  We find that the hierarchical organization of the potential energy landscape
in a model supercooled liquid can be related to a change in the spatial
distribution of soft normal modes. For groups of nearby minima, between which
fast relaxation processes typically occur, the localization of the soft modes
is very similar. The spatial distribution of soft regions changes, instead, for
minima between which transitions relevant to structural relaxation occur. This
may be the reason why the soft modes are able to predict spatial
heterogeneities in the dynamics. Nevertheless, the very softest modes are only
weakly correlated with dynamical heterogeneities, and instead show higher
statistical overlap with regions in the local minima that would undergo
non-affine rearrangements if subjected to a shear deformation. This feature of
the supercooled liquid is reminiscent of the behavior of non-affine
deformations in amorphous solids, where the very softest modes identify the
{\it loci} of plastic instabilities.
