Noncrystallographic symmetry is present whenever you have collected diffraction data from a crystal containing two or more copies of a molecule where these copies are not related by the normal symmetry of the crystal. The diffraction data provide unique ``snapshots'' of each copy. The knowledge that the underlying pattern is the same in each copy introduces a great deal of additional information, which can be used to solve the structure.
The crystallographic symmetry also provides a great deal of information. However, because the relationship between the copies is exact we always choose to use this type of symmetry as constraints, and because of its mathematical nature we can apply the constraint in reciprocal space. During data collection it is assumed that the differences between symmetry related reflections are due entirely to noise. The intensities are averaged to remove this noise.
In effect we are using noncrystallographic symmetry the same way. The way we incorporate this information is different because the noncrystallographic symmetry does not pass through to reciprocal space in so simple a fashion. The restraints, or constraints, must be applied in real space.
A knowledge of noncrystallographic symmetry introduces restrictions on the phases of the reflections in a fashion that crystallographic symmetry does not. In a diffraction pattern the reflections are far enough apart that each of their phases are uncorrelated to that of their neighbors. Noncrystallographic symmetry allows one to determine what the intensity of a point between two reflections would be if it could be measured. The higher the copy-number of the symmetry the greater the number of points between each pair of reflections and the greater the information about their phases.
TNT is not a phasing program, nor is its goal to perform density modification. TNT improves the agreement of a model to a set of observations. Noncrystallographic symmetry can be used in this process in two ways; The symmetry can be forced to be exact (a constraint) or can be used as a suggestion that the molecules should be similar to one another (a restraint).