Strict NCS (constraints) in refinement

Non-crystallographic symmetry (NCS) can (and in many cases should) be included in refinement. In CNS two models for NCS are available:

• Strict (constraints) - the model consists of a protomer. Matrices explicitly define the relationship between protomers. These matrices are used to generate the complete asymmetric unit. The relationships between protomers are fixed because the matrices do not change during refinement.
• Restrained (restraints) - the model consists of all protomers. The relationship between protomers is defined by selections of equivalent atoms. These relationships are used to superimpose all related molecules and calculate deviations from the average structure. The relationships between protomers are not fixed because the matrices used to superimpose protomers are constantly changing during refinement.

Non-crystallographic symmetry is defined with the CNS auxiliary file ncs.def. This has sections for strict NCS and NCS restraints (either one or the other can be used at a given moment). Here we will perform a simulated annealing for a model with strict NCS with two molecules in the asymmetric unit. The model consists of a single protomer and the strict NCS matrix that is used internally to generate the dimer. The strict NCS symmetry is defined with the CNS task file ncs_strict.def. The matrices could have come from experimental phasing or, as in this case, from analysis of the two molecules located by molecular replacement. The CNS task file get_ncs_matrices.inp can be used to determine NCS operators between molecules. The operators are defined as realspace rotation and translation:

After the strict NCS has been defined a round of simulated annealing is performed:

      cns_solve < anneal_strict.inp > anneal_strict.out [41 minutes]

Note that in the case of strict NCS in CNS the matrices defined only are used to generate the full asymmetric unit for the purposes of structure factor calculation and nonbonded interactions within the asymmetric unit between NCS related protomers. Symmetry related interactions are only calculate for the protomer in the model (ie. symmetry is not applied to the NCS operators). In some cases this can lead to missing symmetry related interactions between the protomer in the model and NCS related protomers. This can be overcome by defining matrices that are only used for nonbonded interactions. There is a section in the ncs.def file for this: