Considerable insight into the functional activity of proteins and enzymes can be obtained by studying the low-energy conformational distortions that the biopolymer can sustain. We carry out the characterization of these large scale structural changes for a protein of considerable pharmaceutical interest, the human $\beta$-secretase. Starting from the crystallographic structure of the protein, we use the recently introduced beta-Gaussian model to identify, with negligible computational expenditure, the most significant distortion occurring in thermal equilibrium and the associated time scales. The application of this strategy allows to gain considerable insight into the putative functional movements and, furthermore, helps to identify a handful of key regions in the protein which have an important mechanical influence on the enzymatic activity despite being spatially distant from the active site. The results obtained within the Gaussian model are validated through an extensive comparison against an all-atom Molecular Dynamics simulation.