ROTFUN

ROTFUN calculates fast rotation function of two Patterson functions [1,2]. The rotation function is defined as the following.
Cr(R)= sqrt{< P1 | RP2 > / [<P1 | P1> < P2 | P2>]} x100.0
The brackets (<|>) indicate the integral over a spherical volume of the two enclosed functions, and R is the rotation operator. Two angular systems, Eulerian (alpha, beta, gamma) and spherical polar (phi, theta, kappa), are available for sampling the rotation function.

To report bugs, please contact

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

Input file

Two formatted (3I4,2E12.4) ALM files created by the program ALMN are required, which contain the Al,m,n coefficients of the Patterson maps. The two sets of input Al,m,n coefficients should be calculated with the same integral radius and usually the same resolution limits.

Output file

ROTFUN creates a modified Ten Eyck format map file [5] of the fast rotation function. The a3 coordinate (gamma or kappa) changes fastest, a1 (alpha or phi) secondly, and a2 (beta or theta) slowest (ie. sections).

Convention

The angular coordinates of the solution peaks read from the output fast rotation function map should be applied to the search model. Both the Eulerian and polar angular system is defined with respect to the orthogonal system (x, y, z).

The Eulerian angles (alpha, beta, gamma) are defined as the following: a rotation gamma of the object about the z axis, followed by a rotation beta of the object about y, and then a rotation gamma of the object about z.

The spherical polar angular system (phi, theta, kappa) is defined as the following: phi is the longitude of the rotation axis relative to the polar axis (z), with phi=0.0 on the z-x plane; theta is the latitude of the rotation axis from the polar axis (ie. z), with theta=0.0 on the +z-axis; kappa is the rotation angle about the axis.

Commands

ROTFUN 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.

ALMN_O*, ALMN_M*, CELL, EULER , GRID , INCLUDE , LAYOUT*, POLAR, RF*, SELF, SSS, STEP , SYMMETRY and !comment.
ALMN_O file_name
ALMN_O identifies the file name of the Al,m,n coefficients of the "observed" Patterson map.
ALMN_M file_name
ALMN_M identifies the file name of the Al,m,n coefficients of the Patterson map of the model structure in a model cell. For simplicity, the model cell can be chosen as the observed crystal cell lattice with a unitary symmetry. For a self rotation function calculation, the ALMN_M file is usually the same as ALMN_O file.
CELL a, b, c, alpha, beta, gamma, convention_number
CELL inputs the cell parameters, which will be used only if the SSS option is selected. The convention used to define the orthogonal (xyz )coordinate system relative to the crystal (abc) coordinate system is specified by an integer code from 1 to 8. The same code number should be used in the program ALMN.
EULER alpha_0, beta_0, gamma_0
EULER selects the eulerian angular system (alpha, beta, gamma). alpha_0, beta_0 and gamma_0 will be applied to the ALMN_M coefficients before the rotation search. The default (alpha_0, beta_0, gamma_0) is (0., 0., 0.).
GRID x_grid, y_grid, z_grid
GRID defines the gridding along the three angular axes (0°-360°). The x_grid, y_grid, z_grid should be smaller than 360, and the remainder of 360/grid should be exactly zero. The default of GRID is (360,360,360). If GRID option is used explicitly, STEP will be set to (1, 1, 1) in the grid units, and the output file will be a standard Ten Eyck format map file.
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.
LAYOUT a1_start, a1_end, a2_start, a2_end, a3_start a3_end
LAYOUT inputs the regions of the rotation function in grid units (which are defined by the GRID card or its default value). For determining the unique regions of a rotation function, see reference [3], or use the program EDPDB [8].
POLAR phi_0, theta_0, kappa_0
POLAR selects the spherical polar angular system (phi, theta, kappa). The corresponding rotation function is called a locked rotation function [4]. phi_0, theta_0 and kappa_0 will be applied to the ALMN_M coefficients before the rotation search. The default (phi_0, theta_0, kappa_0) is (0., 0., 0.). By default, ROTFUN uses the Eulerian (alpha, beta, gamma) angular system [1].
RF file_name
RF defines the file name of the output map of the rotation function.
SELF alpha, beta, gamma
SELF activates the option of simultaneous search for self-rotation function related molecules in a cross-rotation function [7]. SELF is a time consuming option (at 3.5 Å resolution, 20.0 Å integral radius, it is about 25 times slower than the ordinary Eulerian version of fast rotation function). SELF only works in the Eulerian angular system, and the input (alpha, beta, gamma) is one of the self rotation function solution. The cell parameters are required for the SELF option.
SSS
SSS activates the option of Simultaneous Search for Symmetry-related molecules in a cross-rotation function [6,7]. SSS is a time consuming option (at 3.5 Å resolution, 20.0 Å integral radius, it is about 25 times slower than the ordinary Eulerian version of fast rotation function). SSS only works in the Eulerian angular system. Normally, it does not give a better result than the ordinary rotation function. If the search model has non crystallographic symmetry which is similar to the crystallographic symmetry, this option can prove useful. The input of cell parameters and symmetry operators are required for the SSS option.
STEP step_1, step_2, step_3
STEP inputs the increments of the three angles in degree units. If the input is different from (1, 1, 1), the output file will not be a standard Ten Eyck map file [5]. The modified Ten Eyck map can be read by the peak-pick program PEKCHK. The default is (5, 5, 5). See also GRID.
SYMMETRY symmetry_operator
SYMMETRY inputs the symmetry operator in the international table format. The symmetry information will be used only if the SSS option is selected. Only the rotational component of the symmetry operator will be used. The SYMMETRY card can be repeated up to 32 (max_symm) times.
!comment
Any input line starting with a semicolon (;) or an exclamation mark (!) will be ignored.

Examples

The following example is of a T4 lysozyme mutant crystal. The crystal belongs to the space group R32.

(1) an example VAX/VMS command file for a self rotation function. 

	$ RUN MRCHK_ROOT:[EXE]ROTFUN
	; non-POLAR     
	ALMN_O           OBS.ALM
	ALMN_M           OBS.ALM
	LAYOUT           0 180 0 180 0 360
	STEP             3 3 3 
	RF               SELF_RF.MAP
	$
(2) an example VAX/VMS command file for a cross rotation function, in the polar angular system. 
	$ RUN MRCHK_ROOT:[EXE]ROTFUN
	POLAR     
	ALMN_O           OBS.ALM
	ALMN_M           MODEL.ALM
	LAYOUT           0 180 0 180 0 360
	STEP             3 3 3 
	RF               CROSS_RF.MAP
	$
(3) an example VAX/VMS command file for a cross rotation function, with simultaneous search of symmetry related molecules. 
	$ RUN MRCHK_ROOT:[EXE]ROTFUN
	; non-POLAR     
	ALMN_O           OBS.ALM
	ALMN_M           MODEL.ALM
	LAYOUT           0 180 0 180 0 360
	STEP             5 5 5 
	SSS
	CELL             172. 172. 80. 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 
	RF               CROSS_RF_SSS.MAP
	$

References

1. Crowther R.A. (1972). The Molecular Replacement Method. edited by M.G. Rossmann, pp173-183. New York:Gordon & Brech.

2. Kabsch W. (1986). "Rotation Function" (working notes)

3. Rao S.N. et al. (1980). Acta Cryst. A36, 878-884. "Rotation Function Space Group"

4. Tanaka N. (1977). Acta Cryst. A33, 191-193

5. Trunrod, D., (1987). TNT refinement program package. Acta Cryst. A43, 489-503.

6. Yeates T.O. (1989). Acts Cryst. A45,309-314.

7. 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.

8. Zhang, X-J and Matthews W.B. (1995). EDPDB: A Multi-Functional Tool for Protein Structure Analysis. J. Appl. Cryst. .

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