Reconstruction of orientations of a moving protein domain from paramagnetic data

We study the inverse problem of determining the position of the moving C-terminal domain in a metalloprotein from measurements of its mean paramagnetic tensor $\bar\chi$. The latter can be represented as a finite sum involving the corresponding magnetic susceptibility tensor $\chi$ and a finite number of rotations. We obtain an optimal estimate for the maximum probability that the C-terminal domain can assume a given orientation, and we show that only three rotations are required in the representation of $\bar\chi$, and that in general two are not enough.