biotite.structure.superimpose

biotite.structure.superimpose(fixed, mobile, atom_mask=None)[source]

Superimpose structures onto a fixed structure.

The superimposition is performed using the Kabsch algorithm 12, so that the RMSD between the superimposed and the fixed structure is minimized.

Parameters
fixedAtomArray, shape(n,) or ndarray, shape(n,), dtype=float

The fixed structure. Alternatively coordinates can be given.

mobile: AtomArray, shape(n,) or AtomArrayStack, shape(m,n) or ndarray, shape(n,), dtype=float or ndarray, shape(m,n), dtype=float

The structure(s) which is/are superimposed on the fixed structure. Each atom at index i in mobile must correspond the atom at index i in fixed to obtain correct results. Alternatively coordinates can be given.

atom_mask: ndarray, dtype=bool, optional

If given, only the atoms covered by this boolean mask will be considered for superimposition. This means that the algorithm will minimize the RMSD based on the covered atoms instead of all atoms. The returned superimposed structure will contain all atoms of the input structure, regardless of this parameter.

Returns
fittedAtomArray or AtomArrayStack or ndarray, shape(n,), dtype=float or ndarray, shape(m,n), dtype=float

A copy of the mobile structure(s), superimposed on the fixed structure. Only coordinates are returned, if coordinates were given in mobile.

transformationtuple or tuple list

The tuple contains the transformations that were applied on mobile. This can be used in apply_superimposition() in order to transform another AtomArray in the same way. The first element contains the translation vector for moving the centroid into the origin. The second element contains the rotation matrix. The third element contains the translation vector for moving the structure onto the fixed. The three transformations are performed sequentially.

Notes

The transformation tuple can be used in superimpose_apply() in order to transform another AtomArray in the same way. This can come in handy, in case you want to superimpose two structures with different amount of atoms. Often the two structures need to be filtered in order to obtain the same size and annotation arrays. After superimposition the transformation can be applied on the original structure using superimpose_apply().

References

1

W. Kabsch, “A solution for the best rotation to relate two sets of vectors,” Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, vol. 32, pp. 922–923, September 1976. doi: 10.1107/S0567739476001873

2

W. Kabsch, “A discussion of the solution for the best rotation to relate two sets of vectors,” Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, vol. 34, pp. 827–828, September 1978. doi: 10.1107/S0567739478001680

Examples

At first two models of a structure are taken and one of them is randomly rotated/translated. Consequently the RMSD is quite large:

>>> array1 = atom_array_stack[0]
>>> array2 = atom_array_stack[1]
>>> array2 = translate(array2, [1,2,3])
>>> array2 = rotate(array2, [1,2,3])
>>> print("{:.3f}".format(rmsd(array1, array2)))
11.260

RMSD decreases after superimposition of only CA atoms:

>>> array2_fit, transformation = superimpose(
...     array1, array2, atom_mask=(array2.atom_name == "CA")
... )
>>> print("{:.3f}".format(rmsd(array1, array2_fit)))
1.961

RMSD is even lower when all atoms are considered in the superimposition:

>>> array2_fit, transformation = superimpose(array1, array2)
>>> print("{:.3f}".format(rmsd(array1, array2_fit)))
1.928