PDZ (Post-synaptic density-95/discs large/zonula occludens-1) domains are relatively small (80 to 120 residues) protein binding modules central in the organization of receptor clusters and in the association of cellular proteins. Their main function is to bind C-terminals of selected proteins that are recognized through specific amino-acids in their carboxyl end. Binding is associated with a deformation of the PDZ native structure and is responsible for dynamical changes in regions not in direct contact with the target. We investigate how this deformation is related to the harmonic dynamics of the PDZ structure and show that one low-frequency collective normal mode, characterized by the concerted movements of different secondary structures, is involved in the binding process. Our results suggest that even minimal structural changes are responsible of communication between distant regions of the protein, in agreement with recent Nuclear Magnetic Resonance (NMR) experiments. Thus PDZ domains are a very clear example of how collective normal modes are able to characterize the relation between function and dynamics of proteins, and to provide indications on the precursors of binding/unbonding events.