Appendix A: NCS in TNT

Content

• NCS "objects" definition
• Hard NCS
• Soft NCS
• Final remarks

NCS "objects" definition

For each "object" showing NCS, a CLUSTER card must be input. The NCS "object" has a name and an identical span for each chain. For example, two NCS "objects" in the structure of the M6I mutant for lysozyme T44 are described using the following cards:

CLUSTER NTERM RESIDUE 11 - 59 CHAINS A B C D CLUSTER CTERM RESIDUE 1 - 10 RESIDUE 60 - 162 CHAINS A B C D

The first "object" (called NTERM) consists of the residues 11 to 59 for each of the 4 chains A, B, C and D. The second "object" (CTERM) is more complicated, as it is made from 2 non-successive parts of each chains, the residues 1 to 10 and 60 to 162.

In this example, the complete structure (from residue 1 to 162) is part of at least one of the NCS "objects" defined above. Generally, this is not required, and the hinge region could be refined separately in each chain:

CLUSTER NTERM RESIDUE 12 - 58 CHAINS A B C D CLUSTER CTERM RESIDUE 1 - 9 RESIDUE 61 - 162 CHAINS A B C D

In this case, residues 10, 11, 59 and 60 would not be part of any NCS and thus would be refined separately.

Obvioulsy, such definition of NCS "objects" is valid only if chains A, B, C and D have identical sequences. One can make sure of this by using chain types instead of repeating 4 times the same information about primary (and even some secondary) sequence. In the case of the lysozyme T44, the 4 chains A, B, C and D are copies of a single protomer, PROT. The first few lines of the sequence file would therefore read:

CHAIN A PROT CHAIN B PROT CHAIN C PROT CHAIN D PROT RESIDUE PROT|1 ALA 2 PEPTIDE ...

Once the definition of those "objects" is complete, the NCS module can be used in two disctinct fashion:

Hard NCS

Here, TNT refines only one copy of the tetramer. The other copies are generated by the known NCS operators. It is unfortunately not possible to refine those operators simultanously with the protomer structural parameters. The NCS operators are defined in two steps:

1. an operator is assigned to each part of the structure which exhibit NCS
2. the operators themselves are described with a name and the rotation/translation associated

CLUSTER NTERM NCS A NTE-A B NTE-B C NTE-C D-NTE D NCS NTE-A MATRIXC 1.0 0.0 0.0 0.0 - 0.0 1.0 0.0 0.0 - 0.0 0.0 1.0 0.0 NCS NTE-B MATRIXC r11 r12 r13 t1 - r21 r22 r23 t2 - r31 r32 r33 t3 ... CLUSTER CTERM NCS A CTE-A B CTE-B C CTE-C D-CTE D NCS CTE-A MATRIXC 1.0 0.0 0.0 0.0 - 0.0 1.0 0.0 0.0 - 0.0 0.0 1.0 0.0 NCS CTE-B MATRIXC r11 r12 r13 t1 - r21 r22 r23 t2 - r31 r32 r33 t3 ...

The matrices relating the protomer to its non-crystallographic equivalents are defined as the operation bringing a particular copy onto a prototype location. Usually, this prototype location coincide with the protomer, so one matrix is the identity (but this is not required).

Soft NCS

Alternatively, one can use NCS to apply non-crystallographic symmetry restraints (soft NCS). In this case the complete structure is refined and the various NCS-related components need not to be identical. The module computes a residual based on the differences between the various non-crystallographic copies of the protomer (or "object"). This residual is added to x-ray and stereochemical "observations" to form the function minimised in BUSTER or TNT. Derivatives of this residual with respect to the complete set of coordinates (protomer + copies) must also be computed and written.

On the contrary to hard NCS, NCS restraints don't need explicit specification of the NCS operators, as the full structure (i.e. the complete tetramer in the example above) is refined. A WEIGHT card is necessary to put NCS restraints on the same scale as the other residuals.

Final remarks

It is important to remember that the CLUSTER card takes chain names rather than chain types to define the span of domains. This is because the domain definition is mostly related to structure rather than to sequence. Such a definition is thus more flexible, as it allows (for example) a different splitting into domains for different chains.

Although refinement of NCS operators is not directly possible when NCS is constrained, there is an approximate workaround: it is possible to treat the several chains (or NCS "objects") as rigid bodies and refine their relative orientations. After rigid-body refinement, the NCS operators are output by the NCS module using the command

PUNCH symop.dat NCS

A standard cycle of hard NCS refinement can then be performed using these operators. This process is not ideal, as it neglects the correlations between the individual protomer's structural parameters and the rotations and translations of the NCS operators. Nevertheless, in some cases it may be better than putting too much trust in the NCS operators. This additional refinement is not very costly, as initial NCS operators are generally close enough from refined ones so that convergence is reached in a very small number of cycles, usually 1. This workaround is not yet implemented in the ML refinement.