If TNT is given a full set of coordinates, and the CLUSTER statements defining the areas of correspondence, it can calculate the transformations which relate one copy to another. In the case where only the unique coordinates are given, as when the scatter command is to be used, the transformations must be supplied by the user.
The transformations are defined to move a particular chain into superimposition with the prototype location for that cluster. While the prototype may be located anywhere in space, usually one places the prototype at the location of one of the chains. In the case of hemoglobin discussed in the last section, the ALPHA prototype would be located at A1. The transformation of A1 to ALPHA would then be the identity operator. The transformation of A2 to ALPHA would be the same as that of A2 to A1.
The transformations are defined jointly with the CLUSTER and TRANSFORMATION statements. The NCS option on the CLUSTER statement gives the name of the transformation which relates one chain to the prototype. The actual matrix values are associated with that transformation name on the TRANSFORMATION statement. There will be one CLUSTER statement for each cluster and one TRANSFORMATION statement for each chain in each cluster.
As an example, consider the structure of the M6I mutant form of T4 lysozyme. This protein crystallizes with four copies in the asymmetric unit. There is a variable hinge-bending angle between the N-terminal and C-terminal domains. However, the first 10 amino acids move with the C-terminus. The CLUSTER statements for this structure are
CLUSTER NTERM RESIDUE 11 - 59 CHAINS A B C D CLUSTER CTERM RESIDUE 1 - 10 RESIDUE 60 - 162 CHAINS A B C D
The noncrystallographic symmetry operators are defined as follows.
CLUSTER NTER NCS A NTE-A B NTE-B C NTE-C D NTE-D
TRANSFORMATION NTE-A SYSTEM TNT -
MATRIX 1.00000 0.00000 0.00000 -
0.00000 1.00000 0.00000 -
0.00000 0.00000 1.00000 -
SHIFT XYZ 0.0000 0.0000 0.0000 -
SHIFT B 0.00 -
SHIFT OCC 0.0000
TRANSFORMATION NTE-B SYSTEM TNT -
MATRIX 0.65484 0.73147 0.19009 -
0.74936 -0.66109 -0.03759 -
0.09817 0.16706 -0.98105 -
SHIFT XYZ 17.0624 9.1073 10.8902 -
SHIFT B -10.76 -
SHIFT OCC 0.0000
...
CLUSTER CTERM NCS A CTE-A B CTE-B C CTE-C D CTE-D
TRANSFORMATION CTE-A SYSTEM TNT -
MATRIX 1.00000 0.00000 0.00000 -
0.00000 1.00000 0.00000 -
0.00000 0.00000 1.00000 -
SHIFT XYZ 0.0000 0.0000 0.0000 -
SHIFT B 0.00 -
SHIFT OCC 0.0000
TRANSFORMATION CTE-B SYSTEM TNT -
MATRIX 0.66181 0.72421 0.19370 -
0.73855 -0.58551 -0.33426 -
-0.12866 0.36428 -0.92236 -
SHIFT XYZ 17.7401 9.5472 11.6293 -
SHIFT B -5.33 -
SHIFT OCC 0.0000
...