {Fc} are calculated, the model cell should be the same as the
crystal cell with a unitary symmetry, plus any centering operation
[4]. The
model should be at a correct orientation (i.e. the solution of the rotation
function). This Fc file should only contain reflections of one asymmetric
unit of reciprocal space.
FC_A file_name
FC_A inputs the HKL file name of the calculated structure
factors of a
fragment for which the correct translation is already known. The structure
factors should be calculated in the crystal cell with the full symmetry of
the crystal. For the fast translation function, the Patterson function of this
known fragment will be subtracted from that of the observed one. The
subtraction may reduce the noise of the fast translation function map. For
a slow translation function search, the structure factors will be added to
TFc(h). Usually, the modified {TFc(h)} will significantly
enhance the correct peak(s) of the correlation between the {Fc} and
{Fo} data sets.
FO file_name
FO inputs the HKL file name of the observed structure
factors (amplitude).
This Fo file should only contain reflections of one asymmetric unit of
reciprocal space.
RESOLUTION dmin, dmax
RESOLUTION defines the resolution limits of both {Fo}
and {Fc} used in the calculation.
SYMMETRY symmetry_operator
SYMMETRY inputs the symmetry operator in the international
table format. The
symmetry information is used to calculate the total Fc (in a slow
translation function, see Equ. (i-a))
or intermolecular vectors between
symmetry related search models (in the fast translation function). For a
centered space group, only the symmetry operators associated with one
origin are needed. The origin shifts should be included in the structure
factor calculation.
TF file_name
TF defines the output file name of either the fast
translation coefficients
(for fast translation function) or the map of the slow translation function.
ATOM (PDB `ATOM' record format, ('ATOM',26X,3F8.3,2F6.2) )
GRID x_grid, y_grid, z_gridATOMdefines the pseudo atom used for packing search. During a packing search, a protein model is represented as a few (1-10) spheres. The input format is that of a PDB file. The B value is used as the radius of the sphere in Å. A positive occupancy indicates that the sphere is part of the search model. A zero occupancy indicates that the sphere is part of the known fragment. All 'atoms' of the same occupancy are considered as one fragment. The x,y,z are the coordinates of the sphere center. In theCELLcard, if no coordinate alignment convention is specified, the x,y,z will be interpreted as fractional coordinate. Otherwise, the x,y,z will be interpreted as orthogonal coordinates in Å. Since intra-fragment contact will be excluded from the packing search, the spheres in one fragment are allowed to overlap with each other.
GRID defines the gridding along the three cell edges.
The gridding
numbers should be positive integers. Usually, a slow translation function
requires fine gridding. For example, for 4.0 Å angstrom data, the gridding
is better to be close or finer than 2.0 Å/grid.
LAYOUT x_start, x_end, y_start, y_end, z_start,
z_end
LAYOUT inputs the range of the slow translation function
search in grid units.
LIST N
LIST defines the frequency of a update report about the
slow translation
function search. The program will list out the updated best peak in every
N point calculation. The default is no report.
ORIGIN x_frac, y_frac, z_frac
PACK min_R, max_P, C0ORIGINdefines the positions of multiple origins of non-primitive space group crystal in fractional coordinates. This information is used for packing search only. There should be oneORIGINcard for each of the multiple origins.
PACKactivates the packing search option. DefineR(i,j)= distance(i,j) / [radius(i)+radius(j)] P= sum[ 1.0 - max(1.0,R(i,j)) ]Any position of a intermolecular contact with R(i,j) < min_R, or of a P > max_P, will be considered as a rejected position. The first criteria detects an individual bad contact. The second one, which only works when min_Rij < 1., detects multiple bad contacts at a given position. The ij pair runs over all the inter-fragment pseudo atom pairs. The output value of a rejected position will be set to C0, instead of being calculated with Equ. i. Since a packing search is usually much faster than a Ct(T) calculation, the packing search option may speed up the overall calculation. The default C0 is the average value of the map over all the accepted positions.
FASTactivates the option of calculating a fast translation function [2, 4]. By default, the program TRANSFUN will calculate the slow translation function. Sym_1 and Sym_2 are integers specifying the symmetry operator in the order of inputSYMMETRYcards. The search vector is from the molecule of symmetry operator Sym_1 to that of Sym_2. Frac is the structure fraction of the search model, plus the known structural part if any, in one asymmetric unit. Scale is multiplied on each of the output coefficients to make sure that they fit in the HKL/TNT format('HKL',1X,3I4,2F10.2). ThisFASTcard should be followed by aTFcard.
R32. There are two protein molecules per asymmetric
unit.
(1) an example VAX/VMS command file of a fast translation function search. The intermolecular vectors are from the molecule of symmetry `-x,y-x,-z' to that of `-y,x-y,z'. Therefore, the peaks will be at positions 'x-y,2x-2y,2z'.
$ run mrchk_exe:transfun cell 172.6 172.6 80.4 90 90 120 symmetry x, y, z symmetry -y, x-y, z symmetry y-x, -x, z symmetry y, x, -z symmetry -x, y-x, -z symmetry x-y, -y, -z resolut 4., 8. fast 5, 2, 0.5, 0.1 fo fobs.hkl fc fmodel.hkl tf fast_tf.hkl $(2) an example VAX/VMS command file of a slow translation function search.
$ run mrchk_exe:transfun cell 172.6 172.6 80.4 90 90 120 6 symmetry x, y, z symmetry -y, x-y, z symmetry y-x, -x, z symmetry y, x, -z symmetry -x, y-x, -z symmetry x-y, -y, -z resolut 4., 8. fo fobs.hkl fc fmodel.hkl tf slow_tf.map grid 84 84 42 layout 0 83 0 83 0 13 list 1000 $
(3) an example VAX/VMS command file of a slow translation function search, which incorporates information from known structural part and uses packing search option to speed up the calculation.
$ run mrchk_exe:transfun cell 172.6 172.6 80.4 90 90 120 6 symm x, y, z symm -y, x-y, z symm y-x, -x, z symm y, x, -z symm -x, y-x, -z symm x-y, -y, -z resolut 4., 8. fo Fobs.HKL fc Fmodel.HKL fc_a Fmodel_a.HKL tf Slow_TF.MAP grid 84 84 42 layout 0 83 0 83 0 13 list 1000 pack 0.8, 1.5 origin 0., 0., 0. origin 0.3333, 0.6667, 0.6667 origin 0.6667, 0.3333, 0.3333 ; format: (A4,26X,3F8.3,2F6.2) ATOM 1 N SH 1 147.300 32.800 55.700 0.00 12.5 ATOM 2 C SH 1 142.800 18.800 39.600 0.00 12.5 ATOM 3 N SH 2 -3.400 6.700 7.900 1.00 12.5 ATOM 4 C SH 2 3.200 -6.400 -7.600 1.00 12.5 $
2. Crowther R.A. & Blow D.M., 1967. Acta Cryst. 23, 544.
3. Tronrud, D. et. al. (1987). TNT refinement package. Acta Cryst. A43, 489-503.
4. 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.